TSTP Solution File: SWW252+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW252+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:15:59 EDT 2022
% Result : Timeout 300.04s 300.24s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW252+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 5 13:51:19 EDT 2022
% 0.11/0.34 % CPUTime :
% 1.64/2.01 ============================== Prover9 ===============================
% 1.64/2.01 Prover9 (32) version 2009-11A, November 2009.
% 1.64/2.01 Process 4428 was started by sandbox2 on n029.cluster.edu,
% 1.64/2.01 Sun Jun 5 13:51:20 2022
% 1.64/2.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4267_n029.cluster.edu".
% 1.64/2.01 ============================== end of head ===========================
% 1.64/2.01
% 1.64/2.01 ============================== INPUT =================================
% 1.64/2.01
% 1.64/2.01 % Reading from file /tmp/Prover9_4267_n029.cluster.edu
% 1.64/2.01
% 1.64/2.01 set(prolog_style_variables).
% 1.64/2.01 set(auto2).
% 1.64/2.01 % set(auto2) -> set(auto).
% 1.64/2.01 % set(auto) -> set(auto_inference).
% 1.64/2.01 % set(auto) -> set(auto_setup).
% 1.64/2.01 % set(auto_setup) -> set(predicate_elim).
% 1.64/2.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.64/2.01 % set(auto) -> set(auto_limits).
% 1.64/2.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.64/2.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.64/2.01 % set(auto) -> set(auto_denials).
% 1.64/2.01 % set(auto) -> set(auto_process).
% 1.64/2.01 % set(auto2) -> assign(new_constants, 1).
% 1.64/2.01 % set(auto2) -> assign(fold_denial_max, 3).
% 1.64/2.02 % set(auto2) -> assign(max_weight, "200.000").
% 1.64/2.02 % set(auto2) -> assign(max_hours, 1).
% 1.64/2.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.64/2.02 % set(auto2) -> assign(max_seconds, 0).
% 1.64/2.02 % set(auto2) -> assign(max_minutes, 5).
% 1.64/2.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.64/2.02 % set(auto2) -> set(sort_initial_sos).
% 1.64/2.02 % set(auto2) -> assign(sos_limit, -1).
% 1.64/2.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.64/2.02 % set(auto2) -> assign(max_megs, 400).
% 1.64/2.02 % set(auto2) -> assign(stats, some).
% 1.64/2.02 % set(auto2) -> clear(echo_input).
% 1.64/2.02 % set(auto2) -> set(quiet).
% 1.64/2.02 % set(auto2) -> clear(print_initial_clauses).
% 1.64/2.02 % set(auto2) -> clear(print_given).
% 1.64/2.02 assign(lrs_ticks,-1).
% 1.64/2.02 assign(sos_limit,10000).
% 1.64/2.02 assign(order,kbo).
% 1.64/2.02 set(lex_order_vars).
% 1.64/2.02 clear(print_given).
% 1.64/2.02
% 1.64/2.02 % formulas(sos). % not echoed (1258 formulas)
% 1.64/2.02
% 1.64/2.02 ============================== end of input ==========================
% 1.64/2.02
% 1.64/2.02 % From the command line: assign(max_seconds, 300).
% 1.64/2.02
% 1.64/2.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.64/2.02
% 1.64/2.02 % Formulas that are not ordinary clauses:
% 1.64/2.02 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].
% 1.64/2.02 2 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n)))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 3 (all B_z hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) # label(fact_qr) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 4 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n)))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 5 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 6 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 7 (all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,V_n_2)) -> (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat,V_P_2),c_Nat_OSuc)))))) # label(fact_Least__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 8 (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].
% 1.64/2.02 9 (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].
% 1.64/2.02 10 (all V_pb_2 all V_a_2 all T_a (class_Rings_Oidom(T_a) -> (c_Polynomial_Osmult(T_a,V_a_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) | V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_smult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 11 (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].
% 1.64/2.02 12 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) <-> (exists B_m V_n_2 = hAPP(c_Nat_OSuc,B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 13 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 14 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 15 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p))) # label(fact_smult__smult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 16 (all V_f_2 all T_b all T_a (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2) <-> (all B_x all B_y hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)))) # label(fact_constant__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 17 (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) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__smult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 18 (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) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)))) # label(fact_coeff__smult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 19 (all V_y all V_x (hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 20 (all V_nat_H_2 all V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 21 (all V_n hAPP(c_Nat_OSuc,V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 22 (all V_n V_n != hAPP(c_Nat_OSuc,V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 23 (all V_P_2 all V_n_2 all V_m_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 24 (all V_t all V_s (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 25 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 26 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 27 (all V_y all V_x (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 28 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 29 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 30 (all V_qa_2 all V_pb_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qa_2) <-> V_pb_2 = V_qa_2))) # label(fact_poly__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 31 (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].
% 1.64/2.02 32 (all V_qa_2 all V_pb_2 all T_a (class_Groups_Ozero(T_a) -> (V_pb_2 = V_qa_2 <-> (all B_n hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_qa_2),B_n))))) # label(fact_expand__poly__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 33 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 34 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 35 (all V_nat_H_1 hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 36 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 37 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 38 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 39 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 40 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 41 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 42 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 43 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 44 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 45 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 46 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 47 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 48 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> (hAPP(c_Nat_OSuc,V_m) != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 49 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 50 (all V_m all V_n (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 51 (all V_m_2 all V_n_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 52 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 53 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 54 (all V_n_2 all V_m_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 55 (all V_pb_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <-> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_poly__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 56 (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].
% 1.64/2.02 57 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = hAPP(c_Nat_OSuc,B_j) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)))))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 58 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 59 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(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].
% 1.64/2.02 60 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(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))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 61 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(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))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 62 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(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) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 63 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 64 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 65 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 66 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(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) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 67 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.02 68 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 69 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 70 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 71 (all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 72 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 73 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 74 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 75 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 76 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 77 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 78 (all V_q all V_a all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_mult__smult__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 79 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_mult__smult__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 80 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 81 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 82 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 83 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 84 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 85 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 86 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 87 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 88 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))))) # label(fact_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 89 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 90 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 91 (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].
% 1.64/2.02 92 (all V_b_2 all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2) <-> V_a_2 = V_b_2))) # label(fact_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 93 (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].
% 1.64/2.02 94 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 95 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 96 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 97 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 98 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a) | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 99 (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].
% 1.64/2.02 100 (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].
% 1.64/2.02 101 (all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 102 (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].
% 1.64/2.02 103 (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].
% 1.64/2.02 104 (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].
% 1.64/2.02 105 (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].
% 1.64/2.02 106 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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].
% 1.64/2.02 107 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 108 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 109 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 110 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 111 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 112 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 113 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 114 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 115 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 116 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 117 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 118 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 119 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 120 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 121 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 122 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 123 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 124 (all B_x hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),B_x))) # label(fact_q_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 125 (all V_P_2 all V_k_2 all T_a (class_Orderings_Owellorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),c_Orderings_Oord__class_OLeast(T_a,V_P_2))) -> -hBOOL(hAPP(V_P_2,V_k_2))))) # label(fact_not__less__Least) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 126 (all V_a_2 all V_pb_2 all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Polynomial_Oorder(T_a,V_a_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_order__root) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 127 (all V_pb_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_pb_2)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))) -> (-c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2)) -> (exists B_z hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) # label(fact_less_Ohyps) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 128 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 129 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 130 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 131 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 132 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 133 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 134 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 135 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 136 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 137 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 138 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 139 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 140 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 141 (all V_a_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 142 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 143 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 144 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_p) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),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].
% 1.64/2.02 145 (all V_n all V_q all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)))) # label(fact_coeff__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 146 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 147 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 148 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 149 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_a_2 != V_b_2 & V_ca_2 != V_d_2 <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 150 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 151 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 152 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 153 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 154 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) <-> V_w_2 = V_x_2 | V_y_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 155 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 156 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 157 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 158 (all V_d all V_c all V_b all V_a all V_r all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_r != c_Groups_Ozero__class_Ozero(T_a) -> (V_a = V_b & V_c != V_d -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 159 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 160 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 161 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 162 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),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].
% 1.64/2.02 163 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),hAPP(hAPP(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].
% 1.64/2.02 164 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (V_x != V_y -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 165 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 166 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 167 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 168 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 169 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 170 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 171 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 172 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 173 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 174 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 175 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 176 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 177 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 178 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 179 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 180 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 181 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 182 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 183 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_x_2 != V_y_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 184 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 185 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 186 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 187 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 188 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 189 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 190 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 191 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 192 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 193 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 194 (all V_P_2 all T_a (class_Orderings_Owellorder(T_a) -> ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1))) -> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2)))))) # label(fact_LeastI__ex) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 195 (all V_pb_2 all T_a (class_Groups_Ozero(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 196 (all V_k_2 all V_P_2 all T_a (class_Orderings_Owellorder(T_a) -> (hBOOL(hAPP(V_P_2,V_k_2)) -> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2)))))) # label(fact_LeastI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 197 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 198 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 199 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 200 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 201 (exists B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) & (all B_x hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),B_x))))) # label(fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 202 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) -> (exists B_z hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_z) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) # label(fact_calculation) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 203 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 204 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 205 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 206 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 207 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 208 -(all B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) -> -(all B_x hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),B_x))))) # label(fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 209 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 210 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 211 (all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 212 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 213 (all V_n all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 214 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.02 215 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 216 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 217 (all V_j all V_i -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 218 (all V_i all V_j -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 219 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 220 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 221 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 222 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 223 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 224 (all V_n all V_m all V_l all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 225 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 226 (all V_k all V_j all V_u all V_i hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 227 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 228 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 229 (all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = V_q)) # label(fact_add__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 230 (all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p)) # label(fact_add__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 231 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),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].
% 1.64/2.03 232 (all V_r all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)))) # label(fact_mult__poly__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 233 (all V_n_2 all V_m_2 (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 234 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 235 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 236 (all V_m all V_i hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 237 (all V_m all V_i hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 238 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> (exists B_k V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 239 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 240 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 241 (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].
% 1.64/2.03 242 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 243 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 244 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 245 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 246 (all V_ca_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2) <-> V_b_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 247 (all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2) <-> V_b_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 248 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 249 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 250 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 251 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 252 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 253 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 254 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 255 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 256 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 257 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 258 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 259 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 260 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 261 (all B_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))))) # label(fact_c) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 262 (all V_qa_2 all V_pb_2 all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_pb_2),V_qa_2) = c_Polynomial_OAbs__poly(T_a,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a)),c_Polynomial_Ocoeff(T_a,V_pb_2))),c_Polynomial_Ocoeff(T_a,V_qa_2))))) # label(fact_plus__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 263 (all V_pb_2 all V_a_2 all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,V_a_2,V_pb_2) = c_Polynomial_OAbs__poly(T_a,hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2)),c_Polynomial_Ocoeff(T_a,V_pb_2))))) # label(fact_smult__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 264 (all V_pb_2 all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Odegree(T_a,V_pb_2) = c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat,c_HOL_OAll(tc_Nat_Onat)),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat,c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat,c_fimplies)),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),c_COMBC(tc_Nat_Onat,T_a,tc_HOL_Obool,hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),tc_Nat_Onat,c_fequal),c_Polynomial_Ocoeff(T_a,V_pb_2)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_degree__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 265 (all V_a all V_p 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),B_x))))) # label(fact_poly__offset) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 266 (all B_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))))) # label(fact_cq0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 267 (all V_m_2 all V_Q_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,V_n_2)) -> (hBOOL(hAPP(V_Q_2,V_m_2)) -> (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> ((all B_k (hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k))) <-> hBOOL(hAPP(V_Q_2,B_k)))) -> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2))))))) # label(fact_Least__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 268 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 269 (all V_z all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))))) # label(fact_complex__mod__triangle__sub) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 270 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))))) # label(fact_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 271 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 272 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 273 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 274 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 275 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 276 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))))) # label(fact_norm__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 277 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 278 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 279 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) -> hBOOL(hAPP(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].
% 1.64/2.03 280 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 281 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 282 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 283 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 284 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 285 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 286 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 287 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 288 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 289 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) -> hBOOL(hAPP(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].
% 1.64/2.03 290 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 291 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 292 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 293 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) <-> (all B_x hBOOL(hAPP(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].
% 1.64/2.03 294 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))))) # label(fact_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 295 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 296 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 297 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_norm__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 298 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 299 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) # label(fact_norm__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 300 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))))))) # label(fact_norm__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 301 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))))))) # label(fact_norm__add__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 302 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 303 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 304 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 305 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 306 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 307 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 308 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 309 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 310 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 311 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 312 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 313 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 314 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 315 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 316 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 317 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 318 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 319 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 320 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 321 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 322 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 323 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) & class_Rings_Odivision__ring__inverse__zero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)))) # label(fact_norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 324 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 325 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 326 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 327 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 328 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 329 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 330 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 331 (all V_k_2 all V_P_2 all T_a (class_Orderings_Owellorder(T_a) -> (hBOOL(hAPP(V_P_2,V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_OLeast(T_a,V_P_2)),V_k_2))))) # label(fact_Least__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 332 (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].
% 1.64/2.03 333 (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].
% 1.64/2.03 334 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))))) # label(fact_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 335 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 336 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 337 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 338 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 339 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 340 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 341 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 342 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 343 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 344 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 345 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 346 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 347 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 348 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 349 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 350 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 351 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 352 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 353 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 354 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 355 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 356 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 357 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 358 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 359 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 360 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 361 (all V_q all V_n all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_q)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(T_a,hAPP(hAPP(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].
% 1.64/2.03 362 (all V_q all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(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,hAPP(hAPP(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].
% 1.64/2.03 363 (all V_p all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(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,hAPP(hAPP(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].
% 1.64/2.03 364 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 365 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 366 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = hAPP(hAPP(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].
% 1.64/2.03 367 (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].
% 1.64/2.03 368 (all V_n all V_p all T_a (class_Groups_Ozero(T_a) -> (hBOOL(hAPP(hAPP(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].
% 1.64/2.03 369 (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].
% 1.64/2.03 370 (all V_pb_2 all T_a (class_Groups_Ozero(T_a) -> (hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_leading__coeff__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 371 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 372 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 373 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 374 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 375 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 376 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 377 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 378 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 379 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 380 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 381 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 382 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 383 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 384 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 385 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 386 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 387 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 388 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 389 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 390 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 391 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q))) = hAPP(hAPP(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].
% 1.64/2.03 392 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.64/2.03 393 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)))))) # label(fact_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 394 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.64/2.03 395 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_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].
% 1.64/2.03 396 (all T_a (class_Groups_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OAbs__poly(T_a,c_COMBK(T_a,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 397 (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) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p))))) # label(fact_psize__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 398 (all V_x all V_r all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r),c_RealVector_Onorm__class_Onorm(T_a,V_x))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r))))))) # label(fact_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 399 (all V_y all V_x all V_c all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) -> V_x = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 400 (all V_r_2 all V_qa_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_qa_2,V_r_2) <-> V_x_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_qa_2),V_y_2)),V_r_2) & (V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> V_qa_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)) | hBOOL(hAPP(hAPP(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].
% 1.64/2.03 401 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 402 (all V_y all V_z all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 403 (all V_pb_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_pb_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2))))))) # label(fact_pos__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 404 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_le0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 405 (all V_l_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2)) <-> (exists B_n V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 406 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 407 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 408 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 409 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) & -hBOOL(hAPP(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].
% 1.64/2.03 410 (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].
% 1.64/2.03 411 (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].
% 1.64/2.03 412 (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].
% 1.64/2.03 413 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 414 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 415 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n))) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 416 (all V_n_2 all V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 417 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) | V_m_2 = hAPP(c_Nat_OSuc,V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 418 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 419 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 420 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> V_m = hAPP(c_Nat_OSuc,V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 421 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 422 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 423 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 424 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 425 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (V_m != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 426 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) | V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 427 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.03 428 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 429 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> (exists B_k V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 430 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 431 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 432 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 433 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 434 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 435 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 436 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 437 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 438 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 439 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 440 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 441 (all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 442 (all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 443 (all V_r_2 all V_qa_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_qa_2,V_r_2) <-> V_qa_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].
% 1.64/2.04 444 (all V_r_2 all V_qa_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_qa_2,V_r_2) <-> V_qa_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].
% 1.64/2.04 445 (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].
% 1.64/2.04 446 (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].
% 1.64/2.04 447 (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].
% 1.64/2.04 448 (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].
% 1.64/2.04 449 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 450 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 451 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 452 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 453 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 454 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 455 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 456 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 457 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_pos__poly__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 458 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_pos__poly__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 459 (all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hBOOL(hAPP(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].
% 1.64/2.04 460 (all V_q all V_n all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(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].
% 1.64/2.04 461 (all V_n_2 hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2))) # label(fact_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 462 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)))) # label(fact_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 463 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 464 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 465 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 466 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H)),V_r)))))) # label(fact_pdivmod__rel__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 467 (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) -> hBOOL(hAPP(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].
% 1.64/2.04 468 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))),hAPP(hAPP(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].
% 1.64/2.04 469 (all V_a all V_p all T_a (class_Rings_Oidom(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> hBOOL(hAPP(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].
% 1.64/2.04 470 (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].
% 1.64/2.04 471 (all V_n all V_p all T_a (class_Groups_Ozero(T_a) -> (hBOOL(hAPP(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)) | hBOOL(hAPP(hAPP(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].
% 1.64/2.04 472 (all V_u all V_y all V_x1 all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x1)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)))))))) # label(fact_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 473 (all V_u all V_y all V_x1 all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x1)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u))))))) # label(fact_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 474 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 475 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 476 (all V_y_2 all V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 477 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 478 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k))))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 479 (all V_n all V_m (V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 480 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 481 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n))) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 482 (all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w))) # label(fact_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 483 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)))) # label(fact_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 484 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))))) # label(fact_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 485 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) -> V_z = V_w))) # label(fact_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 486 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 487 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 488 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 489 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) & V_x_2 != V_y_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 490 (all V_b_2 all V_a_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 491 (all V_b_2 all V_a_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 492 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))))) # label(fact_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 493 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))) # label(fact_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 494 (all V_y all V_x all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)))))) # label(fact_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 495 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 496 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x_2),V_y_2))))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 497 (all V_x_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 498 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 499 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 500 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_a all B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))))) # label(fact_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 501 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q))),hAPP(hAPP(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].
% 1.64/2.04 502 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Odecseq(T_a,V_X_2) <-> (all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))))))) # label(fact_decseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 503 (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].
% 1.64/2.04 504 (all V_p all V_r exists B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_m)) & (all B_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z)),V_r)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z))),B_m)))))) # label(fact_poly__bound__exists) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 505 (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].
% 1.64/2.04 506 (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].
% 1.64/2.04 507 (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].
% 1.64/2.04 508 (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].
% 1.64/2.04 509 (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].
% 1.64/2.04 510 (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].
% 1.64/2.04 511 (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].
% 1.64/2.04 512 (all V_p all V_n all T_a (class_Groups_Ozero(T_a) -> ((all B_i (hBOOL(hAPP(hAPP(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))) -> hBOOL(hAPP(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].
