TSTP Solution File: SWW191+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW191+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 01:15:47 EDT 2022
% Result : Timeout 300.03s 300.24s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW191+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 4 12:50:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.24/2.56 ============================== Prover9 ===============================
% 2.24/2.56 Prover9 (32) version 2009-11A, November 2009.
% 2.24/2.56 Process 7776 was started by sandbox2 on n029.cluster.edu,
% 2.24/2.56 Sat Jun 4 12:50:35 2022
% 2.24/2.56 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7623_n029.cluster.edu".
% 2.24/2.56 ============================== end of head ===========================
% 2.24/2.56
% 2.24/2.56 ============================== INPUT =================================
% 2.24/2.56
% 2.24/2.56 % Reading from file /tmp/Prover9_7623_n029.cluster.edu
% 2.24/2.56
% 2.24/2.56 set(prolog_style_variables).
% 2.24/2.56 set(auto2).
% 2.24/2.56 % set(auto2) -> set(auto).
% 2.24/2.56 % set(auto) -> set(auto_inference).
% 2.24/2.56 % set(auto) -> set(auto_setup).
% 2.24/2.56 % set(auto_setup) -> set(predicate_elim).
% 2.24/2.56 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.24/2.56 % set(auto) -> set(auto_limits).
% 2.24/2.56 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.24/2.56 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.24/2.56 % set(auto) -> set(auto_denials).
% 2.24/2.56 % set(auto) -> set(auto_process).
% 2.24/2.56 % set(auto2) -> assign(new_constants, 1).
% 2.24/2.56 % set(auto2) -> assign(fold_denial_max, 3).
% 2.24/2.56 % set(auto2) -> assign(max_weight, "200.000").
% 2.24/2.56 % set(auto2) -> assign(max_hours, 1).
% 2.24/2.56 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.24/2.56 % set(auto2) -> assign(max_seconds, 0).
% 2.24/2.56 % set(auto2) -> assign(max_minutes, 5).
% 2.24/2.56 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.24/2.56 % set(auto2) -> set(sort_initial_sos).
% 2.24/2.56 % set(auto2) -> assign(sos_limit, -1).
% 2.24/2.56 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.24/2.56 % set(auto2) -> assign(max_megs, 400).
% 2.24/2.56 % set(auto2) -> assign(stats, some).
% 2.24/2.56 % set(auto2) -> clear(echo_input).
% 2.24/2.56 % set(auto2) -> set(quiet).
% 2.24/2.56 % set(auto2) -> clear(print_initial_clauses).
% 2.24/2.56 % set(auto2) -> clear(print_given).
% 2.24/2.56 assign(lrs_ticks,-1).
% 2.24/2.56 assign(sos_limit,10000).
% 2.24/2.56 assign(order,kbo).
% 2.24/2.56 set(lex_order_vars).
% 2.24/2.56 clear(print_given).
% 2.24/2.56
% 2.24/2.56 % formulas(sos). % not echoed (1212 formulas)
% 2.24/2.56
% 2.24/2.56 ============================== end of input ==========================
% 2.24/2.56
% 2.24/2.56 % From the command line: assign(max_seconds, 300).
% 2.24/2.56
% 2.24/2.56 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.24/2.56
% 2.24/2.56 % Formulas that are not ordinary clauses:
% 2.24/2.56 1 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 2 (all B_z (hBOOL(hAPP(v_P,B_z)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_z,v_y____))) # label(fact_nox) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 3 (all B_x (hBOOL(hAPP(v_P,B_x)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_x,v_L____))) # label(fact_L_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 4 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 5 (all V_z_2 (hBOOL(hAPP(v_P,V_z_2)) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,V_z_2) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____)))) # label(fact_calculation) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 6 (all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w)) # label(fact_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 7 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z))) # label(fact_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 8 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)))) # label(fact_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 9 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) -> (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].