% 1.64/2.04 513 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 514 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 515 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_a all B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))))) # label(fact_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 516 (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].
% 1.64/2.04 517 (all V_ca_2 all V_pb_2 all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Polynomial_Osynthetic__div(T_a,V_pb_2,V_ca_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> c_Polynomial_Odegree(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_synthetic__div__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 518 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)))))))) # label(fact_Bseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 519 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Oincseq(T_a,V_X_2) <-> (all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))))))) # label(fact_incseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 520 (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].
% 1.64/2.04 521 (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].
% 1.64/2.04 522 (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].
% 1.64/2.04 523 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (hBOOL(hAPP(hAPP(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].
% 1.64/2.04 524 (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].
% 1.64/2.04 525 (all V_k_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) -> c_SEQ_OBseq(T_a,hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))))) # label(fact_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 526 (all V_k_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_Bseq__offset) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 527 (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].
% 1.64/2.04 528 (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)) | hBOOL(hAPP(hAPP(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].
% 1.64/2.04 529 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 530 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 531 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 532 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 533 (all V_n all V_m all V_k hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 534 (all V_k all V_n all V_m hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 535 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(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].
% 1.64/2.04 536 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(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].
% 1.64/2.04 537 (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 = hAPP(hAPP(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].
% 1.64/2.04 538 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.04 539 (all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(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].
% 1.64/2.04 540 (all V_n all V_m ((hAPP(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,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (hAPP(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,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(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].
% 1.64/2.04 541 (all V_n all V_m (hBOOL(hAPP(hAPP(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].
% 1.64/2.04 542 (all V_n all V_m hBOOL(hAPP(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].
% 1.64/2.04 543 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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].
% 1.64/2.04 544 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)) # label(fact_mod__mult__self4) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 545 (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 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) -> (V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_P_2,B_j)))))))) # label(fact_split__mod) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 546 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))))) # label(fact_mod__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 547 (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].
% 1.64/2.04 548 (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].
% 1.64/2.04 549 (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].
% 1.64/2.04 550 (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].
% 1.64/2.04 551 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.04 552 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_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,hAPP(hAPP(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].
% 1.64/2.04 553 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_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].
% 1.64/2.04 554 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_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].
% 1.64/2.04 555 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.04 556 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.04 557 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.04 558 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 559 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 560 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 561 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 562 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 563 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 564 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 565 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 566 (all V_X_2 all V_K_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2)) -> ((all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2))) -> c_SEQ_OBseq(T_a,V_X_2))))) # label(fact_BseqI) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 567 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) -> (exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)))))))) # label(fact_BseqD) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 568 (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].
% 1.64/2.04 569 (all V_K_2 all V_X_2 all V_N_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> ((all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)))) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_BseqI2_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 570 (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].
% 1.64/2.04 571 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_norm__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 572 (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].
% 1.64/2.04 573 (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].
% 1.64/2.04 574 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 575 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 576 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 577 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 578 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 579 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 580 (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].
% 1.64/2.04 581 (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].
% 1.64/2.04 582 (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].
% 1.64/2.04 583 (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].
% 1.64/2.04 584 (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].
% 1.64/2.04 585 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 586 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 587 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 588 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 589 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z) # label(fact_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 590 (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].
% 1.64/2.04 591 (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].
% 1.64/2.04 592 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 593 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 594 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 595 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 596 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 597 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 598 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 599 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 600 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 601 (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].
% 1.64/2.04 602 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Oone__class_Oone(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b))) # label(fact_inverse__unique) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 603 (all V_n hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 604 (all V_n hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 605 (all V_n all V_m (V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) -> V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 606 (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].
% 1.64/2.04 607 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))))))) # label(fact_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 608 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))))))) # label(fact_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 609 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 610 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(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].
% 1.64/2.04 611 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(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].
% 1.64/2.04 612 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) & hBOOL(hAPP(hAPP(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].
% 1.64/2.04 613 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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].
% 1.64/2.04 614 (all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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].
% 1.64/2.04 615 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),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].
% 1.64/2.04 616 (all V_m all V_k (hBOOL(hAPP(hAPP(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,hAPP(c_Nat_OSuc,hAPP(hAPP(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].
% 1.64/2.04 617 (all V_x (V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 618 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 619 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.64/2.04 620 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)),c_Groups_Oone__class_Oone(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(hAPP(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].
% 1.64/2.04 621 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) & hBOOL(hAPP(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].
% 1.64/2.04 622 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 623 (all V_y all V_x all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((all B_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y))))) -> hBOOL(hAPP(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].
% 1.64/2.04 624 (all V_p all V_n all T_a (class_Groups_Ozero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Polynomial_Odegree(T_a,V_p))) -> (exists B_i (hBOOL(hAPP(hAPP(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].
% 1.64/2.04 625 (all V_y all V_n all V_x (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y),V_x)) -> (exists B_q V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)))))) # label(fact_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 626 (all V_n_2 all V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_P_2,V_n_2)) -> (exists B_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) & (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) -> -hBOOL(hAPP(V_P_2,B_i)))) & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 627 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 628 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 629 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x)))) # label(fact_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 630 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))))) # label(fact_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 631 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))))) # label(fact_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 632 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x)))) # label(fact_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 633 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 634 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 635 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)))) # label(fact_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 636 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 637 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))))))) # label(fact_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 638 (all V_x all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) -> c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 639 (all V_i_2 all V_P_2 all V_pb_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_pb_2)) -> (hBOOL(hAPP(V_P_2,B_i)) -> hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_pb_2)))))) -> (hBOOL(hAPP(V_P_2,V_i_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_pb_2)) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_mod__induct__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 640 -(all B_c -(all B_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_c))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w)))))) # label(fact__096_B_Bthesis_O_A_I_B_Bc_O_AALL_Aw_O_Acmod_A_Ipoly_Ap_Ac_J_A_060_061_Acmod_A_Ipoly_Ap_Aw_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 641 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 642 (all V_n c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 643 (all V_n c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 644 (all V_m_2 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2) <-> V_n_2 = V_m_2)) # label(fact_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 645 (all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 646 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 647 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 648 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)))) # label(fact_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.04 649 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 650 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 651 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))))) # label(fact_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 652 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 653 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n))))) # label(fact_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 654 (all V_n c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 655 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x)))) # label(fact_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 656 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))))) # label(fact_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 657 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)))) # label(fact_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 658 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 659 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))))) # label(fact_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 660 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 661 (all V_a_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2))))) # label(fact_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 662 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_N)))))))) # label(fact_Bseq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 663 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_N all B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_N)))))))) # label(fact_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 664 (all V_a_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))))) # label(fact_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 665 (all V_x hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 666 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))))) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_N)))))))) # label(fact_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 667 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_K (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))))) <-> (exists B_N all B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_N)))))))) # label(fact_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 668 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n))))) # label(fact_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 669 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a))) # label(fact_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 670 (all V_n all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n))))) # label(fact_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 671 (all V_x all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) -> c_RComplete_Onatfloor(V_x) = V_n))) # label(fact_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 672 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a))) # label(fact_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 673 (all V_x all V_y (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_n))),V_y)))))))) # label(fact_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 674 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (exists B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_n)))),V_x))))) # label(fact_reals__Archimedean) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 675 (all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_r),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_n)))))))) # label(fact_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 676 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))))) # label(fact_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 677 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (all B_y exists B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x)))))) # label(fact_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 678 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))) # label(fact_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 679 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 680 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 681 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 682 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 683 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 684 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))))) # label(fact_norm__power__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 685 (all V_x all V_n all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n))) # label(fact_poly__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 686 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 687 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 688 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) # label(fact_norm__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 689 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 690 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2))))) # label(fact_Bseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 691 (all V_n all V_r all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),hAPP(c_Nat_OSuc,V_n))),V_r)))))) # label(fact_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 692 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 693 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 694 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))))) # label(fact_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 695 (all V_n all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))))) # label(fact_nat__one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 696 (all V_n_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 697 (all V_m_2 all V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 698 (all V_n hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 699 (all V_n all V_m all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 700 (all V_n_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 701 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 702 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 703 (all V_n all V_m hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))) # label(fact_power__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 704 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)) # label(fact_real__of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 705 (all V_n all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n))),hAPP(hAPP(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].
% 1.64/2.05 706 (all V_n all V_x (V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n))) # label(fact_natfloor__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 707 (all V_n all V_a all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_field__power__not__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 708 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 709 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 710 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 711 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 712 (all V_n all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n))) # label(fact_power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 713 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a)) # label(fact_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 714 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))) # label(fact_power__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 715 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 716 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 717 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 718 (all V_n_2 all V_a_2 all T_a (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 719 (all V_n_2 all V_m_2 all V_a_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) <-> V_m_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 720 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_power__0__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 721 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a))) # label(fact_power__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 722 (all V_n all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 723 (all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 724 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 725 (all V_n 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n)))) # label(fact_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 726 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 727 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> V_a = V_b))))) # label(fact_power__inject__base) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 728 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 729 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 730 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 731 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 732 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))))))) # label(fact_power__gt1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 733 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 734 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))))) # label(fact_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 735 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 736 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 737 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 738 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 739 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 740 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> V_a = V_b)))))) # label(fact_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 741 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 742 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 743 (all V_n all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (exists B_z hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))))) # label(fact_reduce__poly__simple) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 744 (all T_a (class_Power_Opower(T_a) -> c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)))) # label(fact_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 745 (all V_x all V_p all V_n all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__replicate__append) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 746 (all V_y all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m)) # label(fact_zpower__zmod) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 747 (all V_d_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> (exists B_q V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)))) # label(fact_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 748 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) # label(fact_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 749 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)) # label(fact_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 750 (all V_y all V_q_1 all V_b_1 all V_a_1 (V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 751 (all V_q all V_r all V_b all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) # label(fact_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 752 (all V_q all V_r all V_b all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))))) # label(fact_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 753 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))))))) # label(fact_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 754 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))))) # label(fact_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 755 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_P_2,V_n_2))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_i all B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_P_2,B_j))))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_P_2,B_j))))))) # label(fact_split__zmod) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 756 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 757 (all V_b_2 all V_n_2 all V_a_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_Omonom(T_a,V_a_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2) <-> V_a_2 = V_b_2))) # label(fact_monom__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 758 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 759 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 760 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 761 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 762 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))))))))) # label(fact_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 763 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))))))) # label(fact_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 764 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))))))))) # label(fact_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 765 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))))))) # label(fact_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 766 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) # label(fact_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 767 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)))))) # label(fact_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 768 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 769 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 770 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 771 (all V_q all V_r all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)))))) # label(fact_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 772 (all V_q all V_r all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) # label(fact_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 773 (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].
% 1.64/2.05 774 (all V_n_2 all V_a_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_Omonom(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_monom__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 775 (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].
% 1.64/2.05 776 (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].
% 1.64/2.05 777 (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n))) # label(fact_smult__monom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 778 (all V_n all V_a all T_a (class_Groups_Ozero(T_a) -> hBOOL(hAPP(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].
% 1.64/2.05 779 (all V_b all V_n all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n))) # label(fact_add__monom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 780 (all V_a_2 all V_times_2 all V_one_2 all T_a hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2) # label(fact_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 781 (all V_n_2 all V_a_2 all V_times_2 all V_one_2 all T_a hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2))) # label(fact_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 782 (all V_m_2 all V_a_2 all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Omonom(T_a,V_a_2,V_m_2) = c_Polynomial_OAbs__poly(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBC(tc_Nat_Onat,T_a,tc_fun(T_a,T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Nat_Onat,c_If(T_a)),hAPP(c_fequal,V_m_2)),V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_monom__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 783 (all V_x all V_n all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))) # label(fact_poly__monom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 784 (all V_n all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)))) # label(fact_mult__monom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 785 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2))))) # label(fact_monoseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 786 (all V_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a & (all B_y (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a -> B_y = B_x))))))) # label(fact_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 787 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 788 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 789 (all V_z all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 790 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 791 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) | V_w_2 = V_z_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 792 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 793 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 794 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 795 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 796 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 797 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 798 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 799 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 800 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) | V_x = V_y | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 801 (all V_w_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) & V_z_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 802 (all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w))) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 803 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 804 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k))))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 805 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 806 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 807 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 808 (all V_z all V_z_H all V_w all V_w_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 809 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))) # label(fact_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 810 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_pos__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 811 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)))) # label(fact_pos__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 812 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 813 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_neg__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 814 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_neg__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 815 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 816 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 817 (all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)))) # label(fact_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 818 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_neg__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 819 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)))) # label(fact_pos__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 820 (all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 821 (all V_b c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 822 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Oincseq(T_a,V_X_2) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_incseq__imp__monoseq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 823 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Odecseq(T_a,V_X_2) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_decseq__imp__monoseq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 824 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Omonoseq(T_a,V_X_2) <-> (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,hAPP(c_Nat_OSuc,B_n))))) | (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,hAPP(c_Nat_OSuc,B_n))),hAPP(V_X_2,B_n))))))) # label(fact_monoseq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 825 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Omonoseq(T_a,V_X_2) <-> (all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))))) | (all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))))))) # label(fact_monoseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 826 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 827 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 828 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 829 (all V_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_r (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a))))) # label(fact_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 830 (all V_n all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)))) # label(fact_ln__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 831 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x_2),V_y_2)))))) # label(fact_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 832 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_ln__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 833 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),V_x)))) # label(fact_ln__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 834 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)))))) # label(fact_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 835 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))))) # label(fact_ln__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.05 836 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))))) # label(fact_ln__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 837 (all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))))) # label(fact_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 838 (all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 839 (all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 840 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))))) # label(fact_ln__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 841 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))))) # label(fact_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 842 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))))) # label(fact_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 843 (all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))))) # label(fact_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 844 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y))))) # label(fact_ln__mult) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 845 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)))) # label(fact_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 846 (all V_n_2 all V_P_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 847 (all V_n_2 all V_P_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 848 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 849 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 850 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a))) # label(fact_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 851 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a))) # label(fact_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 852 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c = c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)) & (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 853 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_div__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 854 (all V_a (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zdiv__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 855 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 856 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 857 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 858 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 859 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))))) # label(fact_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 860 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 861 (all V_b c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zdiv__zero) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 862 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 863 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 864 (all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 865 (all V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a)) # label(fact_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 866 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 867 (all V_b all V_a_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))))) # label(fact_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 868 (all V_b all V_a_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)))))) # label(fact_zdiv__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 869 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 870 (all V_b all V_b_H all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))))) # label(fact_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 871 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 872 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 873 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 874 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 875 (all V_b all V_b_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))))))) # label(fact_zdiv__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 876 (all V_b_2 all V_a_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))))) # label(fact_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 877 (all V_i_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2))))) # label(fact_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 878 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))))) # label(fact_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 879 (all V_k_2 all V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)))) # label(fact_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 880 (all V_k all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x))))) # label(fact_int__div__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 881 (all V_b all V_a all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))) # label(fact_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 882 (all V_k all V_b all V_a hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 883 (all V_k all V_a all V_b hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 884 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 885 (all V_b all V_a V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 886 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 887 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 888 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 889 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 890 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a)) # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 891 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 892 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 893 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 894 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 895 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_i ((exists B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (all B_i ((exists B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))))) # label(fact_split__zdiv) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 896 (all V_r_1 all V_y all V_b_1 all V_a_1 (V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 897 (all V_b all V_a all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 898 (all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 899 (all V_n all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_r (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),hAPP(c_Nat_OSuc,V_n)) = V_a)))) # label(fact_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 900 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n))) # label(fact_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 901 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 902 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))) # label(fact_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 903 (all V_n all V_m all V_k ((V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)))) # label(fact_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 904 (all V_m c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m) # label(fact_div__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 905 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_div__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 906 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))))) # label(fact_le__div__geq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 907 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m))) # label(fact_div__le__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 908 (all V_k all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))))) # label(fact_div__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 909 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))))) # label(fact_div__if) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 910 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))))) # label(fact_div__geq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 911 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))) # label(fact_div__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 912 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_pdivmod__rel) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 913 (all V_y all V_x all V_a all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_x),V_y) = c_Polynomial_Osmult(T_a,V_a,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_div__smult__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 914 (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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_q))) # label(fact_div__poly__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 915 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)) # label(fact_div__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 916 (all V_z all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z))) # label(fact_poly__div__mult__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 917 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 918 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 919 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 920 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 921 (all V_k all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)))))) # label(fact_div__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 922 (all V_x all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 923 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m)) # label(fact_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 924 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m)) # label(fact_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 925 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))) # label(fact_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 926 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m))))) # label(fact_div__less__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 927 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),hAPP(hAPP(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].
% 1.64/2.06 928 (all V_b all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_n))) # label(fact_diff__monom) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 929 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 930 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 931 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 932 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 933 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 934 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 935 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) # label(fact_norm__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 936 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 937 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 938 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) -> (V_a_2 = V_b_2 <-> V_ca_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 939 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 940 (all V_n all V_q all V_p all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)))) # label(fact_coeff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 941 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_p) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),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].
% 1.64/2.06 942 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__diff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 943 (all V_qa_2 all V_pb_2 all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_pb_2),V_qa_2) = c_Polynomial_OAbs__poly(T_a,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a)),c_Polynomial_Ocoeff(T_a,V_pb_2))),c_Polynomial_Ocoeff(T_a,V_qa_2))))) # label(fact_minus__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 944 (all V_n all V_m (-hBOOL(hAPP(hAPP(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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))) # label(fact_mod__geq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 945 (all V_n all V_m ((hBOOL(hAPP(hAPP(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) & (-hBOOL(hAPP(hAPP(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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)))) # label(fact_mod__if) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 946 (all V_m all V_n (hBOOL(hAPP(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,hAPP(hAPP(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].
% 1.64/2.06 947 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 948 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 949 (all V_n all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m)))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 950 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 951 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 952 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 953 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 954 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 955 (all V_n all V_m (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 956 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 957 (all V_c all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c)))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 958 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 959 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 960 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 961 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 <-> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 962 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 963 (all V_i_2 all V_j_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 964 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 965 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 966 (all V_m all V_n all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 967 (all V_i_2 all V_k_2 all V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 968 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 969 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 970 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 971 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.06 972 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.06 973 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.06 974 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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].
% 1.64/2.06 975 (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].
% 1.64/2.06 976 (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].
% 1.64/2.06 977 (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].
% 1.64/2.06 978 (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].
% 1.64/2.06 979 (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].
% 1.64/2.06 980 (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].
% 1.64/2.06 981 (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].
% 1.64/2.06 982 (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].
% 1.64/2.06 983 (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].
% 1.64/2.06 984 (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].
% 1.64/2.06 985 (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].
% 1.64/2.06 986 (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].
% 1.64/2.06 987 (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].
% 1.64/2.06 988 (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].
% 1.64/2.06 989 (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].
% 1.64/2.06 990 (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].
% 1.64/2.06 991 (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].
% 1.64/2.06 992 (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].
% 1.64/2.06 993 (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].
% 1.64/2.06 994 (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].
% 1.64/2.06 995 (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].
% 1.64/2.06 996 (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].
% 1.64/2.06 997 (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].
% 1.64/2.06 998 (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].
% 1.64/2.06 999 (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].
% 1.64/2.06 1000 (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].
% 1.64/2.06 1001 (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].
% 1.64/2.06 1002 (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].
% 1.64/2.06 1003 (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].
% 1.64/2.06 1004 (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].
% 1.64/2.06 1005 (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].
% 1.64/2.06 1006 (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].
% 1.64/2.06 1007 (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].
% 1.64/2.06 1008 (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].
% 1.64/2.06 1009 (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].
% 1.64/2.06 1010 (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].
% 1.64/2.06 1011 (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].
% 1.64/2.06 1012 (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].
% 1.64/2.06 1013 (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].
% 1.64/2.06 1014 (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].
% 1.64/2.06 1015 (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].
% 1.64/2.06 1016 (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].
% 1.64/2.06 1017 (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].
% 1.64/2.06 1018 (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].
% 1.64/2.06 1019 (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].
% 1.64/2.06 1020 (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].
% 1.64/2.06 1021 (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].
% 1.64/2.06 1022 (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].
% 1.64/2.06 1023 (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].
% 1.64/2.06 1024 (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].
% 1.64/2.06 1025 (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].
% 1.64/2.06 1026 (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].
% 1.64/2.06 1027 (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].
% 1.64/2.06 1028 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Power_Opower(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Power_Opower) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1029 (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].
% 1.64/2.06 1030 (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].
% 1.64/2.06 1031 (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].
% 1.64/2.06 1032 (all V_Q all V_P all T_b all T_a hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1033 (all V_R_2 all V_Q_2 all V_P_2 all T_c all T_a all T_b hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1034 (all V_R_2 all V_Q_2 all V_P_2 all T_a all T_c all T_b hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1035 (all V_R_2 all V_Q_2 all V_P_2 all T_a all T_c all T_b hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1036 (all V_y_2 all V_x_2 (-hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1037 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1038 (all V_Q_2 all V_P_2 (hBOOL(V_P_2) | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)))) # label(help_c__fimplies__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1039 (all V_P_2 all V_Q_2 (-hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)))) # label(help_c__fimplies__2) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.06 1040 (all V_Q_2 all V_P_2 (-hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) | -hBOOL(V_P_2) | hBOOL(V_Q_2))) # label(help_c__fimplies__3) # label(axiom) # label(non_clause). [assumption].
% 1.64/2.07 1041 -((c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> (v_q____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat,c_HOL_OAll(tc_Nat_Onat)),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat,c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat,c_fimplies)),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_HOL_Obool,hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_HOL_Obool),tc_Nat_Onat,c_fequal),c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & (c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> (v_q____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat,c_HOL_OAll(tc_Nat_Onat)),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat,c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat,c_fimplies)),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_HOL_Obool,hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_HOL_Obool),tc_Nat_Onat,c_fequal),c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))))) & (v_q____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat,c_HOL_OAll(tc_Nat_Onat)),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat,c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat,c_fimplies)),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_HOL_Obool,hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_HOL_Obool),tc_Nat_Onat,c_fequal),c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat,c_HOL_OAll(tc_Nat_Onat)),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat,c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat,c_fimplies)),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_HOL_Obool,hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_HOL_Obool),tc_Nat_Onat,c_fequal),c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.92/2.17
% 1.92/2.17 ============================== end of process non-clausal formulas ===
% 1.92/2.17
% 1.92/2.17 ============================== PROCESS INITIAL CLAUSES ===============
% 1.92/2.17
% 1.92/2.17 ============================== PREDICATE ELIMINATION =================
% 1.92/2.17 1042 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 1.92/2.17 1043 -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(30)].
% 1.92/2.17 1044 -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(30)].
% 1.92/2.17 1045 -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(55)].
% 1.92/2.17 1046 -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(55)].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) != c_Polynomial_Opoly(tc_Int_Oint,B) | A = B. [resolve(1042,a,1043,a)].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) = c_Polynomial_Opoly(tc_Int_Oint,B) | A != B. [resolve(1042,a,1044,a)].
% 1.92/2.17 1047 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Oring__char__0) # label(axiom). [assumption].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(tc_RealDef_Oreal,A) != c_Polynomial_Opoly(tc_RealDef_Oreal,B) | A = B. [resolve(1047,a,1043,a)].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(tc_RealDef_Oreal,A) = c_Polynomial_Opoly(tc_RealDef_Oreal,B) | A != B. [resolve(1047,a,1044,a)].
% 1.92/2.17 1048 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) != c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A = B. [resolve(1048,a,1043,a)].
% 1.92/2.17 Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) = c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A != B. [resolve(1048,a,1044,a)].
% 1.92/2.17 1049 -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(1024)].
% 1.92/2.17 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(1049,b,1043,a)].
% 1.92/2.17 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(1049,b,1044,a)].
% 2.03/2.27 1050 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption].
% 2.03/2.27 1051 -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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(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(59)].
% 2.03/2.27 1052 -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(102)].
% 2.03/2.27 1053 -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(103)].
% 2.03/2.27 1054 -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(104)].
% 2.03/2.27 1055 -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) = B | c_Groups_Ozero__class_Ozero(A) = C | B = C # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(105)].
% 2.03/2.27 1056 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__add) # label(axiom). [clausify(163)].
% 2.03/2.27 1057 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A)) # label(fact_inverse__1) # label(axiom). [clausify(580)].
% 2.03/2.27 1058 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Rings_Oinverse__class_Oinverse(A,B) = C # label(fact_inverse__unique) # label(axiom). [clausify(602)].
% 2.03/2.27 1059 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),B) # label(fact_left__inverse) # label(axiom). [clausify(613)].
% 2.03/2.27 1060 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_right__inverse) # label(axiom). [clausify(615)].
% 2.03/2.27 1061 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Oinverse(A,B)),C) # label(fact_nonzero__power__inverse) # label(axiom). [clausify(725)].
% 2.03/2.27 1062 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B))),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__diff) # label(axiom). [clausify(927)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1050,a,1051,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1050,a,1052,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1050,a,1053,a)].
% 2.03/2.27 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | A = B. [resolve(1050,a,1055,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1050,a,1056,a)].
% 2.03/2.27 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1050,a,1057,a)].
% 2.03/2.27 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = B. [resolve(1050,a,1058,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),A). [resolve(1050,a,1059,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1050,a,1060,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),B). [resolve(1050,a,1061,a)].
% 2.03/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1050,a,1062,a)].
% 2.03/2.27 1063 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption].
% 2.03/2.27 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(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(1063,a,1051,a)].
% 2.03/2.27 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(1063,a,1052,a)].
% 2.15/2.39 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(1063,a,1053,a)].
% 2.15/2.39 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) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | A = B. [resolve(1063,a,1055,a)].
% 2.15/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1063,a,1056,a)].
% 2.15/2.39 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1063,a,1057,a)].
% 2.15/2.39 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = B. [resolve(1063,a,1058,a)].
% 2.15/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),A). [resolve(1063,a,1059,a)].
% 2.15/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1063,a,1060,a)].
% 2.15/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),B). [resolve(1063,a,1061,a)].
% 2.15/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A))),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1063,a,1062,a)].
% 2.15/2.39 1064 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption].
% 2.15/2.39 1065 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_inverse__less__imp__less__neg) # label(axiom). [clausify(60)].
% 2.15/2.39 1066 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_inverse__less__imp__less) # label(axiom). [clausify(61)].
% 2.15/2.39 1067 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__negative__imp__negative) # label(axiom). [clausify(62)].
% 2.15/2.39 1068 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_less__imp__inverse__less__neg) # label(axiom). [clausify(63)].
% 2.15/2.39 1069 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_less__imp__inverse__less) # label(axiom). [clausify(64)].
% 2.15/2.39 1070 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_negative__imp__inverse__negative) # label(axiom). [clausify(65)].
% 2.15/2.39 1071 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | c_Groups_Ozero__class_Ozero(A) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_inverse__positive__imp__positive) # label(axiom). [clausify(66)].
% 2.15/2.39 1072 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_positive__imp__inverse__positive) # label(axiom). [clausify(67)].
% 2.15/2.39 1073 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_inverse__le__imp__le__neg) # label(axiom). [clausify(392)].
% 2.15/2.39 1074 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_inverse__le__imp__le) # label(axiom). [clausify(393)].
% 2.15/2.39 1075 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_le__imp__inverse__le__neg) # label(axiom). [clausify(394)].
% 2.15/2.39 1076 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_le__imp__inverse__le) # label(axiom). [clausify(395)].
% 2.15/2.39 1077 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_one__less__inverse) # label(axiom). [clausify(611)].
% 2.15/2.39 1078 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) # label(fact_one__le__inverse) # label(axiom). [clausify(619)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1064,a,1065,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1064,a,1066,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1064,a,1067,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1068,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1069,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1064,a,1070,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1064,a,1071,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1072,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1064,a,1073,a)].
% 2.15/2.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1064,a,1074,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1075,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1076,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1077,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))). [resolve(1064,a,1078,a)].
% 2.28/2.50 1079 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 2.28/2.50 1080 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(68)].
% 2.28/2.50 1081 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(68)].
% 2.28/2.50 1082 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(69)].
% 2.28/2.50 1083 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(69)].
% 2.28/2.50 1084 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(364)].
% 2.28/2.50 1085 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(364)].
% 2.28/2.50 1086 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(365)].
% 2.28/2.50 1087 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(365)].
% 2.28/2.50 1088 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),B)) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(610)].
% 2.28/2.50 1089 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(610)].
% 2.28/2.50 1090 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),B)) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(610)].
% 2.28/2.50 1091 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(612)].
% 2.28/2.50 1092 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(612)].
% 2.28/2.50 1093 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(612)].
% 2.28/2.50 1094 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(620)].
% 2.28/2.50 1095 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(620)].
% 2.28/2.50 1096 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(620)].
% 2.28/2.50 1097 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(621)].
% 2.28/2.50 1098 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oone__class_Oone(A))) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(621)].
% 2.28/2.50 1099 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Rings_Oinverse__class_Oinverse(A,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oone__class_Oone(A))) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(621)].
% 2.28/2.50 1100 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),f34(B,C,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(623)].
% 2.28/2.50 1101 -class_Fields_Olinordered__field__inverse__zero(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f34(B,C,A)),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(623)].
% 2.28/2.50 1102 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),f34(B,C,A)),C)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(623)].
% 2.28/2.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1079,a,1080,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1079,a,1082,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1079,a,1084,a)].
% 2.28/2.50 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1079,a,1085,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1079,a,1086,a)].
% 2.28/2.50 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1079,a,1087,a)].
% 2.28/2.50 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)). [resolve(1079,a,1088,a)].
% 2.28/2.50 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1079,a,1089,a)].
% 2.40/2.62 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)). [resolve(1079,a,1090,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1079,a,1091,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1079,a,1092,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)). [resolve(1079,a,1094,a)].
% 2.40/2.62 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1079,a,1095,a)].
% 2.40/2.62 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)). [resolve(1079,a,1096,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1079,a,1097,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1079,a,1098,a)].
% 2.40/2.62 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f34(A,B,tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1079,a,1100,a)].
% 2.40/2.62 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),f34(A,B,tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1079,a,1101,a)].
% 2.40/2.62 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),f34(A,B,tc_RealDef_Oreal)),B)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1079,a,1102,a)].
% 2.40/2.62 1103 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 2.40/2.62 1104 -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(91)].
% 2.40/2.62 1105 -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(92)].
% 2.40/2.62 1106 -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(92)].
% 2.40/2.62 1107 -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(93)].
% 2.40/2.62 1108 -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(100)].
% 2.40/2.62 1109 -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(101)].
% 2.40/2.62 1110 -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(101)].
% 2.40/2.62 1111 -class_RealVector_Oreal__normed__div__algebra(A) | -class_Rings_Odivision__ring__inverse__zero(A) | c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Oinverse(A,B)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_norm__inverse) # label(axiom). [clausify(323)].
% 2.40/2.62 1112 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Oinverse(A,B)),C) # label(fact_power__inverse) # label(axiom). [clausify(712)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1103,a,1104,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | A = B. [resolve(1103,a,1105,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | A != B. [resolve(1103,a,1106,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1103,a,1108,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1103,a,1110,a)].
% 2.40/2.62 Derived: -class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)). [resolve(1103,a,1111,b)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),B). [resolve(1103,a,1112,a)].
% 2.40/2.62 1113 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1113,a,1104,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A = B. [resolve(1113,a,1105,a)].
% 2.40/2.62 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A != B. [resolve(1113,a,1106,a)].
% 2.40/2.62 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(1113,a,1108,a)].
% 2.40/2.62 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(1113,a,1110,a)].
% 2.45/2.73 Derived: -class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)). [resolve(1113,a,1111,b)].
% 2.45/2.73 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),B). [resolve(1113,a,1112,a)].
% 2.45/2.73 1114 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom). [assumption].
% 2.45/2.73 1115 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__zero__left) # label(axiom). [clausify(94)].
% 2.45/2.73 1116 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__zero__right) # label(axiom). [clausify(95)].
% 2.45/2.73 1117 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff) # label(axiom). [clausify(718)].
% 2.45/2.73 1118 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C # label(fact_power__eq__0__iff) # label(axiom). [clausify(718)].
% 2.45/2.73 1119 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C # label(fact_power__eq__0__iff) # label(axiom). [clausify(718)].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1114,a,1115,a)].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1114,a,1116,a)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1114,a,1117,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1114,a,1118,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1114,a,1119,b)].
% 2.45/2.73 1120 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(1120,a,1115,a)].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1120,a,1116,a)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1120,a,1117,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1120,a,1118,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1120,a,1119,b)].
% 2.45/2.73 1121 class_Rings_Omult__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Omult__zero) # label(axiom). [assumption].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1121,a,1115,a)].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1121,a,1116,a)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1121,a,1117,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1121,a,1118,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1121,a,1119,b)].
% 2.45/2.73 1122 class_Rings_Omult__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Omult__zero) # label(axiom). [assumption].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1122,a,1115,a)].
% 2.45/2.73 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1122,a,1116,a)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1122,a,1117,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1122,a,1118,b)].
% 2.45/2.73 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1122,a,1119,b)].
% 2.64/2.85 1123 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom). [clausify(1021)].
% 2.64/2.85 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1123,b,1115,a)].
% 2.64/2.85 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1123,b,1116,a)].
% 2.64/2.85 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1123,b,1117,b)].
% 2.64/2.85 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C. [resolve(1123,b,1118,b)].
% 2.64/2.85 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C. [resolve(1123,b,1119,b)].
% 2.64/2.85 1124 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.64/2.85 1125 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(96)].
% 2.64/2.85 1126 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(96)].
% 2.64/2.85 1127 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(96)].
% 2.64/2.85 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1124,a,1125,a)].
% 2.64/2.85 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1124,a,1126,a)].
% 2.64/2.85 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1124,a,1127,a)].
% 2.64/2.85 1128 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.64/2.85 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1128,a,1125,a)].
% 2.64/2.85 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1128,a,1126,a)].
% 2.74/2.97 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1128,a,1127,a)].
% 2.74/2.97 1129 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.74/2.97 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1129,a,1125,a)].
% 2.74/2.97 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1129,a,1126,a)].
% 2.74/2.97 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1129,a,1127,a)].
% 2.74/2.97 1130 -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(992)].
% 2.74/2.97 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1130,b,1125,a)].
% 2.74/2.97 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1130,b,1126,a)].
% 2.74/2.97 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1130,b,1127,a)].
% 2.74/2.97 1131 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 2.74/2.97 1132 -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(99)].
% 2.74/2.97 1133 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(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(106)].
% 2.74/2.97 1134 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Oone__class_Oone(A) != c_Rings_Oinverse__class_Oinverse(A,B) | c_Groups_Oone__class_Oone(A) = B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(581)].
% 2.74/2.97 1135 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Oinverse(A,B) | c_Groups_Oone__class_Oone(A) != B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(581)].
% 2.74/2.97 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1131,a,1133,a)].
% 2.74/2.97 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A. [resolve(1131,a,1134,a)].
% 2.74/2.97 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1131,a,1135,a)].
% 2.74/2.97 1136 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 2.83/3.08 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1136,a,1133,a)].
% 2.83/3.08 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A. [resolve(1136,a,1134,a)].
% 2.83/3.08 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1136,a,1135,a)].
% 2.83/3.08 1137 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 2.83/3.08 1138 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__square__less__zero) # label(axiom). [clausify(107)].
% 2.83/3.08 1139 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__sum__squares__lt__zero) # label(axiom). [clausify(160)].
% 2.83/3.08 1140 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B))) # label(fact_zero__le__square) # label(axiom). [clausify(335)].
% 2.83/3.08 1141 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(389)].
% 2.83/3.08 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1137,a,1138,a)].
% 2.83/3.08 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1137,a,1139,a)].
% 2.83/3.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A))). [resolve(1137,a,1140,a)].
% 2.83/3.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))). [resolve(1137,a,1141,a)].
% 2.83/3.08 1142 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption].
% 2.83/3.08 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1142,a,1138,a)].
% 2.83/3.08 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1142,a,1139,a)].
% 2.83/3.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A))). [resolve(1142,a,1140,a)].
% 2.83/3.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)))). [resolve(1142,a,1141,a)].
% 2.95/3.19 1143 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(1005)].
% 2.95/3.19 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1143,b,1138,a)].
% 2.95/3.19 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1143,b,1139,a)].
% 2.95/3.19 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B))). [resolve(1143,b,1140,a)].
% 2.95/3.19 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)))). [resolve(1143,b,1141,a)].
% 2.95/3.19 1144 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 2.95/3.19 1145 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1146 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1147 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1148 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1149 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1150 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(108)].
% 2.95/3.19 1151 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1152 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1153 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1154 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1155 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1156 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(109)].
% 2.95/3.19 1157 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(110)].
% 2.95/3.19 1158 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(110)].
% 2.95/3.19 1159 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(116)].
% 2.95/3.19 1160 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(116)].
% 2.95/3.19 1161 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__neg__neg) # label(axiom). [clausify(118)].
% 2.95/3.19 1162 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(122)].
% 2.95/3.19 1163 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(123)].
% 2.95/3.19 1164 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(157)].
% 2.95/3.19 1165 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(157)].
% 2.95/3.19 1166 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(157)].
% 2.95/3.19 1167 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(159)].
% 2.95/3.19 1168 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(159)].
% 2.95/3.19 1169 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(159)].
% 2.95/3.19 1170 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1171 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1172 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1173 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1174 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1175 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(336)].
% 2.95/3.19 1176 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1177 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1178 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1179 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1180 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1181 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(337)].
% 2.95/3.19 1182 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(381)].
% 2.95/3.19 1183 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(381)].
% 2.95/3.19 1184 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(382)].
% 2.95/3.19 1185 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(382)].
% 2.95/3.19 1186 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(390)].
% 2.95/3.19 1187 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(390)].