% 2.24/2.56 10 (all B_z (hBOOL(hAPP(v_P,B_z)) -> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,B_z))) # label(fact_yL_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 11 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 12 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 13 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (V_xa_2 = V_ya_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 14 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 15 (exists B_x1 hBOOL(hAPP(v_P,B_x1))) # label(fact_ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 16 (all B_x (hBOOL(hAPP(v_P,B_x)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_x,v_Y____))) # label(fact_Y_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 17 (all V_x (hBOOL(hAPP(v_P,V_x)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____))) # label(fact_Y) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 18 (exists B_z all B_x (hBOOL(hAPP(v_P,B_x)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z))) # label(fact_bz) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 19 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 20 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_xa_2 != V_ya_2 <-> c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) | c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 21 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) | V_xa_2 = V_ya_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 22 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 23 (all V_xa_2 all V_ya_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 24 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 25 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 26 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 27 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 28 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 29 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 30 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 31 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 32 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 33 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 34 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 35 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 36 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 37 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 38 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 39 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (V_x != V_y -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 40 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 41 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 42 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 43 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 44 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 45 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 46 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 47 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 48 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 49 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 50 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 51 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 52 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 53 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 54 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 55 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) | V_xa_2 = V_ya_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 56 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & -c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 57 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & V_xa_2 != V_ya_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 58 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.56 59 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 60 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 61 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) | V_xa_2 = V_ya_2)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 62 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) & V_xa_2 != V_ya_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 63 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 64 (all V_xa_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 65 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 66 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 67 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 68 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 69 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 70 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 71 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 72 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 73 (all V_xa_2 all V_ya_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 74 (all V_xa_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 75 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 76 -((exists B_x1 hBOOL(hAPP(v_P,B_x1))) -> (all B_Y -(all B_x (hBOOL(hAPP(v_P,B_x)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_Y))))) # label(fact__096_B_Bthesis_O_A_I_B_Bx_AY_O_A_091_124_AP_Ax_059_A_B_Bx_O_AP_Ax_A_061_061_062_Ax_A_060_AY_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 77 (all T_a all V_g_2 all V_f_2 all T_b (class_Orderings_Oord(T_b) -> ((all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_le__funI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 78 (all V_z all V_y all T_a (class_Orderings_Odense__linorder(T_a) -> ((all B_x (c_Orderings_Oord__class_Oless(T_a,B_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,B_x,V_z))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)))) # label(fact_dense__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 79 (all V_z all V_y all V_x all T_a (class_Orderings_Odense__linorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> ((all B_w (c_Orderings_Oord__class_Oless(T_a,V_x,B_w) -> (c_Orderings_Oord__class_Oless(T_a,B_w,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,B_w,V_z)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z))))) # label(fact_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 80 (all V_f_2 all V_c_2 all V_a_2 all V_b_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) -> (c_Orderings_Oord__class_Oless__eq(T_b,V_c_2,hAPP(V_f_2,V_b_2)) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless(T_a,B_y,B_x) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x)))) -> c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2))))))) # label(fact_xt5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 81 (all V_f_2 all V_c_2 all V_a_2 all V_b_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) -> (c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_b_2)) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless__eq(T_a,B_y,B_x) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x)))) -> c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2))))))) # label(fact_xt7) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 82 (all V_c_2 all V_f_2 all V_b_2 all V_a_2 all T_b all T_a (class_Orderings_Oorder(T_a) & class_Orderings_Oorder(T_b) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_b_2),V_c_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless(T_a,B_x,B_y) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y)))) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2)))))) # label(fact_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 83 (all V_c_2 