% 2.95/3.19 1188 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(390)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1145,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),A)). [resolve(1144,a,1146,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1147,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),A)). [resolve(1144,a,1148,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(1144,a,1149,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),A)). [resolve(1144,a,1150,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1151,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(1144,a,1152,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1153,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(1144,a,1154,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(1144,a,1155,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(1144,a,1156,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(1144,a,1157,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(1144,a,1159,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(1144,a,1161,a)].
% 2.95/3.19 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1144,a,1164,a)].
% 2.95/3.19 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1144,a,1165,a)].
% 2.95/3.19 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1144,a,1166,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1144,a,1167,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1144,a,1168,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1144,a,1169,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1170,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1171,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1172,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1173,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1144,a,1174,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1175,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1176,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1144,a,1177,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1178,a)].
% 2.95/3.19 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1144,a,1179,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1144,a,1180,a)].
% 2.95/3.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1144,a,1181,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)). [resolve(1144,a,1182,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)). [resolve(1144,a,1183,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1144,a,1184,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1144,a,1185,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1144,a,1186,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1144,a,1187,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1144,a,1188,a)].
% 2.95/3.20 1189 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1145,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),A)). [resolve(1189,a,1146,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1147,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),A)). [resolve(1189,a,1148,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)). [resolve(1189,a,1149,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),A)). [resolve(1189,a,1150,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1151,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),B)). [resolve(1189,a,1152,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1153,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),B)). [resolve(1189,a,1154,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)). [resolve(1189,a,1155,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),B)). [resolve(1189,a,1156,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)). [resolve(1189,a,1157,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),B)). [resolve(1189,a,1159,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))). [resolve(1189,a,1161,a)].
% 2.95/3.20 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1189,a,1164,a)].
% 2.95/3.20 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1189,a,1165,a)].
% 2.95/3.20 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1189,a,1166,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1189,a,1167,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1189,a,1168,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1189,a,1169,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1170,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1171,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1172,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1173,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1189,a,1174,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1175,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1176,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1189,a,1177,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1178,a)].
% 2.95/3.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1189,a,1179,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1189,a,1180,a)].
% 3.00/3.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1189,a,1181,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)). [resolve(1189,a,1182,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)). [resolve(1189,a,1183,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1189,a,1184,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1189,a,1185,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1189,a,1186,a)].
% 3.00/3.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1189,a,1187,a)].
% 3.00/3.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1189,a,1188,a)].
% 3.00/3.21 1190 -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(991)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1145,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),B)). [resolve(1190,b,1146,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1147,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),B)). [resolve(1190,b,1148,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)). [resolve(1190,b,1149,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),B)). [resolve(1190,b,1150,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1151,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),C)). [resolve(1190,b,1152,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1153,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),C)). [resolve(1190,b,1154,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)). [resolve(1190,b,1155,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),C)). [resolve(1190,b,1156,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)). [resolve(1190,b,1157,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),C)). [resolve(1190,b,1159,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))). [resolve(1190,b,1161,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1190,b,1164,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1190,b,1165,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1190,b,1166,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1190,b,1167,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1190,b,1168,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1190,b,1169,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1170,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1171,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1172,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1173,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1190,b,1174,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1175,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1176,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1190,b,1177,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1178,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1190,b,1179,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1190,b,1180,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1190,b,1181,a)].
% 3.00/3.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)). [resolve(1190,b,1182,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)). [resolve(1190,b,1183,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1190,b,1184,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1190,b,1185,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1190,b,1186,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1190,b,1187,a)].
% 3.04/3.32 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1190,b,1188,a)].
% 3.04/3.32 1191 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.04/3.32 1192 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__pos__pos) # label(axiom). [clausify(111)].
% 3.04/3.32 1193 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__pos__neg) # label(axiom). [clausify(112)].
% 3.04/3.32 1194 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__pos__neg2) # label(axiom). [clausify(113)].
% 3.04/3.32 1195 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(114)].
% 3.04/3.32 1196 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(115)].
% 3.04/3.32 1197 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__neg__pos) # label(axiom). [clausify(117)].
% 3.04/3.32 1198 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(119)].
% 3.04/3.32 1199 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(120)].
% 3.04/3.32 1200 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__left__le__imp__le) # label(axiom). [clausify(371)].
% 3.04/3.32 1201 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_mult__right__le__imp__le) # label(axiom). [clausify(372)].
% 3.04/3.32 1202 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__imp__less__left) # label(axiom). [clausify(373)].
% 3.04/3.32 1203 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__less__imp__less__right) # label(axiom). [clausify(375)].
% 3.04/3.32 1204 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(377)].
% 3.04/3.32 1205 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(378)].
% 3.04/3.32 1206 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(379)].
% 3.04/3.32 1207 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__strict__mono) # label(axiom). [clausify(380)].
% 3.04/3.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(1191,a,1192,a)].
% 3.04/3.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1191,a,1193,a)].
% 3.04/3.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1191,a,1194,a)].
% 3.04/3.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1191,a,1195,a)].
% 3.04/3.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1191,a,1196,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1191,a,1201,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(1191,a,1202,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(1191,a,1203,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1191,a,1204,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1191,a,1205,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1191,a,1206,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1191,a,1207,a)].
% 3.04/3.33 1208 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(1208,a,1192,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1208,a,1193,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1208,a,1194,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(1208,a,1195,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1208,a,1196,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))). [resolve(1208,a,1198,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))). [resolve(1208,a,1199,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1208,a,1200,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1208,a,1201,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1208,a,1202,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(1208,a,1203,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1208,a,1204,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1208,a,1205,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1208,a,1206,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1208,a,1207,a)].
% 3.04/3.33 1209 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))). [resolve(1209,a,1192,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1209,a,1193,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1209,a,1194,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1209,a,1195,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1209,a,1196,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1209,a,1201,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)). [resolve(1209,a,1202,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)). [resolve(1209,a,1203,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1209,a,1204,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1209,a,1205,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1209,a,1206,a)].
% 3.04/3.33 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1209,a,1207,a)].
% 3.04/3.34 1210 -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(984)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))). [resolve(1210,b,1192,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1210,b,1193,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1210,b,1194,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1210,b,1195,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1210,b,1196,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1210,b,1201,a)].
% 3.04/3.34 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)). [resolve(1210,b,1202,a)].
% 3.19/3.46 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)). [resolve(1210,b,1203,a)].
% 3.19/3.46 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1210,b,1204,a)].
% 3.19/3.46 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1210,b,1205,a)].
% 3.19/3.46 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1210,b,1206,a)].
% 3.19/3.46 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1210,b,1207,a)].
% 3.19/3.46 1211 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.19/3.46 1212 -class_Rings_Olinordered__comm__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(121)].
% 3.19/3.46 1213 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.43/3.70 1214 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.43/3.70 1215 -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(982)].
% 3.43/3.70 1216 class_Orderings_Owellorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Owellorder) # label(axiom). [assumption].
% 3.43/3.70 1217 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Orderings_Oord__class_OLeast(A,C))) | -hBOOL(hAPP(C,B)) # label(fact_not__less__Least) # label(axiom). [clausify(125)].
% 3.43/3.70 1218 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(A,B))) # label(fact_LeastI__ex) # label(axiom). [clausify(194)].
% 3.43/3.70 1219 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(A,B))) # label(fact_LeastI) # label(axiom). [clausify(196)].
% 3.43/3.70 1220 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_OLeast(A,B)),C)) # label(fact_Least__le) # label(axiom). [clausify(331)].
% 3.43/3.70 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Orderings_Oord__class_OLeast(tc_Nat_Onat,B))) | -hBOOL(hAPP(B,A)). [resolve(1216,a,1217,a)].
% 3.43/3.70 Derived: -hBOOL(hAPP(A,B)) | hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,A))). [resolve(1216,a,1218,a)].
% 3.43/3.70 Derived: -hBOOL(hAPP(A,B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,A)),B)). [resolve(1216,a,1220,a)].
% 3.43/3.70 1221 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.43/3.70 1222 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult_Ozero__left) # label(axiom). [clausify(131)].
% 3.43/3.70 1223 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_mult_Oadd__right) # label(axiom). [clausify(146)].
% 3.43/3.70 1224 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_mult__right_Oadd) # label(axiom). [clausify(148)].
% 3.43/3.70 1225 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_mult_Oadd__left) # label(axiom). [clausify(151)].
% 3.43/3.70 1226 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_mult__left_Oadd) # label(axiom). [clausify(152)].
% 3.43/3.70 1227 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__right_Ozero) # label(axiom). [clausify(197)].
% 3.43/3.70 1228 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult_Ozero__right) # label(axiom). [clausify(198)].
% 3.43/3.70 1229 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__left_Ozero) # label(axiom). [clausify(200)].
% 3.43/3.70 1230 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))) # label(fact_norm__mult__ineq) # label(axiom). [clausify(294)].
% 3.43/3.70 1231 -class_RealVector_Oreal__normed__algebra(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,D)),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E))) # label(fact_norm__mult__less) # label(axiom). [clausify(300)].
% 3.43/3.70 1232 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f14(B,A))) # label(fact_mult__left_Opos__bounded) # label(axiom). [clausify(498)].
% 3.43/3.70 1233 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f14(C,A)))) # label(fact_mult__left_Opos__bounded) # label(axiom). [clausify(498)].
% 3.43/3.70 1234 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f15(B,A))) # label(fact_mult__right_Opos__bounded) # label(axiom). [clausify(499)].
% 3.43/3.70 1235 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),f15(B,A)))) # label(fact_mult__right_Opos__bounded) # label(axiom). [clausify(499)].
% 3.43/3.70 1236 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f16(A))) # label(fact_mult_Opos__bounded) # label(axiom). [clausify(500)].
% 3.43/3.70 1237 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f16(A)))) # label(fact_mult_Opos__bounded) # label(axiom). [clausify(500)].
% 3.43/3.70 1238 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f21(B,A))) # label(fact_mult__left_Ononneg__bounded) # label(axiom). [clausify(513)].
% 3.43/3.70 1239 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f21(C,A)))) # label(fact_mult__left_Ononneg__bounded) # label(axiom). [clausify(513)].
% 3.43/3.70 1240 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f22(B,A))) # label(fact_mult__right_Ononneg__bounded) # label(axiom). [clausify(514)].
% 3.43/3.70 1241 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),f22(B,A)))) # label(fact_mult__right_Ononneg__bounded) # label(axiom). [clausify(514)].
% 3.43/3.70 1242 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f23(A))) # label(fact_mult_Ononneg__bounded) # label(axiom). [clausify(515)].
% 3.43/3.70 1243 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f23(A)))) # label(fact_mult_Ononneg__bounded) # label(axiom). [clausify(515)].
% 3.43/3.70 1244 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f55(C,A)))) # label(fact_mult__left_Obounded) # label(axiom). [clausify(678)].
% 3.43/3.70 1245 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(931)].
% 3.43/3.70 1246 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(932)].
% 3.43/3.70 1247 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),C) # label(fact_mult_Odiff__left) # label(axiom). [clausify(933)].
% 3.43/3.70 1248 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),C) # label(fact_mult__left_Odiff) # label(axiom). [clausify(934)].
% 3.43/3.70 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(1221,a,1223,a)].
% 3.43/3.70 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B). [resolve(1221,a,1225,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))). [resolve(1221,a,1230,a)].
% 3.43/3.70 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1221,a,1231,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f14(A,tc_RealDef_Oreal))). [resolve(1221,a,1232,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f14(B,tc_RealDef_Oreal)))). [resolve(1221,a,1233,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f15(A,tc_RealDef_Oreal))). [resolve(1221,a,1234,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f15(A,tc_RealDef_Oreal)))). [resolve(1221,a,1235,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f16(tc_RealDef_Oreal))). [resolve(1221,a,1236,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f16(tc_RealDef_Oreal)))). [resolve(1221,a,1237,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f21(A,tc_RealDef_Oreal))). [resolve(1221,a,1238,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f21(B,tc_RealDef_Oreal)))). [resolve(1221,a,1239,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f22(A,tc_RealDef_Oreal))). [resolve(1221,a,1240,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f22(A,tc_RealDef_Oreal)))). [resolve(1221,a,1241,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f23(tc_RealDef_Oreal))). [resolve(1221,a,1242,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f23(tc_RealDef_Oreal)))). [resolve(1221,a,1243,a)].
% 3.43/3.70 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f55(B,tc_RealDef_Oreal)))). [resolve(1221,a,1244,a)].
% 3.43/3.70 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)). [resolve(1221,a,1245,a)].
% 3.49/3.71 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C)),B). [resolve(1221,a,1247,a)].
% 3.49/3.71 1249 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.49/3.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(1249,a,1223,a)].
% 3.49/3.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(1249,a,1225,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))). [resolve(1249,a,1230,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1249,a,1231,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f14(A,tc_Complex_Ocomplex))). [resolve(1249,a,1232,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f14(B,tc_Complex_Ocomplex)))). [resolve(1249,a,1233,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f15(A,tc_Complex_Ocomplex))). [resolve(1249,a,1234,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f15(A,tc_Complex_Ocomplex)))). [resolve(1249,a,1235,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f16(tc_Complex_Ocomplex))). [resolve(1249,a,1236,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f16(tc_Complex_Ocomplex)))). [resolve(1249,a,1237,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f21(A,tc_Complex_Ocomplex))). [resolve(1249,a,1238,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f21(B,tc_Complex_Ocomplex)))). [resolve(1249,a,1239,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f22(A,tc_Complex_Ocomplex))). [resolve(1249,a,1240,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f22(A,tc_Complex_Ocomplex)))). [resolve(1249,a,1241,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f23(tc_Complex_Ocomplex))). [resolve(1249,a,1242,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f23(tc_Complex_Ocomplex)))). [resolve(1249,a,1243,a)].
% 3.55/3.82 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f55(B,tc_Complex_Ocomplex)))). [resolve(1249,a,1244,a)].
% 3.55/3.82 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)). [resolve(1249,a,1245,a)].
% 3.55/3.82 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),B). [resolve(1249,a,1247,a)].
% 3.55/3.82 1250 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) # label(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.55/3.82 1251 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(141)].
% 3.55/3.82 1252 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(141)].
% 3.55/3.82 1253 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(149)].
% 3.55/3.82 1254 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(149)].
% 3.55/3.82 1255 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(149)].
% 3.55/3.82 1256 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(154)].
% 3.55/3.82 1257 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(154)].
% 3.55/3.82 1258 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(154)].
% 3.55/3.82 1259 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C != D | E = F | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(158)].
% 3.55/3.82 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1250,a,1251,a)].
% 3.55/3.82 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1250,a,1252,a)].
% 3.55/3.82 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1250,a,1253,a)].
% 3.55/3.82 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1250,a,1254,a)].
% 3.55/3.82 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)). [resolve(1250,a,1255,a)].
% 3.55/3.82 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A = C | B = D. [resolve(1250,a,1256,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A != C. [resolve(1250,a,1257,a)].
% 3.55/3.83 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)). [resolve(1250,a,1259,a)].
% 3.55/3.83 1260 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1260,a,1251,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1260,a,1252,a)].
% 3.55/3.83 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(1260,a,1253,a)].
% 3.55/3.83 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(1260,a,1254,a)].
% 3.55/3.83 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),A)). [resolve(1260,a,1255,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A = C | B = D. [resolve(1260,a,1256,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A != C. [resolve(1260,a,1257,a)].
% 3.55/3.83 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)). [resolve(1260,a,1259,a)].
% 3.55/3.83 1261 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1261,a,1251,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1261,a,1252,a)].
% 3.55/3.83 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1261,a,1253,a)].
% 3.55/3.83 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1261,a,1254,a)].
% 3.55/3.83 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)). [resolve(1261,a,1255,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | A = C | B = D. [resolve(1261,a,1256,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | A != C. [resolve(1261,a,1257,a)].
% 3.55/3.83 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)). [resolve(1261,a,1259,a)].
% 3.55/3.83 1262 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1262,a,1251,a)].
% 3.55/3.83 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1262,a,1252,a)].
% 3.55/3.83 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1262,a,1253,a)].
% 3.55/3.83 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1262,a,1254,a)].
% 3.55/3.84 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A)). [resolve(1262,a,1255,a)].
% 3.55/3.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | A = C | B = D. [resolve(1262,a,1256,a)].
% 3.55/3.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | A != C. [resolve(1262,a,1257,a)].
% 3.55/3.84 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)). [resolve(1262,a,1259,a)].
% 3.55/3.84 1263 -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(979)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1263,b,1251,a)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1263,b,1252,a)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1263,b,1253,a)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1263,b,1254,a)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)). [resolve(1263,b,1255,a)].
% 3.55/3.84 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | B = D | C = E. [resolve(1263,b,1256,a)].
% 3.85/4.08 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | B != D. [resolve(1263,b,1257,a)].
% 3.85/4.08 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | C != D | E = F | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),F)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)). [resolve(1263,b,1259,a)].
% 3.85/4.08 1264 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.85/4.08 1265 -class_Rings_Ocomm__semiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(155)].
% 3.85/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(1264,a,1265,a)].
% 3.85/4.08 1266 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.85/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B). [resolve(1266,a,1265,a)].
% 3.85/4.08 1267 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.85/4.08 1268 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.85/4.08 1269 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1010)].
% 3.85/4.08 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),C). [resolve(1269,b,1265,a)].
% 3.85/4.08 1270 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 3.85/4.08 1271 -class_Rings_Osemiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(156)].
% 3.85/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),D)). [resolve(1270,a,1271,a)].
% 3.96/4.20 1272 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 3.96/4.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),D)). [resolve(1272,a,1271,a)].
% 3.96/4.20 1273 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom). [assumption].
% 3.96/4.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),D)). [resolve(1273,a,1271,a)].
% 3.96/4.20 1274 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption].
% 3.96/4.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),D)). [resolve(1274,a,1271,a)].
% 3.96/4.20 1275 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1025)].
% 3.96/4.20 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)),E)). [resolve(1275,b,1271,a)].
% 3.96/4.20 1276 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.96/4.20 1277 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_pos__add__strict) # label(axiom). [clausify(161)].
% 3.96/4.20 1278 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__le__zero) # label(axiom). [clausify(592)].
% 3.96/4.20 1279 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__le__one) # label(axiom). [clausify(593)].
% 3.96/4.20 1280 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__one) # label(axiom). [clausify(594)].
% 3.96/4.20 1281 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__less__zero) # label(axiom). [clausify(595)].
% 3.96/4.20 1282 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_less__1__mult) # label(axiom). [clausify(596)].
% 3.96/4.20 1283 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A)))) # label(fact_less__add__one) # label(axiom). [clausify(597)].
% 3.96/4.20 1284 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A)))) # label(fact_zero__less__two) # label(axiom). [clausify(609)].
% 3.96/4.20 1285 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),B)) # label(fact_realpow__Suc__le__self) # label(axiom). [clausify(691)].
% 3.96/4.20 1286 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(fact_power__strict__mono) # label(axiom). [clausify(692)].
% 3.96/4.20 1287 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_one__less__power) # label(axiom). [clausify(693)].
% 3.96/4.20 1288 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__le__imp__le__exp) # label(axiom). [clausify(694)].
% 3.96/4.20 1289 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(fact_power__mono) # label(axiom). [clausify(714)].
% 3.96/4.20 1290 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_zero__le__power) # label(axiom). [clausify(715)].
% 3.96/4.20 1291 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_zero__less__power) # label(axiom). [clausify(716)].
% 3.96/4.20 1292 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_one__le__power) # label(axiom). [clausify(717)].
% 3.96/4.20 1293 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C = D # label(fact_power__inject__exp) # label(axiom). [clausify(719)].
% 3.96/4.20 1294 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C != D # label(fact_power__inject__exp) # label(axiom). [clausify(719)].
% 3.96/4.20 1295 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_power__less__imp__less__base) # label(axiom). [clausify(726)].
% 3.96/4.20 1296 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | B = D # label(fact_power__inject__base) # label(axiom). [clausify(727)].
% 3.96/4.20 1297 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_power__le__imp__le__base) # label(axiom). [clausify(728)].
% 3.96/4.20 1298 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) # label(fact_power__gt1__lemma) # label(axiom). [clausify(729)].
% 3.96/4.20 1299 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) # label(fact_power__less__power__Suc) # label(axiom). [clausify(730)].
% 3.96/4.20 1300 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)))) # label(fact_power__gt1) # label(axiom). [clausify(732)].
% 3.96/4.20 1301 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) # label(fact_power__strict__increasing) # label(axiom). [clausify(733)].
% 3.96/4.20 1302 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__less__imp__less__exp) # label(axiom). [clausify(734)].
% 3.96/4.20 1303 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(735)].
% 3.96/4.20 1304 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(735)].
% 3.96/4.20 1305 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) # label(fact_power__increasing) # label(axiom). [clausify(736)].
% 3.96/4.20 1306 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__Suc__less) # label(axiom). [clausify(737)].
% 3.96/4.20 1307 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(A))) # label(fact_power__Suc__less__one) # label(axiom). [clausify(738)].
% 3.96/4.20 1308 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))) # label(fact_power__strict__decreasing) # label(axiom). [clausify(739)].
% 3.96/4.20 1309 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | B = D # label(fact_power__eq__imp__eq__base) # label(axiom). [clausify(740)].
% 3.96/4.20 1310 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))) # label(fact_power__decreasing) # label(axiom). [clausify(741)].
% 3.96/4.20 1311 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(742)].
% 3.96/4.20 1312 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(742)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1276,a,1277,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1276,a,1278,a)].
% 3.96/4.20 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1276,a,1279,a)].
% 3.96/4.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1276,a,1280,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1276,a,1281,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(1276,a,1282,a)].
% 3.96/4.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)))). [resolve(1276,a,1283,a)].
% 3.96/4.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). [resolve(1276,a,1284,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),A)). [resolve(1276,a,1285,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(1276,a,1286,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1276,a,1287,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1276,a,1288,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(1276,a,1289,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1276,a,1290,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1276,a,1291,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1276,a,1292,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B = C. [resolve(1276,a,1293,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B != C. [resolve(1276,a,1294,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(1276,a,1295,a)].
% 3.96/4.20 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | A = C. [resolve(1276,a,1296,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1276,a,1297,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))). [resolve(1276,a,1298,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))). [resolve(1276,a,1299,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)))). [resolve(1276,a,1300,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))). [resolve(1276,a,1301,a)].
% 3.96/4.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1276,a,1302,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))). [resolve(1276,a,1305,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1276,a,1306,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1276,a,1307,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A))). [resolve(1276,a,1308,a)].
% 3.96/4.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1276,a,1309,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A))). [resolve(1276,a,1310,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1276,a,1312,a)].
% 3.96/4.21 1313 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1313,a,1277,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1313,a,1278,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1313,a,1279,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1313,a,1280,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1313,a,1281,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(1313,a,1282,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [resolve(1313,a,1283,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [resolve(1313,a,1284,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),A)). [resolve(1313,a,1285,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C))). [resolve(1313,a,1286,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1313,a,1287,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1313,a,1288,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C))). [resolve(1313,a,1289,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1313,a,1290,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1313,a,1291,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1313,a,1292,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B = C. [resolve(1313,a,1293,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B != C. [resolve(1313,a,1294,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(1313,a,1295,a)].
% 3.96/4.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | A = C. [resolve(1313,a,1296,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1313,a,1297,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))). [resolve(1313,a,1298,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))). [resolve(1313,a,1299,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)))). [resolve(1313,a,1300,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B))). [resolve(1313,a,1301,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1313,a,1302,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B))). [resolve(1313,a,1305,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1313,a,1306,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1313,a,1307,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A))). [resolve(1313,a,1308,a)].
% 3.96/4.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1313,a,1309,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A))). [resolve(1313,a,1310,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1313,a,1312,a)].
% 3.96/4.21 1314 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1314,a,1277,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1314,a,1278,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1314,a,1279,a)].
% 3.96/4.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1314,a,1280,a)].
% 3.96/4.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1314,a,1281,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1282,a)].
% 3.96/4.22 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). [resolve(1314,a,1283,a)].
% 3.96/4.22 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). [resolve(1314,a,1284,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B))),A)). [resolve(1314,a,1285,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C))). [resolve(1314,a,1286,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1287,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1314,a,1288,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C))). [resolve(1314,a,1289,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1290,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1291,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1292,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B = C. [resolve(1314,a,1293,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B != C. [resolve(1314,a,1294,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)). [resolve(1314,a,1295,a)].
% 3.96/4.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | A = C. [resolve(1314,a,1296,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1314,a,1297,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)))). [resolve(1314,a,1298,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)))). [resolve(1314,a,1299,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B)))). [resolve(1314,a,1300,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B))). [resolve(1314,a,1301,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1314,a,1302,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B))). [resolve(1314,a,1305,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1314,a,1306,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1314,a,1307,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A))). [resolve(1314,a,1308,a)].
% 3.96/4.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1314,a,1309,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A))). [resolve(1314,a,1310,a)].
% 3.96/4.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1314,a,1312,a)].
% 3.96/4.22 1315 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(998)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1315,b,1277,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1315,b,1278,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1315,b,1279,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1315,b,1280,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1315,b,1281,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1282,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))))). [resolve(1315,b,1283,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))))). [resolve(1315,b,1284,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C))),B)). [resolve(1315,b,1285,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D))). [resolve(1315,b,1286,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1287,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)). [resolve(1315,b,1288,a)].
% 3.96/4.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D))). [resolve(1315,b,1289,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1290,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1291,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1292,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(1315,b,1293,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C != D. [resolve(1315,b,1294,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)). [resolve(1315,b,1295,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(c_Nat_OSuc,C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | B = D. [resolve(1315,b,1296,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(c_Nat_OSuc,C)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1315,b,1297,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)))). [resolve(1315,b,1298,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)))). [resolve(1315,b,1299,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)))). [resolve(1315,b,1300,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C))). [resolve(1315,b,1301,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)). [resolve(1315,b,1302,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C))). [resolve(1315,b,1305,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1315,b,1306,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1315,b,1307,a)].
% 3.96/4.23 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B))). [resolve(1315,b,1308,a)].
% 4.15/4.37 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | B = D. [resolve(1315,b,1309,a)].
% 4.15/4.37 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B))). [resolve(1315,b,1310,a)].
% 4.15/4.37 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)). [resolve(1315,b,1312,a)].
% 4.15/4.37 1316 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom). [assumption].
% 4.15/4.37 1317 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Rings_Oinverse__class_Oinverse(A,B))),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__add) # label(axiom). [clausify(162)].
% 4.15/4.37 1318 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),E) = B # label(fact_pdivmod__rel__def) # label(axiom). [clausify(400)].
% 4.15/4.37 1319 -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(400)].
% 4.15/4.37 1320 -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 | hBOOL(hAPP(hAPP(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(400)].
% 4.15/4.37 1321 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),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(400)].
% 4.15/4.37 1322 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | -hBOOL(hAPP(hAPP(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(400)].
% 4.15/4.37 1323 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),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(400)].
% 4.15/4.37 1324 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),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(400)].
% 4.15/4.37 1325 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | -hBOOL(hAPP(hAPP(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(400)].
% 4.15/4.37 1326 -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(410)].
% 4.15/4.37 1327 -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(411)].
% 4.15/4.37 1328 -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(412)].
% 4.15/4.37 1329 -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(412)].
% 4.15/4.37 1330 -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(443)].
% 4.15/4.37 1331 -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(443)].
% 4.15/4.37 1332 -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(443)].
% 4.15/4.37 1333 -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(444)].
% 4.15/4.37 1334 -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(444)].
% 4.15/4.37 1335 -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(444)].
% 4.15/4.37 1336 -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(445)].
% 4.15/4.37 1337 -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(446)].
% 4.15/4.37 1338 -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(447)].
% 4.15/4.37 1339 -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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),F),V6,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),V7)),E)) # label(fact_pdivmod__rel__mult) # label(axiom). [clausify(466)].
% 4.15/4.37 1340 -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(470)].
% 4.15/4.37 1341 -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(503)].
% 4.15/4.37 1342 -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(505)].
% 4.15/4.37 1343 -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(506)].
% 4.15/4.37 1344 -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(506)].
% 4.15/4.37 1345 -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(506)].
% 4.15/4.37 1346 -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(507)].
% 4.15/4.37 1347 -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(508)].
% 4.15/4.37 1348 -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(509)].
% 4.15/4.37 1349 -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(516)].
% 4.15/4.37 1350 -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(516)].
% 4.15/4.37 1351 -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(520)].
% 4.15/4.37 1352 -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(521)].
% 4.15/4.37 1353 -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(522)].
% 4.15/4.37 1354 -class_Fields_Ofield(A) | -hBOOL(hAPP(hAPP(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(523)].
% 4.15/4.37 1355 -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(524)].
% 4.15/4.37 1356 -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)) | hBOOL(hAPP(hAPP(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(528)].
% 4.15/4.37 1357 -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(568)].
% 4.15/4.37 1358 -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(568)].
% 4.15/4.37 1359 -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(568)].
% 4.15/4.37 1360 -class_Fields_Ofield(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = c_Polynomial_Opoly__gcd(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) # label(fact_poly__gcd__1__left) # label(axiom). [clausify(590)].
% 4.15/4.37 1361 -class_Fields_Ofield(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = c_Polynomial_Opoly__gcd(A,B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) # label(fact_poly__gcd__1__right) # label(axiom). [clausify(591)].
% 4.15/4.37 1362 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),B) # label(fact_field__inverse) # label(axiom). [clausify(614)].
% 4.15/4.37 1363 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,C),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C)) # label(fact_pdivmod__rel) # label(axiom). [clausify(912)].
% 4.15/4.37 1364 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) = c_Polynomial_Osmult(A,B,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,D)) # label(fact_div__smult__left) # label(axiom). [clausify(913)].
% 4.15/4.37 1365 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,C) = D # label(fact_div__poly__eq) # label(axiom). [clausify(914)].
% 4.15/4.37 1366 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,C),D) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)) # label(fact_poly__div__mult__right) # label(axiom). [clausify(916)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1316,a,1317,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) = A. [resolve(1316,a,1318,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = C. [resolve(1316,a,1319,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = D | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_RealDef_Oreal,D)),c_Polynomial_Odegree(tc_RealDef_Oreal,B))). [resolve(1316,a,1320,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != D. [resolve(1316,a,1321,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_RealDef_Oreal,D)),c_Polynomial_Odegree(tc_RealDef_Oreal,B))). [resolve(1316,a,1322,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B. [resolve(1316,a,1323,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != D. [resolve(1316,a,1324,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_RealDef_Oreal,D)),c_Polynomial_Odegree(tc_RealDef_Oreal,B))). [resolve(1316,a,1325,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,E,F) | C = E. [resolve(1316,a,1326,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,E,F) | D = F. [resolve(1316,a,1327,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B. [resolve(1316,a,1330,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = C. [resolve(1316,a,1331,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != C. [resolve(1316,a,1332,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B. [resolve(1316,a,1333,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,C) | C = A. [resolve(1316,a,1334,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B | C != A. [resolve(1316,a,1335,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1316,a,1336,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A). [resolve(1316,a,1337,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,c_Polynomial_Osmult(tc_RealDef_Oreal,E,A),B,c_Polynomial_Osmult(tc_RealDef_Oreal,E,C),c_Polynomial_Osmult(tc_RealDef_Oreal,E,D)). [resolve(1316,a,1338,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,C,E,F,V6) | c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),E),F,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),V6)),D)). [resolve(1316,a,1339,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,B,C,D,E) | c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,B,c_Polynomial_Osmult(tc_RealDef_Oreal,A,C),c_Polynomial_Osmult(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),D),E). [resolve(1316,a,1340,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Polynomial_Osmult(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_Polynomial_Ocoeff(tc_RealDef_Oreal,A),c_Polynomial_Odegree(tc_RealDef_Oreal,A))),A). [resolve(1316,a,1341,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1316,a,1342,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A. [resolve(1316,a,1343,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B. [resolve(1316,a,1344,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B. [resolve(1316,a,1345,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B),C) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,C)). [resolve(1316,a,1346,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,C)) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,C)). [resolve(1316,a,1347,a)].
% 4.15/4.37 Derived: c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,A). [resolve(1316,a,1348,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,A) = c_Polynomial_Osmult(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_Polynomial_Ocoeff(tc_RealDef_Oreal,B),c_Polynomial_Odegree(tc_RealDef_Oreal,B))),B). [resolve(1316,a,1349,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,A). [resolve(1316,a,1350,a)].
% 4.15/4.37 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Polynomial_Osmult(tc_RealDef_Oreal,A,B),C) = c_Polynomial_Osmult(tc_RealDef_Oreal,A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)). [resolve(1316,a,1351,a)].
% 4.15/4.37 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) = D. [resolve(1316,a,1352,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,c_Polynomial_Osmult(tc_RealDef_Oreal,A,C)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C). [resolve(1316,a,1353,a)].
% 4.15/4.37 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_RealDef_Oreal,A)),c_Polynomial_Odegree(tc_RealDef_Oreal,B))) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) = A. [resolve(1316,a,1354,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_RealDef_Oreal,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A))),c_Polynomial_Odegree(tc_RealDef_Oreal,A))). [resolve(1316,a,1356,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B)),c_Polynomial_Odegree(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B))). [resolve(1316,a,1357,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B)),c_Polynomial_Odegree(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,B))). [resolve(1316,a,1358,a)].
% 4.15/4.37 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,A)),c_Polynomial_Odegree(tc_RealDef_Oreal,c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,B,A))). [resolve(1316,a,1359,a)].
% 4.15/4.37 Derived: c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A). [resolve(1316,a,1360,a)].
% 4.15/4.37 Derived: c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opoly__gcd(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1316,a,1361,a)].
% 4.15/4.37 Derived: c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)). [resolve(1316,a,1363,a)].
% 4.15/4.38 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Polynomial_Osmult(tc_RealDef_Oreal,A,B),C) = c_Polynomial_Osmult(tc_RealDef_Oreal,A,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)). [resolve(1316,a,1364,a)].
% 4.15/4.38 Derived: -c_Polynomial_Opdivmod__rel(tc_RealDef_Oreal,A,B,C,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) = C. [resolve(1316,a,1365,a)].
% 4.15/4.38 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)). [resolve(1316,a,1366,a)].
% 4.15/4.38 1367 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption].
% 4.15/4.38 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A))),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1367,a,1317,a)].
% 4.15/4.38 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B)),D) = A. [resolve(1367,a,1318,a)].
% 4.15/4.38 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(1367,a,1319,a)].
% 4.15/4.38 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 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,D)),c_Polynomial_Odegree(tc_Complex_Ocomplex,B))). [resolve(1367,a,1320,a)].
% 4.15/4.38 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(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(1367,a,1321,a)].
% 4.15/4.38 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(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 | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,D)),c_Polynomial_Odegree(tc_Complex_Ocomplex,B))). [resolve(1367,a,1322,a)].
% 4.15/4.38 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(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(1367,a,1323,a)].
% 4.15/4.38 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(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(1367,a,1324,a)].
% 4.15/4.38 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(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 | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,D)),c_Polynomial_Odegree(tc_Complex_Ocomplex,B))). [resolve(1367,a,1325,a)].
% 4.15/4.38 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(1367,a,1326,a)].
% 4.15/4.38 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(1367,a,1327,a)].
% 4.15/4.38 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(1367,a,1330,a)].
% 4.15/4.38 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(1367,a,1331,a)].
% 4.15/4.38 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(1367,a,1332,a)].
% 4.15/4.38 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(1367,a,1333,a)].
% 4.15/4.38 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(1367,a,1334,a)].
% 4.15/4.38 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(1367,a,1335,a)].
% 4.15/4.38 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(1367,a,1336,a)].
% 4.15/4.38 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(1367,a,1337,a)].
% 4.15/4.38 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(1367,a,1338,a)].
% 4.15/4.38 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),E),F,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),V6)),D)). [resolve(1367,a,1339,a)].
% 4.15/4.38 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(1367,a,1340,a)].
% 4.15/4.38 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(1367,a,1341,a)].
% 4.15/4.38 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(1367,a,1342,a)].
% 4.15/4.38 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(1367,a,1343,a)].
% 4.15/4.38 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(1367,a,1344,a)].
% 4.15/4.38 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(1367,a,1345,a)].
% 4.15/4.38 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(1367,a,1346,a)].
% 4.15/4.38 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(1367,a,1347,a)].
% 4.15/4.38 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A). [resolve(1367,a,1348,a)].
% 4.15/4.38 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(1367,a,1349,a)].
% 4.15/4.38 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(1367,a,1350,a)].
% 4.15/4.38 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(1367,a,1351,a)].
% 4.15/4.38 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(1367,a,1352,a)].
% 4.15/4.38 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(1367,a,1353,a)].
% 4.15/4.38 Derived: -hBOOL(hAPP(hAPP(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(1367,a,1354,a)].
% 4.15/4.38 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)) | hBOOL(hAPP(hAPP(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(1367,a,1356,a)].
% 4.28/4.52 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(1367,a,1357,a)].
% 4.28/4.52 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(1367,a,1358,a)].
% 4.28/4.52 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(1367,a,1359,a)].
% 4.28/4.52 Derived: c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A). [resolve(1367,a,1360,a)].
% 4.28/4.52 Derived: c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1367,a,1361,a)].
% 4.28/4.52 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)). [resolve(1367,a,1363,a)].
% 4.28/4.52 Derived: c_Divides_Odiv__class_Odiv(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_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)). [resolve(1367,a,1364,a)].
% 4.28/4.52 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) = C. [resolve(1367,a,1365,a)].
% 4.28/4.52 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C)). [resolve(1367,a,1366,a)].
% 4.28/4.52 1368 -class_Fields_Ofield(A) | class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [clausify(1009)].
% 4.28/4.52 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1368,a,1316,a)].
% 4.28/4.52 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1368,a,1367,a)].
% 4.28/4.52 1369 -class_Fields_Ofield(A) | class_Divides_Oring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom). [clausify(1020)].
% 4.28/4.52 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1369,a,1316,a)].
% 4.28/4.52 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1369,a,1367,a)].
% 4.28/4.52 1370 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 4.28/4.52 1371 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__cases) # label(axiom). [clausify(164)].