all V_f_2 all V_b_2 all V_a_2 all T_b all T_a (class_Orderings_Oorder(T_a) & class_Orderings_Oorder(T_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_b_2),V_c_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless__eq(T_a,B_x,B_y) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y)))) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2)))))) # label(fact_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 84 (all V_c_2 all V_b_2 all V_f_2 all V_a_2 all T_b all T_a (class_Orderings_Oorder(T_a) & class_Orderings_Oorder(T_b) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_b_2)) -> (c_Orderings_Oord__class_Oless__eq(T_b,V_b_2,V_c_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless__eq(T_b,B_x,B_y) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y)))) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2))))))) # label(fact_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 85 (all V_c_2 all V_b_2 all V_f_2 all V_a_2 all T_b all T_a (class_Orderings_Oorder(T_a) & class_Orderings_Oorder(T_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,hAPP(V_f_2,V_b_2)) -> (c_Orderings_Oord__class_Oless(T_b,V_b_2,V_c_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless(T_b,B_x,B_y) -> c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y)))) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2))))))) # label(fact_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 86 (all V_xa_2 all T_b all T_a (class_Orderings_Otop(T_a) -> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_xa_2) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_top__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 87 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) & -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 88 (all V_x all T_a (class_Orderings_Otop(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)))) # label(fact_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 89 -(all B_L -c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),B_L)) # label(fact__096_B_Bthesis_O_A_I_B_BL_O_AisLub_AUNIV_A_ICollect_AP_J_AL_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 90 (exists B_x1 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),B_x1)) # label(fact__096EX_At_O_AisLub_AUNIV_A_ICollect_AP_J_At_096) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 91 (all V_xa_2 all T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_xa_2))) # label(fact_top1I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 92 (exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1))) # label(fact_thY) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 93 (all V_ya_2 all V_xa_2 all V_S_2 all V_R_2 (c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_xa_2) -> (c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_ya_2) -> V_xa_2 = V_ya_2))) # label(fact_real__isLub__unique) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 94 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 95 (all V_Pa_2 all T_a c_Set_OCollect(T_a,V_Pa_2) = V_Pa_2) # label(fact_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 96 (exists B_x c_member(tc_RealDef_Oreal,B_x,c_Set_OCollect(tc_RealDef_Oreal,v_P))) # label(fact_thx) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 97 (all V_c_2 all V_a_2 all V_b_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) & class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,V_b_2),V_a_2) -> (c_Orderings_Oord__class_Oless(T_b,V_c_2,V_b_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless(T_b,B_y,B_x) -> c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x)))) -> c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2)))))) # label(fact_xt6) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 98 (all V_c_2 all V_a_2 all V_b_2 all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_b_2),V_a_2) -> (c_Orderings_Oord__class_Oless__eq(T_b,V_c_2,V_b_2) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless__eq(T_b,B_y,B_x) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x)))) -> c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2)))))) # label(fact_xt4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 99 (all V_c_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)) -> -(-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 100 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> V_A_2 = V_B_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 101 (all V_xa_2 all T_a c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 102 (all V_c_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 103 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) & V_A_2 != V_B_2)) # label(fact_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 104 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) | V_A_2 = V_B_2)) # label(fact_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 105 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 106 (all V_c_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 107 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 108 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 109 (all V_A_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,V_A_2) <-> hBOOL(hAPP(V_A_2,V_xa_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 110 (all V_ya_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,c_fequal(V_ya_2)) <-> V_xa_2 = V_ya_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 111 (all V_xa_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> (c_member(T_a,V_xa_2,V_A_2) <-> c_member(T_a,V_xa_2,V_B_2)))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 112 (all V_A_2 all T_a all V_ya_2 all V_xa_2 (V_xa_2 = V_ya_2 -> (c_member(T_a,V_xa_2,V_A_2) <-> c_member(T_a,V_ya_2,V_A_2)))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 113 (all V_A_2 all T_a all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> (c_member(T_a,V_b_2,V_A_2) -> c_member(T_a,V_a_2,V_A_2)))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 114 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> -(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_equalityE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 115 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 116 (all V_xa_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_xa_2,V_A_2) -> c_member(T_a,V_xa_2,V_B_2)))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 117 (all V_B_2 all V_A_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_member(T_a,V_xa_2,V_B_2)))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 118 (all V_xa_2 all V_Q_2 all V_Pa_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> (hBOOL(hAPP(V_Pa_2,V_xa_2)) -> hBOOL(hAPP(V_Q_2,V_xa_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 119 (all V_xa_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_xa_2,V_A_2) -> c_member(T_a,V_xa_2,V_B_2)))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 120 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 121 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 122 (all V_Q_2 all T_a all V_xa_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_xa_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> hBOOL(hAPP(V_Q_2,V_xa_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 123 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 124 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 125 (all V_ya_2 all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_ya_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2))))) # label(fact_isLub__le__isUb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 126 (all