% 4.28/4.52 1372 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neqE) # label(axiom). [clausify(179)].
% 4.28/4.52 1373 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | C = B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(180)].
% 4.28/4.52 1374 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | C != B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(180)].
% 4.28/4.52 1375 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__less__linear) # label(axiom). [clausify(181)].
% 4.28/4.52 1376 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | B = C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(182)].
% 4.28/4.52 1377 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(182)].
% 4.28/4.52 1378 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B != C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(182)].
% 4.28/4.52 1379 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(183)].
% 4.28/4.52 1380 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(183)].
% 4.28/4.52 1381 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(183)].
% 4.28/4.52 1382 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__le__cases) # label(axiom). [clausify(278)].
% 4.28/4.52 1383 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__linear) # label(axiom). [clausify(292)].
% 4.28/4.52 1384 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B = C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(309)].
% 4.28/4.52 1385 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B != C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(309)].
% 4.28/4.52 1386 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_leD) # label(axiom). [clausify(311)].
% 4.28/4.52 1387 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | B = C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(314)].
% 4.28/4.52 1388 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | B != C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(314)].
% 4.28/4.52 1389 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__leE) # label(axiom). [clausify(315)].
% 4.28/4.52 1390 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_leI) # label(axiom). [clausify(316)].
% 4.28/4.52 1391 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(320)].
% 4.28/4.52 1392 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(321)].
% 4.28/4.53 1393 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(321)].
% 4.28/4.53 1394 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(322)].
% 4.28/4.53 1395 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(322)].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | B = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(1370,a,1371,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)) | B != A. [resolve(1370,a,1374,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(1370,a,1377,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | A != B. [resolve(1370,a,1378,a)].
% 4.28/4.53 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(1370,a,1381,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1370,a,1382,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | A = B. [resolve(1370,a,1384,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(1370,a,1386,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | A != B. [resolve(1370,a,1388,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(1370,a,1389,a)].
% 4.28/4.53 1396 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | B = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(1396,a,1371,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)) | B != A. [resolve(1396,a,1374,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(1396,a,1377,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | A != B. [resolve(1396,a,1378,a)].
% 4.28/4.53 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(1396,a,1381,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A)). [resolve(1396,a,1382,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | A = B. [resolve(1396,a,1384,a)].
% 4.28/4.53 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(1396,a,1386,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | A != B. [resolve(1396,a,1388,a)].
% 4.28/4.53 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(1396,a,1389,a)].
% 4.28/4.54 1397 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 4.28/4.54 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | B = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1397,a,1371,a)].
% 4.28/4.54 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)) | B != A. [resolve(1397,a,1374,a)].
% 4.28/4.54 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1397,a,1377,a)].
% 4.28/4.54 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | A != B. [resolve(1397,a,1378,a)].
% 4.28/4.54 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1397,a,1381,a)].
% 4.28/4.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1397,a,1382,a)].
% 4.28/4.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | A = B. [resolve(1397,a,1384,a)].
% 4.28/4.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1397,a,1386,a)].
% 4.28/4.54 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | A != B. [resolve(1397,a,1388,a)].
% 4.28/4.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),A)). [resolve(1397,a,1389,a)].
% 4.28/4.54 1398 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1015)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | C = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)). [resolve(1398,b,1371,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)) | C != B. [resolve(1398,b,1374,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)). [resolve(1398,b,1377,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | B != C. [resolve(1398,b,1378,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)). [resolve(1398,b,1381,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),B)). [resolve(1398,b,1382,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | B = C. [resolve(1398,b,1384,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)). [resolve(1398,b,1386,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | B != C. [resolve(1398,b,1388,a)].
% 4.28/4.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),B)). [resolve(1398,b,1389,a)].
% 4.44/4.67 1399 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.44/4.67 1400 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__neg) # label(axiom). [clausify(203)].
% 4.44/4.67 1401 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__pos) # label(axiom). [clausify(204)].
% 4.44/4.67 1402 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(352)].
% 4.44/4.67 1403 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B))) # label(fact_add__increasing2) # label(axiom). [clausify(353)].
% 4.44/4.67 1404 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__increasing) # label(axiom). [clausify(354)].
% 4.44/4.67 1405 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(355)].
% 4.44/4.67 1406 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(355)].
% 4.44/4.67 1407 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(355)].
% 4.44/4.67 1408 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(356)].
% 4.44/4.67 1409 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__neg) # label(axiom). [clausify(383)].
% 4.44/4.67 1410 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__nonpos) # label(axiom). [clausify(384)].
% 4.44/4.67 1411 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing2) # label(axiom). [clausify(385)].
% 4.44/4.67 1412 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing) # label(axiom). [clausify(386)].
% 4.44/4.67 1413 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__pos) # label(axiom). [clausify(387)].
% 4.44/4.67 1414 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__nonneg) # label(axiom). [clausify(388)].
% 4.44/4.67 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1399,a,1400,a)].
% 4.44/4.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1399,a,1402,a)].
% 4.44/4.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A))). [resolve(1399,a,1403,a)].
% 4.44/4.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1399,a,1404,a)].
% 4.44/4.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1399,a,1405,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1399,a,1406,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1399,a,1407,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1399,a,1409,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1399,a,1410,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1399,a,1411,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1399,a,1412,a)].
% 4.44/4.68 1415 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1415,a,1400,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1415,a,1402,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A))). [resolve(1415,a,1403,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1415,a,1404,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1415,a,1405,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1415,a,1406,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1415,a,1407,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1415,a,1409,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1415,a,1410,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1415,a,1411,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1415,a,1412,a)].
% 4.44/4.68 1416 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.44/4.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1416,a,1400,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1416,a,1402,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),A))). [resolve(1416,a,1403,a)].
% 4.44/4.68 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1416,a,1404,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1416,a,1405,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1416,a,1406,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1416,a,1407,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1416,a,1409,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1416,a,1410,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1416,a,1411,a)].
% 4.44/4.69 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1416,a,1412,a)].
% 4.44/4.69 1417 -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(986)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1417,b,1400,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1417,b,1402,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),B))). [resolve(1417,b,1403,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1417,b,1404,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1417,b,1405,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1417,b,1406,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1417,b,1407,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1417,b,1409,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1417,b,1410,a)].
% 4.44/4.69 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1417,b,1411,a)].
% 4.56/4.83 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1417,b,1412,a)].
% 4.56/4.83 1418 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 4.56/4.83 1419 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(205)].
% 4.56/4.83 1420 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(205)].
% 4.56/4.83 1421 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(207)].
% 4.56/4.83 1422 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(207)].
% 4.56/4.83 1423 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(251)].
% 4.56/4.83 1424 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(251)].
% 4.56/4.83 1425 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(254)].
% 4.56/4.83 1426 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(254)].
% 4.56/4.83 1427 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(357)].
% 4.56/4.83 1428 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(357)].
% 4.56/4.83 1429 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(358)].
% 4.56/4.84 1430 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(358)].
% 4.56/4.84 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1419,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1418,a,1421,a)].
% 4.56/4.84 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1418,a,1423,a)].
% 4.56/4.84 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1418,a,1424,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1427,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1418,a,1429,a)].
% 4.56/4.84 1431 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 4.56/4.84 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1431,a,1419,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1431,a,1421,a)].
% 4.56/4.84 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1431,a,1423,a)].
% 4.56/4.84 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1431,a,1424,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1431,a,1427,a)].
% 4.56/4.84 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1431,a,1429,a)].
% 4.56/4.84 1432 -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(987)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1432,b,1419,a)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1432,b,1421,a)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1432,b,1423,a)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1432,b,1424,a)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1432,b,1427,a)].
% 4.75/4.98 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1432,b,1429,a)].
% 4.75/4.98 1433 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.75/4.98 1434 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(209)].
% 4.75/4.98 1435 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(255)].
% 4.75/4.98 1436 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(255)].
% 4.75/4.98 1437 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(256)].
% 4.75/4.98 1438 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(256)].
% 4.75/4.98 1439 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(260)].
% 4.75/4.98 1440 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(324)].
% 4.75/4.98 1441 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(325)].
% 4.75/4.98 1442 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(329)].
% 4.75/4.98 1443 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(329)].
% 4.75/4.98 1444 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(330)].
% 4.75/4.98 1445 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(330)].
% 4.75/4.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(1433,a,1434,a)].
% 4.75/4.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(1433,a,1435,a)].
% 4.75/4.98 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(1433,a,1436,a)].
% 4.75/4.98 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(1433,a,1438,a)].
% 4.75/4.98 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1433,a,1440,a)].
% 4.75/4.98 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1433,a,1441,a)].
% 4.75/4.98 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1433,a,1443,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1433,a,1445,a)].
% 4.75/4.99 1446 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].
% 4.75/4.99 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1446,a,1434,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(1446,a,1435,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(1446,a,1436,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(1446,a,1438,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1446,a,1440,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1446,a,1441,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1446,a,1443,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1446,a,1445,a)].
% 4.75/4.99 1447 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.75/4.99 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)). [resolve(1447,a,1434,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)). [resolve(1447,a,1435,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),C)). [resolve(1447,a,1436,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),B),C)). [resolve(1447,a,1438,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1447,a,1440,a)].
% 4.75/4.99 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1447,a,1441,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1447,a,1443,a)].
% 4.75/4.99 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1447,a,1445,a)].
% 4.75/4.99 1448 -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(981)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)). [resolve(1448,b,1434,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)). [resolve(1448,b,1435,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),D)). [resolve(1448,b,1436,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),C),D)). [resolve(1448,b,1438,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1448,b,1440,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1448,b,1441,a)].
% 4.75/4.99 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1448,b,1443,a)].
% 5.03/5.28 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1448,b,1445,a)].
% 5.03/5.28 1449 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.03/5.28 1450 -class_Groups_Oab__semigroup__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(242)].
% 5.03/5.28 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(1449,a,1450,a)].
% 5.03/5.28 1451 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.03/5.28 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1451,a,1450,a)].
% 5.03/5.28 1452 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.03/5.28 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1452,a,1450,a)].
% 5.03/5.28 1453 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.03/5.28 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(1453,a,1450,a)].
% 5.03/5.28 1454 -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(999)].
% 5.03/5.28 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(1454,b,1450,a)].
% 5.03/5.28 1455 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.03/5.28 1456 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(243)].
% 5.03/5.28 1457 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(245)].
% 5.03/5.28 1458 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__cancel) # label(axiom). [clausify(246)].
% 5.03/5.28 1459 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B != D # label(fact_add__right__cancel) # label(axiom). [clausify(246)].
% 5.03/5.28 1460 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(247)].
% 5.03/5.29 1461 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(247)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(1455,a,1456,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(1455,a,1457,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A != C. [resolve(1455,a,1459,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B != C. [resolve(1455,a,1461,a)].
% 5.03/5.29 1462 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A = C. [resolve(1462,a,1456,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B = C. [resolve(1462,a,1457,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A != C. [resolve(1462,a,1459,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B != C. [resolve(1462,a,1461,a)].
% 5.03/5.29 1463 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C. [resolve(1463,a,1456,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(1463,a,1457,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A != C. [resolve(1463,a,1459,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B != C. [resolve(1463,a,1461,a)].
% 5.03/5.29 1464 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(1464,a,1456,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(1464,a,1457,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A != C. [resolve(1464,a,1459,a)].
% 5.03/5.29 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B != C. [resolve(1464,a,1461,a)].
% 5.03/5.29 1465 -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(996)].
% 5.03/5.29 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C) | B = D. [resolve(1465,b,1456,a)].
% 5.03/5.29 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(1465,b,1457,a)].
% 5.34/5.58 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C) | B != D. [resolve(1465,b,1459,a)].
% 5.34/5.58 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C != D. [resolve(1465,b,1461,a)].
% 5.34/5.58 1466 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 1467 -class_Groups_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(244)].
% 5.34/5.58 1468 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 1469 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 1470 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 1471 -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(988)].
% 5.34/5.58 1472 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 1473 -class_Groups_Oab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(248)].
% 5.34/5.58 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(1472,a,1473,a)].
% 5.34/5.58 1474 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1474,a,1473,a)].
% 5.34/5.58 1475 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(1475,a,1473,a)].
% 5.34/5.58 1476 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.34/5.58 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(1476,a,1473,a)].
% 5.34/5.58 1477 -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(1001)].
% 5.34/5.58 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D)). [resolve(1477,b,1473,a)].
% 5.65/5.87 1478 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.65/5.87 1479 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0__left) # label(axiom). [clausify(249)].
% 5.65/5.87 1480 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(252)].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(1478,a,1479,a)].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1478,a,1480,a)].
% 5.65/5.87 1481 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(1481,a,1479,a)].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1481,a,1480,a)].
% 5.65/5.87 1482 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(1482,a,1479,a)].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1482,a,1480,a)].
% 5.65/5.87 1483 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(1483,a,1479,a)].
% 5.65/5.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1483,a,1480,a)].
% 5.65/5.87 1484 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1018)].
% 5.65/5.87 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = B. [resolve(1484,b,1479,a)].
% 5.65/5.87 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1484,b,1480,a)].
% 5.65/5.87 1485 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.65/5.87 1486 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))) # label(fact_add__strict__right__mono) # label(axiom). [clausify(257)].
% 5.65/5.87 1487 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) # label(fact_add__strict__left__mono) # label(axiom). [clausify(258)].
% 5.65/5.87 1488 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__strict__mono) # label(axiom). [clausify(259)].
% 5.65/5.87 1489 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__le__less__mono) # label(axiom). [clausify(359)].
% 5.65/5.88 1490 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__less__le__mono) # label(axiom). [clausify(360)].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(1485,a,1488,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(1485,a,1489,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(1485,a,1490,a)].
% 5.65/5.88 1491 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(1491,a,1488,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(1491,a,1489,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(1491,a,1490,a)].
% 5.65/5.88 1492 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1492,a,1488,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1492,a,1489,a)].
% 5.65/5.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1492,a,1490,a)].
% 5.81/6.02 1493 -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(980)].
% 5.81/6.02 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E))). [resolve(1493,b,1488,a)].
% 5.81/6.02 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E))). [resolve(1493,b,1489,a)].
% 5.81/6.02 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E))). [resolve(1493,b,1490,a)].
% 5.81/6.02 1494 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 5.81/6.02 1495 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))) # label(fact_norm__triangle__ineq) # label(axiom). [clausify(270)].
% 5.81/6.02 1496 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) # label(fact_norm__ge__zero) # label(axiom). [clausify(276)].
% 5.81/6.02 1497 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__le__zero__iff) # label(axiom). [clausify(277)].
% 5.81/6.02 1498 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__le__zero__iff) # label(axiom). [clausify(277)].
% 5.81/6.02 1499 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_norm__not__less__zero) # label(axiom). [clausify(295)].
% 5.81/6.02 1500 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__eq__zero) # label(axiom). [clausify(296)].
% 5.81/6.02 1501 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__eq__zero) # label(axiom). [clausify(296)].
% 5.81/6.02 1502 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__zero) # label(axiom). [clausify(297)].
% 5.81/6.02 1503 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(298)].
% 5.81/6.02 1504 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(298)].
% 5.81/6.02 1505 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,D)),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),E))) # label(fact_norm__add__less) # label(axiom). [clausify(301)].
% 5.81/6.02 1506 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D)))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_norm__ratiotest__lemma) # label(axiom). [clausify(399)].
% 5.81/6.02 1507 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(B,A))) # label(fact_Bseq__def) # label(axiom). [clausify(518)].
% 5.81/6.02 1508 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f24(B,A))) # label(fact_Bseq__def) # label(axiom). [clausify(518)].
% 5.81/6.02 1509 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f25(B,A,C)))),C)) # label(fact_Bseq__def) # label(axiom). [clausify(518)].
% 5.81/6.02 1510 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_SEQ_OBseq(A,hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))) # label(fact_Bseq__ignore__initial__segment) # label(axiom). [clausify(525)].
% 5.81/6.02 1511 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))) | c_SEQ_OBseq(A,B) # label(fact_Bseq__offset) # label(axiom). [clausify(526)].
% 5.81/6.02 1512 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f31(C,B,A)))),B)) | c_SEQ_OBseq(A,C) # label(fact_BseqI) # label(axiom). [clausify(566)].
% 5.81/6.02 1513 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f32(B,A))) # label(fact_BseqD) # label(axiom). [clausify(567)].
% 5.81/6.02 1514 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f32(B,A))) # label(fact_BseqD) # label(axiom). [clausify(567)].
% 5.81/6.02 1515 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),f33(C,D,B,A))) | c_SEQ_OBseq(A,D) # label(fact_BseqI2_H) # label(axiom). [clausify(569)].
% 5.81/6.02 1516 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f33(C,B,D,A)))),C)) | c_SEQ_OBseq(A,B) # label(fact_BseqI2_H) # label(axiom). [clausify(569)].
% 5.81/6.02 1517 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f39(B,A))))) # label(fact_Bseq__iff) # label(axiom). [clausify(662)].
% 5.81/6.02 1518 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f40(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))) # label(fact_Bseq__iff) # label(axiom). [clausify(662)].
% 5.81/6.02 1519 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f41(B,A))))) # label(fact_Bseq__iff1a) # label(axiom). [clausify(663)].
% 5.81/6.02 1520 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(B,f42(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))) # label(fact_Bseq__iff1a) # label(axiom). [clausify(663)].
% 5.81/6.02 1521 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f43(C,A,B)))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f44(C,A))))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(666)].
% 5.81/6.02 1522 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f45(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f46(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(666)].
% 5.81/6.02 1523 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f45(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f46(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,D)))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(666)].
% 5.81/6.02 1524 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f47(C,A,B)))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f48(C,A))))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(667)].
% 5.81/6.02 1525 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f49(B,A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(B,f50(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(667)].
% 5.81/6.02 1526 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f49(B,A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(B,f50(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,D)))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(667)].
% 5.81/6.02 1527 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)) = c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B)) # label(fact_norm__minus__commute) # label(axiom). [clausify(935)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))). [resolve(1494,a,1495,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))). [resolve(1494,a,1496,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1494,a,1497,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1494,a,1498,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1494,a,1499,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1494,a,1500,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1494,a,1501,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1494,a,1502,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1494,a,1503,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1494,a,1504,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1494,a,1505,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1494,a,1506,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(A,tc_RealDef_Oreal))). [resolve(1494,a,1507,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f24(A,tc_RealDef_Oreal))). [resolve(1494,a,1508,a)].
% 5.81/6.03 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f25(A,tc_RealDef_Oreal,B)))),B)). [resolve(1494,a,1509,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))). [resolve(1494,a,1510,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1494,a,1511,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f31(B,A,tc_RealDef_Oreal)))),A)) | c_SEQ_OBseq(tc_RealDef_Oreal,B). [resolve(1494,a,1512,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f32(A,tc_RealDef_Oreal))). [resolve(1494,a,1513,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f32(A,tc_RealDef_Oreal))). [resolve(1494,a,1514,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),f33(B,C,A,tc_RealDef_Oreal))) | c_SEQ_OBseq(tc_RealDef_Oreal,C). [resolve(1494,a,1515,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f33(B,A,C,tc_RealDef_Oreal)))),B)) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1494,a,1516,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f39(A,tc_RealDef_Oreal))))). [resolve(1494,a,1517,a)].