V_ya_2 all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)) -> (c_member(T_a,V_ya_2,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2))))) # label(fact_isUbD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 127 (all V_ya_2 all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> (c_member(T_a,V_ya_2,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2))))) # label(fact_isLubD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 128 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))))) # label(fact_isLub__isUb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 129 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)) -> c_member(T_a,V_xa_2,V_R_2)))) # label(fact_isUbD2a) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 130 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> c_member(T_a,V_xa_2,V_R_2)))) # label(fact_isLubD1a) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 131 (all V_xa_2 all T_a c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 132 (all V_S_2 ((exists B_X c_member(tc_RealDef_Oreal,B_X,V_S_2)) -> ((exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1))) -> (exists B_x1 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,B_x1))))) # label(fact_reals__complete) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 133 (all V_S_2 ((exists B_x c_member(tc_RealDef_Oreal,B_x,V_S_2)) & (exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1))) -> (exists B_x1 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,B_x1)))) # label(fact_lemma__reals__complete) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 134 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 135 (all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> c_Lubs_Oubs(T_a,V_R_2,V_S_2) = c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2)))) # label(fact_ubs__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 136 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)) -> (c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2))) -> c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2))))) # label(fact_isLubI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 137 (all V_ya_2 all V_xa_2 all V_Pa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2) -> (c_member(T_a,V_ya_2,c_Set_OCollect(T_a,V_Pa_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2))))) # label(fact_leastPD3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 138 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)))) # label(fact_isLubD3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 139 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2) -> c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)))) # label(fact_isLubI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 140 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) <-> c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)))) # label(fact_isLub__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 141 (all V_R_2 all V_xa_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2) -> (c_member(T_a,V_xa_2,V_R_2) -> hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)))))) # label(fact_isUbI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 142 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)) <-> c_Lubs_Osetle(T_a,V_S_2,V_xa_2) & c_member(T_a,V_xa_2,V_R_2)))) # label(fact_isUb__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 143 (all V_ya_2 all V_S_2 all V_xa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_Osetge(T_a,V_xa_2,V_S_2) -> (c_member(T_a,V_ya_2,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2))))) # label(fact_setgeD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 144 (all V_xa_2 all V_Pa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2) -> hBOOL(hAPP(V_Pa_2,V_xa_2))))) # label(fact_leastPD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 145 (all V_xa_2 all V_Pa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2) <-> hBOOL(hAPP(V_Pa_2,V_xa_2)) & c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2))))) # label(fact_leastP__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 146 (all V_xa_2 all V_Pa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2) -> c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2))))) # label(fact_leastPD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 147 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> c_Lubs_Osetge(T_a,V_xa_2,c_Lubs_Oubs(T_a,V_R_2,V_S_2))))) # label(fact_isLub__ubs) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 148 (all V_xa_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2) <-> (all B_x (c_member(T_a,B_x,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,B_x,V_xa_2)))))) # label(fact_setle__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 149 (all V_S_2 all V_xa_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_Osetge(T_a,V_xa_2,V_S_2) <-> (all B_x (c_member(T_a,B_x,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,B_x)))))) # label(fact_setge__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 150 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2) -> c_Lubs_Osetle(T_a,V_S_2,V_xa_2)))) # label(fact_isLubD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 151 (all V_xa_2 all V_S_2 all V_R_2 all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)) -> c_Lubs_Osetle(T_a,V_S_2,V_xa_2)))) # label(fact_isUbD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 152 (all V_ya_2 all V_xa_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2) -> (c_member(T_a,V_ya_2,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2))))) # label(fact_setleD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 153 (all V_u_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> ((all B_y (c_member(T_a,B_y,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,B_y,V_u_2))) -> hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2))))) # label(fact_isUb__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 154 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Predicate_OPowp(T_a,V_A_2),c_Predicate_OPowp(T_a,V_B_2)))) # label(fact_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 155 (all V_B_2 all V_A_2 all T_a ((all B_x (c_member(T_a,B_x,V_A_2) -> c_member(T_a,B_x,V_B_2))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 156 (all V_xa_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> ((all B_x (c_member(T_a,B_x,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,B_x,V_xa_2))) -> c_Lubs_Osetle(T_a,V_S_2,V_xa_2)))) # label(fact_setleI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 157 (all V_xa_2 all V_S_2 all T_a (class_Orderings_Oord(T_a) -> ((all B_x (c_member(T_a,B_x,V_S_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,B_x))) -> c_Lubs_Osetge(T_a,V_xa_2,V_S_2)))) # label(fact_setgeI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 158 (all T_a all V_Q_2 all V_Pa_2 ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Q_2,B_x)))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_OCollect(T_a,V_Pa_2),c_Set_OCollect(T_a,V_Q_2)))) # label(fact_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 159 (all V_A_2 all T_a ((all B_x c_member(T_a,B_x,V_A_2)) -> c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 160 (all T_a exists B_x c_member(T_a,B_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_UNIV__witness) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 161 (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 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> 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].
% 2.24/2.57 162 (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 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> 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].
% 2.24/2.57 163 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)))) # label(fact_Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 164 (all V_ya_2 all V_xa_2 all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Oorder(T_a) -> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2) -> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2)))))) # label(fact_strict__monoD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 165 (all V_ya_2 all V_xa_2 all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Olinorder(T_a) -> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2) -> (c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2))))) # label(fact_strict__mono__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 166 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) <-> (-c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2) & (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_a_2) | c_Orderings_Oord__class_Oless(T_a,V_b_2,V_d_2))) & c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2)))) # label(fact_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 167 (all V_ya_2 all V_xa_2 all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Olinorder(T_a) -> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2) -> (c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2))))) # label(fact_strict__mono__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 168 (all V_B_2 all V_A_2 all V_xa_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2) <-> c_member(T_a,V_xa_2,V_B_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 169 (all V_A_2 all V_b_2 all V_a_2 all T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2)) -> (V_a_2 != V_b_2 -> c_member(T_a,V_a_2,V_A_2)))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 170 (all V_b_2 all V_B_2 all V_a_2 all T_a ((-c_member(T_a,V_a_2,V_B_2) -> V_a_2 = V_b_2) -> c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)))) # label(fact_insertCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 171 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2)))) # label(fact_PowI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 172 (all V_A_2 all T_a c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_A_2))) # label(fact_Pow__top) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 173 (all V_ya_2 all V_xa_2 all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Olinorder(T_a) -> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2) -> (hAPP(V_f_2,V_xa_2) = hAPP(V_f_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_strict__mono__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 174 (all V_xa_2 all V_A_2 all V_ya_2 all T_a (hBOOL(hAPP(c_Set_Oinsert(T_a,V_ya_2,V_A_2),V_xa_2)) <-> V_ya_2 = V_xa_2 | hBOOL(hAPP(V_A_2,V_xa_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 175 (all V_A_2 all V_ya_2 all V_xa_2 all T_a c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_ya_2,V_A_2)) = c_Set_Oinsert(T_a,V_ya_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 176 (all V_A_2 all V_xa_2 all T_a c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2)) = c_Set_Oinsert(T_a,V_xa_2,V_A_2)) # label(fact_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 177 (all V_B_2 all V_a_2 all T_a c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))) # label(fact_insertI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 178 (all V_A_2 all V_b_2 all V_a_2 all T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2)) <-> V_a_2 = V_b_2 | c_member(T_a,V_a_2,V_A_2))) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 179 (all V_B_2 all V_A_2 all V_xa_2 all T_a (-c_member(T_a,V_xa_2,V_A_2) -> (-c_member(T_a,V_xa_2,V_B_2) -> (c_Set_Oinsert(T_a,V_xa_2,V_A_2) = c_Set_Oinsert(T_a,V_xa_2,V_B_2) <-> V_A_2 = V_B_2)))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 180 (all V_b_2 all V_B_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_B_2) -> c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)))) # label(fact_insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 181 (all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> c_Set_Oinsert(T_a,V_a_2,V_A_2) = V_A_2)) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 182 (all V_a_2 all V_D_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2)))) # label(fact_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 183 (all V_b_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 184 (all V_a_2 all V_B_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))) # label(fact_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 185 (all T_a c_Set_OPow(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) # label(fact_Pow__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 186 (all V_B_2 all V_A_2 all T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_PowD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 187 (all V_B_2 all V_A_2 all T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 188 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) <-> -c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2)))) # label(fact_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 189 (all V_B_2 all V_A_2 all V_xa_2 all T_a (-c_member(T_a,V_xa_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 190 (all V_k_2 all V_less__eq_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)))) # label(fact_ord_OatMost__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 191 (all V_k_2 all V_less__eq_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)))) # label(fact_ord_OatLeast__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 192 (all V_k_2 all V_less_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)) <-> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)))) # label(fact_ord_OlessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 193 (all V_k_2 all V_less_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)) <-> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)))) # label(fact_ord_OgreaterThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 194 (all V_u_2 all V_l_2 all V_less__eq_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))) # label(fact_ord_OatLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 195 (all V_u_2 all V_l_2 all V_less_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)) <-> hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))) # label(fact_ord_OgreaterThanLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 196 (all V_u_2 all V_l_2 all V_less_2 all V_less__eq_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))) # label(fact_ord_OatLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 197 (all V_u_2 all V_l_2 all V_less_2 all V_less__eq_2 all V_i_2 all T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)) <-> hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))) # label(fact_ord_OgreaterThanAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 198 (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 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> 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 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> 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].