% 5.81/6.03 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f40(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1494,a,1518,a)].
% 5.81/6.03 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f41(A,tc_RealDef_Oreal))))). [resolve(1494,a,1519,a)].
% 5.81/6.03 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f42(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1494,a,1520,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f43(B,tc_RealDef_Oreal,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f44(B,tc_RealDef_Oreal))))). [resolve(1494,a,1521,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f45(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f46(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1494,a,1522,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f45(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f46(A,tc_RealDef_Oreal,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))). [resolve(1494,a,1523,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f47(B,tc_RealDef_Oreal,A)))),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f48(B,tc_RealDef_Oreal))))). [resolve(1494,a,1524,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f49(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f50(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1494,a,1525,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f49(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f50(A,tc_RealDef_Oreal,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))). [resolve(1494,a,1526,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A)). [resolve(1494,a,1527,a)].
% 5.81/6.03 1528 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))). [resolve(1528,a,1495,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))). [resolve(1528,a,1496,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1528,a,1497,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1528,a,1498,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1528,a,1499,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1528,a,1500,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1528,a,1501,a)].
% 5.81/6.03 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1528,a,1502,a)].
% 5.81/6.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1528,a,1503,a)].
% 5.81/6.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1528,a,1504,a)].
% 5.81/6.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1528,a,1505,a)].
% 5.81/6.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1528,a,1506,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(A,tc_Complex_Ocomplex))). [resolve(1528,a,1507,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f24(A,tc_Complex_Ocomplex))). [resolve(1528,a,1508,a)].
% 5.81/6.04 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f25(A,tc_Complex_Ocomplex,B)))),B)). [resolve(1528,a,1509,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_SEQ_OBseq(tc_Complex_Ocomplex,hAPP(c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))). [resolve(1528,a,1510,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,hAPP(c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1528,a,1511,a)].
% 5.81/6.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f31(B,A,tc_Complex_Ocomplex)))),A)) | c_SEQ_OBseq(tc_Complex_Ocomplex,B). [resolve(1528,a,1512,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f32(A,tc_Complex_Ocomplex))). [resolve(1528,a,1513,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f32(A,tc_Complex_Ocomplex))). [resolve(1528,a,1514,a)].
% 5.81/6.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),f33(B,C,A,tc_Complex_Ocomplex))) | c_SEQ_OBseq(tc_Complex_Ocomplex,C). [resolve(1528,a,1515,a)].
% 5.81/6.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f33(B,A,C,tc_Complex_Ocomplex)))),B)) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1528,a,1516,a)].
% 5.81/6.04 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f39(A,tc_Complex_Ocomplex))))). [resolve(1528,a,1517,a)].
% 5.81/6.04 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f40(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1528,a,1518,a)].
% 5.95/6.19 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f41(A,tc_Complex_Ocomplex))))). [resolve(1528,a,1519,a)].
% 5.95/6.19 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f42(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1528,a,1520,a)].
% 5.95/6.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f43(B,tc_Complex_Ocomplex,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f44(B,tc_Complex_Ocomplex))))). [resolve(1528,a,1521,a)].
% 5.95/6.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f45(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f46(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1528,a,1522,a)].
% 5.95/6.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f45(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f46(A,tc_Complex_Ocomplex,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))). [resolve(1528,a,1523,a)].
% 5.95/6.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f47(B,tc_Complex_Ocomplex,A)))),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,f48(B,tc_Complex_Ocomplex))))). [resolve(1528,a,1524,a)].
% 5.95/6.19 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f49(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f50(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)))). [resolve(1528,a,1525,a)].
% 5.95/6.19 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f49(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f50(A,tc_Complex_Ocomplex,C)))),c_RealDef_Oreal(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)))). [resolve(1528,a,1526,a)].
% 5.95/6.19 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A)). [resolve(1528,a,1527,a)].
% 5.95/6.19 1529 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.95/6.19 1530 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__mono) # label(axiom). [clausify(326)].
% 5.95/6.19 1531 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) # label(fact_add__left__mono) # label(axiom). [clausify(327)].
% 6.11/6.33 1532 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))) # label(fact_add__right__mono) # label(axiom). [clausify(328)].
% 6.11/6.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(1529,a,1530,a)].
% 6.11/6.33 1533 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 6.11/6.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(1533,a,1530,a)].
% 6.11/6.33 1534 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 6.11/6.33 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(1534,a,1530,a)].
% 6.11/6.33 1535 -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(985)].
% 6.11/6.33 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E))). [resolve(1535,b,1530,a)].
% 6.11/6.33 1536 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.11/6.33 1537 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(338)].
% 6.11/6.33 1538 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(339)].
% 6.11/6.33 1539 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(340)].
% 6.11/6.33 1540 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(341)].
% 6.23/6.48 1541 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_split__mult__neg__le) # label(axiom). [clausify(351)].
% 6.23/6.48 1542 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_split__mult__neg__le) # label(axiom). [clausify(351)].
% 6.23/6.48 1543 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(1543,a,1537,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1543,a,1538,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1543,a,1539,a)].
% 6.23/6.48 1544 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.23/6.48 1545 -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(990)].
% 6.23/6.48 1546 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 6.23/6.48 1547 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(342)].
% 6.23/6.48 1548 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(346)].
% 6.23/6.48 1549 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(347)].
% 6.23/6.48 1550 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_split__mult__pos__le) # label(axiom). [clausify(350)].
% 6.23/6.48 1551 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_split__mult__pos__le) # label(axiom). [clausify(350)].
% 6.23/6.48 1552 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(917)].
% 6.23/6.48 1553 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(917)].
% 6.23/6.48 1554 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(918)].
% 6.23/6.48 1555 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(918)].
% 6.23/6.48 1556 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(919)].
% 6.23/6.48 1557 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(919)].
% 6.23/6.48 1558 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(920)].
% 6.23/6.48 1559 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(920)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(1546,a,1548,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(1546,a,1549,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1546,a,1552,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1546,a,1553,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1546,a,1554,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1546,a,1555,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1546,a,1556,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1546,a,1557,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1546,a,1558,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1546,a,1559,a)].
% 6.23/6.48 1560 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))). [resolve(1560,a,1548,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))). [resolve(1560,a,1549,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C)),E)). [resolve(1560,a,1552,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C)),E)). [resolve(1560,a,1553,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E))). [resolve(1560,a,1554,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E))). [resolve(1560,a,1555,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C)),E)). [resolve(1560,a,1556,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C)),E)). [resolve(1560,a,1557,a)].
% 6.23/6.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E))). [resolve(1560,a,1558,a)].
% 6.23/6.48 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E))). [resolve(1560,a,1559,a)].
% 6.28/6.49 1561 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1013)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))). [resolve(1561,b,1548,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B))). [resolve(1561,b,1549,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1561,b,1552,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1561,b,1553,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1561,b,1554,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1561,b,1555,a)].
% 6.28/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1561,b,1556,a)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1561,b,1557,a)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1561,b,1558,a)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1561,b,1559,a)].
% 6.41/6.63 1562 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.41/6.63 1563 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) # label(fact_mult__right__mono) # label(axiom). [clausify(343)].
% 6.41/6.63 1564 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_mult__left__mono) # label(axiom). [clausify(344)].
% 6.41/6.63 1565 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__mono_H) # label(axiom). [clausify(348)].
% 6.41/6.63 1566 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__mono) # label(axiom). [clausify(349)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(1562,a,1563,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(1562,a,1564,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1562,a,1565,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(1562,a,1566,a)].
% 6.41/6.63 1567 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))). [resolve(1567,a,1563,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))). [resolve(1567,a,1564,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1567,a,1565,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(1567,a,1566,a)].
% 6.41/6.63 1568 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C))). [resolve(1568,a,1563,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B))). [resolve(1568,a,1564,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1568,a,1565,a)].
% 6.41/6.63 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D))). [resolve(1568,a,1566,a)].
% 6.41/6.63 1569 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(1002)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))). [resolve(1569,b,1563,a)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C))). [resolve(1569,b,1564,a)].
% 6.41/6.63 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1569,b,1565,a)].
% 6.80/7.03 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E))). [resolve(1569,b,1566,a)].
% 6.80/7.03 1570 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.80/7.03 1571 -class_Rings_Oordered__comm__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(345)].
% 6.80/7.03 1572 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.80/7.03 1573 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.80/7.03 1574 -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(993)].
% 6.80/7.03 1575 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.80/7.03 1576 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__left__less__imp__less) # label(axiom). [clausify(374)].
% 6.80/7.03 1577 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__right__less__imp__less) # label(axiom). [clausify(376)].
% 6.80/7.03 1578 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.80/7.03 1579 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.80/7.03 1580 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(997)].
% 6.80/7.03 1581 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))) # label(fact_decseq__def) # label(axiom). [clausify(502)].
% 6.80/7.03 1582 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))) # label(fact_decseq__def) # label(axiom). [clausify(502)].
% 6.80/7.03 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))). [resolve(1581,b,1582,b)].
% 7.10/7.33 1583 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))) # label(fact_decseq__def) # label(axiom). [clausify(502)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))). [resolve(1583,b,1582,b)].
% 7.10/7.33 1584 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_decseq__imp__monoseq) # label(axiom). [clausify(823)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))). [resolve(1584,b,1581,b)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))). [resolve(1584,b,1583,b)].
% 7.10/7.33 1585 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))) # label(fact_incseq__def) # label(axiom). [clausify(519)].
% 7.10/7.33 1586 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) # label(fact_incseq__def) # label(axiom). [clausify(519)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))). [resolve(1585,b,1586,b)].
% 7.10/7.33 1587 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))) # label(fact_incseq__def) # label(axiom). [clausify(519)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))). [resolve(1587,b,1586,b)].
% 7.10/7.33 1588 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_incseq__imp__monoseq) # label(axiom). [clausify(822)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))). [resolve(1588,b,1585,b)].
% 7.10/7.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))). [resolve(1588,b,1587,b)].
% 7.10/7.33 1589 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 7.10/7.33 1590 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom). [clausify(529)].
% 7.10/7.33 1591 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom). [clausify(530)].
% 7.10/7.33 1592 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom). [clausify(531)].
% 7.10/7.33 1593 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom). [clausify(532)].
% 7.10/7.33 1594 -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(547)].
% 7.10/7.33 1595 -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(548)].
% 7.10/7.33 1596 -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(549)].
% 7.10/7.33 1597 -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(550)].
% 7.10/7.33 1598 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),F),C) # label(fact_mod__mult__cong) # label(axiom). [clausify(551)].
% 7.10/7.33 1599 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_zmod__simps_I4_J) # label(axiom). [clausify(552)].
% 7.10/7.33 1600 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,D)),C) # label(fact_mod__mult__mult2) # label(axiom). [clausify(553)].
% 7.10/7.33 1601 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_mod__mult__mult1) # label(axiom). [clausify(554)].
% 7.10/7.33 1602 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__eq) # label(axiom). [clausify(555)].
% 7.10/7.33 1603 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__left__eq) # label(axiom). [clausify(556)].
% 7.10/7.33 1604 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) # label(fact_mod__mult__right__eq) # label(axiom). [clausify(557)].
% 7.10/7.33 1605 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),F),C) # label(fact_mod__add__cong) # label(axiom). [clausify(558)].
% 7.10/7.33 1606 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_zmod__simps_I1_J) # label(axiom). [clausify(559)].
% 7.10/7.33 1607 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_zmod__simps_I2_J) # label(axiom). [clausify(560)].
% 7.10/7.33 1608 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__eq) # label(axiom). [clausify(561)].
% 7.10/7.33 1609 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__left__eq) # label(axiom). [clausify(562)].
% 7.10/7.33 1610 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_mod__add__right__eq) # label(axiom). [clausify(563)].
% 7.10/7.33 1611 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom). [clausify(564)].
% 7.10/7.33 1612 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom). [clausify(565)].
% 7.10/7.33 1613 -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(601)].
% 7.10/7.33 1614 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1) # label(axiom). [clausify(848)].
% 7.10/7.33 1615 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult2) # label(axiom). [clausify(849)].
% 7.10/7.33 1616 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = C # label(fact_div__mult__self1__is__id) # label(axiom). [clausify(850)].
% 7.10/7.33 1617 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),B) = C # label(fact_div__mult__self2__is__id) # label(axiom). [clausify(851)].
% 7.10/7.33 1618 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(852)].
% 7.10/7.33 1619 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(852)].
% 7.10/7.33 1620 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_div__self) # label(axiom). [clausify(853)].
% 7.10/7.33 1621 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_div__by__1) # label(axiom). [clausify(855)].
% 7.10/7.33 1622 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__div__trivial) # label(axiom). [clausify(856)].
% 7.10/7.33 1623 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__0) # label(axiom). [clausify(862)].
% 7.10/7.33 1624 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__by__0) # label(axiom). [clausify(863)].
% 7.10/7.33 1625 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self1) # label(axiom). [clausify(886)].
% 7.10/7.33 1626 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self2) # label(axiom). [clausify(887)].
% 7.10/7.33 1627 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self2) # label(axiom). [clausify(888)].
% 7.10/7.33 1628 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self1) # label(axiom). [clausify(889)].
% 7.10/7.33 1629 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)) = B # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(890)].
% 7.10/7.33 1630 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B))),c_Divides_Odiv__class_Omod(A,C,B)) = C # label(fact_mod__div__equality2) # label(axiom). [clausify(891)].
% 7.10/7.33 1631 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)),c_Divides_Odiv__class_Omod(A,B,C)) = B # label(fact_mod__div__equality) # label(axiom). [clausify(892)].
% 7.10/7.33 1632 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B))),c_Divides_Odiv__class_Omod(A,C,B))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D) # label(fact_div__mod__equality2) # label(axiom). [clausify(893)].
% 7.10/7.33 1633 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)),c_Divides_Odiv__class_Omod(A,B,C))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) # label(fact_div__mod__equality) # label(axiom). [clausify(894)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C). [resolve(1589,a,1590,a)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(1589,a,1591,a)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1592,a)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1593,a)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(1589,a,1594,a)].
% 7.10/7.33 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1595,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1589,a,1596,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1597,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),E),B). [resolve(1589,a,1598,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B). [resolve(1589,a,1599,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C)),B). [resolve(1589,a,1600,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)). [resolve(1589,a,1601,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B). [resolve(1589,a,1602,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C). [resolve(1589,a,1604,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),E),B). [resolve(1589,a,1605,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(1589,a,1606,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),C). [resolve(1589,a,1607,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(1589,a,1608,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A). [resolve(1589,a,1611,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(1589,a,1612,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1613,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C). [resolve(1589,a,1614,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C). [resolve(1589,a,1615,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = B. [resolve(1589,a,1616,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),A) = B. [resolve(1589,a,1617,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1618,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1589,a,1620,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1589,a,1621,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1622,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1623,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1589,a,1624,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1589,a,1625,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1589,a,1626,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1589,a,1627,a)].
% 7.10/7.34 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1589,a,1628,a)].
% 7.10/7.34 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)) = A. [resolve(1589,a,1629,a)].
% 7.10/7.34 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)) = B. [resolve(1589,a,1630,a)].
% 7.10/7.34 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)) = A. [resolve(1589,a,1631,a)].
% 7.10/7.34 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(1589,a,1632,a)].
% 7.10/7.34 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(1589,a,1633,a)].
% 7.10/7.34 1634 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C). [resolve(1634,a,1590,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1634,a,1591,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1592,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1593,a)].
% 7.10/7.34 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(1634,a,1594,a)].
% 7.10/7.34 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(1634,a,1595,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1634,a,1596,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1597,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),E),B). [resolve(1634,a,1598,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B). [resolve(1634,a,1599,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C)),B). [resolve(1634,a,1600,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)). [resolve(1634,a,1601,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B). [resolve(1634,a,1602,a)].
% 7.10/7.34 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),C). [resolve(1634,a,1604,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E),B). [resolve(1634,a,1605,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(1634,a,1606,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C). [resolve(1634,a,1607,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(1634,a,1608,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A). [resolve(1634,a,1611,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1634,a,1612,a)].
% 7.15/7.35 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(1634,a,1613,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C). [resolve(1634,a,1614,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C). [resolve(1634,a,1615,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = B. [resolve(1634,a,1616,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),A) = B. [resolve(1634,a,1617,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1618,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,A) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1634,a,1620,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1634,a,1621,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1622,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1623,a)].
% 7.15/7.35 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1634,a,1624,a)].
% 7.15/7.35 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1634,a,1625,a)].
% 7.16/7.40 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1634,a,1626,a)].
% 7.16/7.40 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1634,a,1627,a)].
% 7.16/7.40 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1634,a,1628,a)].
% 7.16/7.40 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)) = A. [resolve(1634,a,1629,a)].
% 7.16/7.40 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A)) = B. [resolve(1634,a,1630,a)].
% 7.16/7.40 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)) = A. [resolve(1634,a,1631,a)].
% 7.16/7.40 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C). [resolve(1634,a,1632,a)].
% 7.16/7.40 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C). [resolve(1634,a,1633,a)].
% 7.16/7.40 1635 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1368,a,1316,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C). [resolve(1635,a,1590,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B). [resolve(1635,a,1591,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1592,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1593,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B). [resolve(1635,a,1594,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1595,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = A. [resolve(1635,a,1596,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1597,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),E),B). [resolve(1635,a,1598,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1635,a,1599,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C)),B). [resolve(1635,a,1600,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)). [resolve(1635,a,1601,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1635,a,1602,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),C). [resolve(1635,a,1604,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),E),B). [resolve(1635,a,1605,a)].
% 7.16/7.40 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1635,a,1606,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),C). [resolve(1635,a,1607,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1635,a,1608,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A). [resolve(1635,a,1611,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B). [resolve(1635,a,1612,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1613,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C). [resolve(1635,a,1614,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C). [resolve(1635,a,1615,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = B. [resolve(1635,a,1616,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),A) = B. [resolve(1635,a,1617,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1618,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1620,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = A. [resolve(1635,a,1621,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1622,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1623,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1635,a,1624,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)). [resolve(1635,a,1625,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)). [resolve(1635,a,1626,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1635,a,1627,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1635,a,1628,a)].
% 7.16/7.41 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B)) = A. [resolve(1635,a,1629,a)].
% 7.16/7.41 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A))),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)) = B. [resolve(1635,a,1630,a)].
% 7.16/7.41 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)) = A. [resolve(1635,a,1631,a)].
% 7.16/7.41 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A))),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C). [resolve(1635,a,1632,a)].
% 7.16/7.41 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C). [resolve(1635,a,1633,a)].
% 7.16/7.41 1636 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1368,a,1367,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),hAPP(hAPP(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(1636,a,1590,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),hAPP(hAPP(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(1636,a,1591,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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(1636,a,1592,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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(1636,a,1593,a)].
% 7.16/7.41 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(1636,a,1594,a)].
% 7.16/7.41 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(1636,a,1595,a)].