% 2.24/2.57 199 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 200 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 201 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 202 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.57 203 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (V_m != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 204 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) | V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 205 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 206 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 207 (all V_y all V_x (V_x != V_y -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 208 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 209 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 210 (all V_t all V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 211 (all V_Pa_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 212 (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].
% 2.24/2.58 213 (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].
% 2.24/2.58 214 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 215 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 216 (all V_n all V_m (V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 217 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 218 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n)) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 219 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> ((all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_monoI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 220 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> ((all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_monoI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 221 (all V_n_2 all V_m_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_m_2),c_SetInterval_Oord__class_OlessThan(T_a,V_n_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_m_2,V_n_2)))) # label(fact_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 222 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_greaterThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 223 (all V_f_2 all T_a all T_b (class_Orderings_Oorder(T_b) & class_Orderings_Oorder(T_a) -> ((all B_x all B_y (c_Orderings_Oord__class_Oless(T_a,B_x,B_y) -> c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y)))) -> c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)))) # label(fact_strict__monoI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 224 (all V_k_2 all V_i_2 all T_a (class_Orderings_Oord(T_a) -> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_k_2,V_i_2)))) # label(fact_greaterThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 225 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2),c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)))) # label(fact_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 226 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2) = c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 227 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2) = c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_greaterThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 228 (all V_k_2 all V_i_2 all T_a (class_Orderings_Oord(T_a) -> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OlessThan(T_a,V_k_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_i_2,V_k_2)))) # label(fact_lessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 229 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_xa_2),c_SetInterval_Oord__class_OatMost(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)))) # label(fact_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 230 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2),c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_atLeast__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 231 (all V_k_2 all V_i_2 all T_a (class_Orderings_Oord(T_a) -> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatMost(T_a,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_i_2,V_k_2)))) # label(fact_atMost__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 232 (all V_k_2 all V_i_2 all T_a (class_Orderings_Oord(T_a) -> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatLeast(T_a,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_k_2,V_i_2)))) # label(fact_atLeast__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 233 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> 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].
% 2.24/2.58 234 (all V_j_2 all V_i_2 all V_f_2 ((all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,B_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_i),hAPP(V_f_2,B_j)))) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2))))) # label(fact_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 235 (all V_A_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,V_A_2) -> -(all B_B (V_A_2 = c_Set_Oinsert(T_a,V_xa_2,B_B) -> c_member(T_a,V_xa_2,B_B))))) # label(fact_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 236 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2) = c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_atLeast__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 237 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OatMost(T_a,V_xa_2) = c_SetInterval_Oord__class_OatMost(T_a,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 238 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2)) = c_SetInterval_Oord__class_OatLeast(T_a,V_l_2)))) # label(fact_ivl__disj__un_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 239 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatMost(T_a,V_u_2)))) # label(fact_ivl__disj__un_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 240 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) -> 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].
% 2.24/2.58 241 (all V_x 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].