% 7.16/7.41 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(1636,a,1596,a)].
% 7.16/7.41 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(1636,a,1597,a)].
% 7.16/7.41 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),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),E),B). [resolve(1636,a,1598,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1636,a,1599,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B)) = hAPP(hAPP(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(1636,a,1600,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = hAPP(hAPP(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(1636,a,1601,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1636,a,1602,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),C). [resolve(1636,a,1604,a)].
% 7.16/7.41 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),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),E),B). [resolve(1636,a,1605,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1636,a,1606,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),C). [resolve(1636,a,1607,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1636,a,1608,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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(1636,a,1611,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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(1636,a,1612,a)].
% 7.16/7.41 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(1636,a,1613,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1636,a,1614,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1636,a,1615,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = B. [resolve(1636,a,1616,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),A) = B. [resolve(1636,a,1617,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1636,a,1618,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1636,a,1620,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = A. [resolve(1636,a,1621,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1636,a,1622,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1636,a,1623,a)].
% 7.16/7.41 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1636,a,1624,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)). [resolve(1636,a,1625,a)].
% 7.16/7.41 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)). [resolve(1636,a,1626,a)].
% 7.27/7.51 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1636,a,1627,a)].
% 7.27/7.51 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1636,a,1628,a)].
% 7.27/7.51 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B)) = A. [resolve(1636,a,1629,a)].
% 7.27/7.51 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A))),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)) = B. [resolve(1636,a,1630,a)].
% 7.27/7.51 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)) = A. [resolve(1636,a,1631,a)].
% 7.27/7.51 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A))),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C). [resolve(1636,a,1632,a)].
% 7.27/7.51 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C). [resolve(1636,a,1633,a)].
% 7.27/7.51 1637 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 7.27/7.51 1638 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A)) # label(fact_norm__one) # label(axiom). [clausify(571)].
% 7.27/7.51 1639 -class_RealVector_Oreal__normed__algebra__1(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C))) # label(fact_norm__power__ineq) # label(axiom). [clausify(684)].
% 7.44/7.65 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1637,a,1638,a)].
% 7.44/7.65 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B))). [resolve(1637,a,1639,a)].
% 7.44/7.65 1640 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 7.44/7.65 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1640,a,1638,a)].
% 7.44/7.65 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B))). [resolve(1640,a,1639,a)].
% 7.44/7.65 1641 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 7.44/7.65 1642 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(574)].
% 7.44/7.65 1643 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(576)].
% 7.44/7.65 1644 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__commutes) # label(axiom). [clausify(708)].
% 7.44/7.65 1645 -class_Groups_Omonoid__mult(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_power__one) # label(axiom). [clausify(710)].
% 7.44/7.65 1646 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) # label(fact_power__mult) # label(axiom). [clausify(711)].
% 7.44/7.65 1647 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_power__one__right) # label(axiom). [clausify(713)].
% 7.44/7.65 1648 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(fact_power__Suc2) # label(axiom). [clausify(721)].
% 7.44/7.65 1649 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(fact_power__add) # label(axiom). [clausify(724)].
% 7.44/7.65 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(1641,a,1642,a)].
% 7.44/7.65 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1641,a,1643,a)].
% 7.44/7.65 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1641,a,1644,a)].
% 7.44/7.65 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A). [resolve(1641,a,1645,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1641,a,1646,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1641,a,1647,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(1641,a,1648,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)). [resolve(1641,a,1649,a)].
% 7.46/7.66 1650 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(1650,a,1642,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1650,a,1643,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1650,a,1644,a)].
% 7.46/7.66 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A). [resolve(1650,a,1645,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1650,a,1646,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1650,a,1647,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A). [resolve(1650,a,1648,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)). [resolve(1650,a,1649,a)].
% 7.46/7.66 1651 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(1651,a,1642,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1651,a,1643,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1651,a,1644,a)].
% 7.46/7.66 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). [resolve(1651,a,1645,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1651,a,1646,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1651,a,1647,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A). [resolve(1651,a,1648,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)). [resolve(1651,a,1649,a)].
% 7.46/7.66 1652 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(1652,a,1642,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1652,a,1643,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(1652,a,1644,a)].
% 7.46/7.66 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(1652,a,1645,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1652,a,1646,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1652,a,1647,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(1652,a,1648,a)].
% 7.46/7.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)). [resolve(1652,a,1649,a)].
% 7.46/7.66 1653 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1016)].
% 7.46/7.66 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B) = B. [resolve(1653,b,1642,a)].
% 7.46/7.66 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1653,b,1643,a)].
% 7.46/7.66 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1653,b,1644,a)].
% 7.46/7.66 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B). [resolve(1653,b,1645,a)].
% 7.46/7.66 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)). [resolve(1653,b,1646,a)].
% 7.57/7.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B. [resolve(1653,b,1647,a)].
% 7.57/7.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B). [resolve(1653,b,1648,a)].
% 7.57/7.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)). [resolve(1653,b,1649,a)].
% 7.57/7.82 1654 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.57/7.82 1655 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1) # label(axiom). [clausify(575)].
% 7.57/7.82 1656 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(577)].
% 7.57/7.82 1657 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mult__distrib) # label(axiom). [clausify(709)].
% 7.57/7.82 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(1654,a,1657,a)].
% 7.57/7.82 1658 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.57/7.82 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)). [resolve(1658,a,1657,a)].
% 7.57/7.82 1659 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.57/7.82 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)). [resolve(1659,a,1657,a)].
% 7.57/7.82 1660 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.57/7.82 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(1660,a,1657,a)].
% 7.57/7.82 1661 -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(1000)].
% 7.57/7.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)). [resolve(1661,b,1657,a)].
% 7.93/8.13 1662 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 7.93/8.13 1663 -class_Rings_Olinordered__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),F)) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)) # label(fact_convex__bound__le) # label(axiom). [clausify(618)].
% 7.93/8.13 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),E)) | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C))),B)). [resolve(1662,a,1663,a)].
% 7.93/8.13 1664 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 7.93/8.13 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),E)) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),D),E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C))),B)). [resolve(1664,a,1663,a)].
% 7.93/8.13 1665 -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(994)].
% 7.93/8.13 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),F)) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),E),F) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D))),C)). [resolve(1665,b,1663,a)].
% 7.93/8.13 1666 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 7.93/8.13 1667 -class_Rings_Olinordered__semiring__1__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),F)) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)) # label(fact_convex__bound__lt) # label(axiom). [clausify(622)].
% 8.08/8.29 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),E)) | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C))),B)). [resolve(1666,a,1667,a)].
% 8.08/8.29 1668 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 8.08/8.29 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),E)) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C))),B)). [resolve(1668,a,1667,a)].
% 8.08/8.29 1669 -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(983)].
% 8.08/8.29 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),F)) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),E),F) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D))),C)). [resolve(1669,b,1667,a)].
% 8.08/8.29 1670 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 8.08/8.29 1671 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) # label(fact_field__power__not__zero) # label(axiom). [clausify(707)].
% 8.08/8.29 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B). [resolve(1670,a,1671,a)].
% 8.08/8.29 1672 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 8.08/8.29 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B). [resolve(1672,a,1671,a)].
% 8.08/8.29 1673 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 8.25/8.45 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B). [resolve(1673,a,1671,a)].
% 8.25/8.45 1674 -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(989)].
% 8.25/8.45 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C). [resolve(1674,b,1671,a)].
% 8.25/8.45 1675 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom). [assumption].
% 8.25/8.45 1676 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_OSuc,B)) # label(fact_power__0__Suc) # label(axiom). [clausify(720)].
% 8.25/8.45 1677 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(731)].
% 8.25/8.45 1678 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(731)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_OSuc,A)). [resolve(1675,a,1676,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1675,a,1677,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1675,a,1678,b)].
% 8.25/8.45 1679 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom). [assumption].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,A)). [resolve(1679,a,1676,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(1679,a,1677,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(1679,a,1678,b)].
% 8.25/8.45 1680 class_Rings_Osemiring__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__0) # label(axiom). [assumption].
% 8.25/8.45 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_Nat_OSuc,A)). [resolve(1680,a,1676,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1680,a,1677,b)].
% 8.25/8.45 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1680,a,1678,b)].
% 8.38/8.58 1681 class_Rings_Osemiring__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__0) # label(axiom). [assumption].
% 8.38/8.58 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_Nat_OSuc,A)). [resolve(1681,a,1676,b)].
% 8.38/8.58 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1681,a,1677,b)].
% 8.38/8.58 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1681,a,1678,b)].
% 8.38/8.58 1682 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom). [clausify(1019)].
% 8.38/8.58 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(c_Nat_OSuc,B)). [resolve(1682,b,1676,b)].
% 8.38/8.58 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1682,b,1677,b)].
% 8.38/8.58 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1682,b,1678,b)].
% 8.38/8.58 1683 -class_Orderings_Oorder(A) | -c_SEQ_Omonoseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))) # label(fact_monoseq__Suc) # label(axiom). [clausify(824)].
% 8.38/8.58 1684 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)) # label(fact_monoseq__realpow) # label(axiom). [clausify(785)].
% 8.38/8.58 Derived: -class_Orderings_Oorder(tc_RealDef_Oreal) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,B)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1683,b,1684,c)].
% 8.38/8.58 1685 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f63(B,A))),hAPP(B,hAPP(c_Nat_OSuc,f63(B,A))))) # label(fact_monoseq__Suc) # label(axiom). [clausify(824)].
% 8.38/8.58 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f63(B,A))),hAPP(B,hAPP(c_Nat_OSuc,f63(B,A))))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1685,b,1683,b)].
% 8.38/8.59 1686 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,f64(B,A)))),hAPP(B,f64(B,A)))) # label(fact_monoseq__Suc) # label(axiom). [clausify(824)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,f64(B,A)))),hAPP(B,f64(B,A)))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1686,b,1683,b)].
% 8.38/8.59 1687 -class_Orderings_Oorder(A) | -c_SEQ_Omonoseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))) # label(fact_monoseq__def) # label(axiom). [clausify(825)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,B)),hAPP(D,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,F)),hAPP(D,E))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,f63(D,A))),hAPP(D,hAPP(c_Nat_OSuc,f63(D,A))))). [resolve(1687,b,1685,b)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,B)),hAPP(D,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,F)),hAPP(D,E))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(D,hAPP(c_Nat_OSuc,f64(D,A)))),hAPP(D,f64(D,A)))). [resolve(1687,b,1686,b)].
% 8.38/8.59 1688 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f65(B,A)),f66(B,A))) # label(fact_monoseq__def) # label(axiom). [clausify(825)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f65(B,A)),f66(B,A))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1688,b,1683,b)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f65(B,A)),f66(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1688,b,1687,b)].
% 8.38/8.59 1689 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f65(B,A))),hAPP(B,f66(B,A)))) # label(fact_monoseq__def) # label(axiom). [clausify(825)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f65(B,A))),hAPP(B,f66(B,A)))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1689,b,1683,b)].
% 8.38/8.59 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f65(B,A))),hAPP(B,f66(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1689,b,1687,b)].
% 8.44/8.68 1690 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f67(B,A)),f68(B,A))) # label(fact_monoseq__def) # label(axiom). [clausify(825)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f67(B,A)),f68(B,A))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1690,b,1683,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f67(B,A)),f68(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1690,b,1687,b)].
% 8.44/8.68 1691 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f68(B,A))),hAPP(B,f67(B,A)))) # label(fact_monoseq__def) # label(axiom). [clausify(825)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f68(B,A))),hAPP(B,f67(B,A)))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1691,b,1683,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f68(B,A))),hAPP(B,f67(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1691,b,1687,b)].
% 8.44/8.68 1692 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))). [resolve(1584,b,1581,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1692,b,1683,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f17(B,A)),f18(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1692,b,1687,b)].
% 8.44/8.68 1693 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))). [resolve(1584,b,1583,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1693,b,1683,b)].
% 8.44/8.68 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f18(B,A))),hAPP(B,f17(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1693,b,1687,b)].
% 8.53/8.75 1694 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))). [resolve(1588,b,1585,b)].
% 8.53/8.75 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1694,b,1683,b)].
% 8.53/8.75 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f26(B,A)),f27(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1694,b,1687,b)].
% 8.53/8.75 1695 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))). [resolve(1588,b,1587,b)].
% 8.53/8.75 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,hAPP(c_Nat_OSuc,C)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,hAPP(c_Nat_OSuc,D))),hAPP(B,D))). [resolve(1695,b,1683,b)].
% 8.53/8.75 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f26(B,A))),hAPP(B,f27(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E),F)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F)),hAPP(B,E))). [resolve(1695,b,1687,b)].
% 8.53/8.75 1696 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 8.53/8.75 1697 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(922)].
% 8.53/8.75 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1696,a,1697,a)].
% 8.53/8.75 1698 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption].
% 8.53/8.75 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1698,a,1697,a)].
% 8.53/8.75 1699 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption].
% 8.53/8.75 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))). [resolve(1699,a,1697,a)].
% 8.71/8.90 1700 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1027)].
% 8.71/8.90 Derived: -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1700,b,1697,a)].
% 8.71/8.90 1701 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 8.71/8.90 1702 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(969)].
% 8.71/8.90 1703 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(969)].
% 8.71/8.90 1704 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(970)].
% 8.71/8.90 1705 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(970)].
% 8.71/8.90 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1701,a,1702,a)].
% 8.71/8.90 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1701,a,1703,a)].
% 8.71/8.90 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1701,a,1704,a)].
% 8.71/8.90 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1701,a,1705,a)].
% 8.71/8.90 1706 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 8.71/8.90 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1706,a,1702,a)].
% 8.71/8.90 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1706,a,1703,a)].
% 8.85/9.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1706,a,1704,a)].
% 8.85/9.06 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1706,a,1705,a)].
% 8.85/9.06 1707 -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(995)].
% 8.85/9.06 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1707,b,1702,a)].
% 8.85/9.06 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1707,b,1703,a)].
% 8.85/9.06 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1707,b,1704,a)].
% 8.85/9.06 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1707,b,1705,a)].
% 8.85/9.06 1708 class_Divides_Oring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 8.85/9.06 1709 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),D) # label(fact_mod__diff__right__eq) # label(axiom). [clausify(971)].
% 8.85/9.06 1710 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D),C) # label(fact_mod__diff__left__eq) # label(axiom). [clausify(972)].
% 8.85/9.06 1711 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D),C) # label(fact_mod__diff__eq) # label(axiom). [clausify(973)].
% 8.85/9.06 1712 -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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),F),C) # label(fact_mod__diff__cong) # label(axiom). [clausify(974)].
% 8.85/9.06 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),C). [resolve(1708,a,1709,a)].
% 8.85/9.06 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C),B). [resolve(1708,a,1710,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C),B). [resolve(1708,a,1711,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),E),B). [resolve(1708,a,1712,a)].
% 8.91/9.11 1713 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1369,a,1316,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),C). [resolve(1713,a,1709,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1713,a,1710,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B). [resolve(1713,a,1711,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),E),B). [resolve(1713,a,1712,a)].
% 8.91/9.11 1714 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1369,a,1367,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),C). [resolve(1714,a,1709,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1714,a,1710,a)].
% 8.91/9.11 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B). [resolve(1714,a,1711,a)].
% 10.32/10.53 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),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),E),B). [resolve(1714,a,1712,a)].
% 10.32/10.53
% 10.32/10.53 ============================== end predicate elimination =============
% 10.32/10.53
% 10.32/10.53 Auto_denials: (non-Horn, no changes).
% 10.32/10.53
% 10.32/10.53 Term ordering decisions:
% 10.32/10.53 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_Nat_Onat=1. tc_Complex_Ocomplex=1. c_Nat_OSuc=1. tc_HOL_Obool=1. v_q____=1. v_pa____=1. c_fequal=1. c_fimplies=1. v_c____=1. v_p=1. c1=1. c2=1. c3=1. c4=1. hAPP=1. c_Orderings_Oord__class_Oless__eq=1. c_Rings_Oinverse__class_Oinverse=1. c_RealVector_Onorm__class_Onorm=1. tc_fun=1. c_RealDef_Oreal=1. c_Polynomial_Odegree=1. c_Polynomial_Opoly=1. c_Polynomial_Ocoeff=1. c_Orderings_Oord__class_OLeast=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Polynomial_OAbs__poly=1. f1=1. f6=1. f8=1. f9=1. f12=1. f13=1. f14=1. f15=1. f17=1. f18=1. f19=1. f21=1. f22=1. f24=1. f26=1. f27=1. f28=1. f32=1. f37=1. f39=1. f41=1. f44=1. f45=1. f48=1. f49=1. f51=1. f54=1. f55=1. f56=1. f57=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f78=1. c_Groups_Ozero__class_Ozero=1. tc_Polynomial_Opoly=1. c_Orderings_Oord__class_Oless=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oplus__class_Oplus=1. c_Groups_Oone__class_Oone=1. c_Power_Opower__class_Opower=1. c_Groups_Ominus__class_Ominus=1. c_Transcendental_Oln=1. c_RComplete_Onatfloor=1. c_RComplete_Onatceiling=1. c_HOL_OAll=1. c_If=1. f2=1. f7=1. f16=1. f23=1. f52=1. f53=1. c_Divides_Odiv__class_Omod=1. c_Divides_Odiv__class_Odiv=1. c_Polynomial_Osmult=1. c_Polynomial_Opoly__gcd=1. c_Polynomial_Omonom=1. c_COMBS=1. c_Power_Opower_Opower=1. c_Polynomial_Oorder=1. c_Polynomial_Opcompose=1. c_Polynomial_Osynthetic__div=1. c_COMBK=1. f3=1. f4=1. f5=1. f20=1. f25=1. f29=1. f30=1. f31=1. f34=1. f35=1. f36=1. f38=1. f40=1. f42=1. f43=1. f46=1. f47=1. f50=1. f58=1. f59=1. f60=1. f61=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. c_COMBB=1. f10=1. f11=1. f33=1. c_COMBC=1.
% 10.32/10.53
% 10.32/10.53 ============================== end of process initial clauses ========
% 10.32/10.53
% 10.32/10.53 ============================== CLAUSES FOR SEARCH ====================
% 10.32/10.53
% 10.32/10.53 ============================== end of clauses for search =============
% 10.32/10.53
% 10.32/10.53 ============================== SEARCH ================================
% 10.32/10.53
% 10.32/10.53 % Starting search at 7.87 seconds.
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=61.000, iters=3441
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=58.000, iters=3390
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=55.000, iters=3376
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=54.000, iters=3398
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=52.000, iters=3369
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=50.000, iters=3360
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=47.000, iters=3347
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=46.000, iters=3401
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=45.000, iters=3336
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=44.000, iters=3408
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=43.000, iters=3413
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=42.000, iters=3339
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=41.000, iters=3336
% 10.32/10.53
% 10.32/10.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 81 (0.00 of 8.52 sec).
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=40.000, iters=3391
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=39.000, iters=3368
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=38.000, iters=3385
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=37.000, iters=3440
% 10.32/10.53
% 10.32/10.53 Low Water (keep): wt=36.000, iters=3349
% 10.32/10.53
% 10.32/10.53 Low Water Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------