% 2.24/2.58 242 (all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> (exists B_B (V_A_2 = c_Set_Oinsert(T_a,V_a_2,B_B) & -c_member(T_a,V_a_2,B_B))))) # label(fact_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 243 (all V_n_2 all V_f_2 (c_SEQ_Osubseq(V_f_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_f_2,V_n_2)))) # label(fact_seq__suble) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 244 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> 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].
% 2.24/2.58 245 (all V_xa_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)) -> (-hBOOL(hAPP(V_A_2,V_xa_2)) -> hBOOL(hAPP(V_B_2,V_xa_2))))) # label(fact_sup1E) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 246 (all T_a all V_A_2 all V_xa_2 all V_B_2 ((-hBOOL(hAPP(V_B_2,V_xa_2)) -> hBOOL(hAPP(V_A_2,V_xa_2))) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)))) # label(fact_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 247 (all V_A_2 all V_B_2 all V_c_2 all T_a ((-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,V_A_2)) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 248 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> (-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 249 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 250 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_le0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 251 (all V_n_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_n_2)) # label(fact_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 252 (all V_x 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].
% 2.24/2.58 253 (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].
% 2.24/2.58 254 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) = V_A_2) # label(fact_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 255 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 256 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 257 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 258 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 259 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((exists B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x (c_member(T_a,B_x,V_A_2) & hBOOL(hAPP(V_Pa_2,B_x)))) | (exists B_x (c_member(T_a,B_x,V_B_2) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 260 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((all B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> hBOOL(hAPP(V_Pa_2,B_x)))) & (all B_x (c_member(T_a,B_x,V_B_2) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 261 (all V_B_2 all T_a all V_xa_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_xa_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)))) # label(fact_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 262 (all V_A_2 all T_a all V_xa_2 all V_B_2 (hBOOL(hAPP(V_B_2,V_xa_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)))) # label(fact_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 263 (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].
% 2.24/2.58 264 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) -> 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].
% 2.24/2.58 265 (all V_A_2 all V_B_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 266 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 267 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) <-> c_member(T_a,V_c_2,V_A_2) | c_member(T_a,V_c_2,V_B_2))) # label(fact_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 268 (all V_B_2 all V_a_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 269 (all V_C_2 all V_B_2 all V_a_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 270 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Un__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 271 (all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Un__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 272 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 273 (all V_A_2 all V_B_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 274 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 275 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 276 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2)) # label(fact_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 277 (all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)))) # label(fact_Un__least) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 278 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 279 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)),c_Set_OPow(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Un__Pow__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 280 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 281 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 282 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 283 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 284 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 285 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 286 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 287 (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].
% 2.24/2.58 288 (all V_m_2 all V_n_2 (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)) <-> 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].
% 2.24/2.58 289 (all V_m_2 all V_n_2 (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)) <-> 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].
% 2.24/2.58 290 (all V_x 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].
% 2.24/2.58 291 (all V_f_2 (c_SEQ_Osubseq(V_f_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_m),hAPP(V_f_2,B_n)))))) # label(fact_subseq__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 292 (all V_xa_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2) = c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)))) # label(fact_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 293 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__top__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 294 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Otop__class_Otop(T_a),V_x) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__top__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 295 (all V_Pa_2 all V_n_2 ((all B_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,V_n_2) -> hBOOL(hAPP(V_Pa_2,B_m)))) <-> (all B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__nat__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 296 (all V_Pa_2 all V_n_2 ((exists B_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,V_n_2) & hBOOL(hAPP(V_Pa_2,B_m)))) <-> (exists B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ex__nat__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 297 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_less__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 298 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_less__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 299 (all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a) = V_a)) # label(fact_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 300 (all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x) = V_x)) # label(fact_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 301 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a))) # label(fact_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 302 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x))) # label(fact_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 303 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 304 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))) # label(fact_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 305 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 306 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 307 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 308 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 309 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 310 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 311 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 312 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 313 (all V_x all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x))))) # label(fact_le__supE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 314 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d)))))) # label(fact_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 315 (all V_z all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x))))) # label(fact_sup__least) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 316 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x))))) # label(fact_le__supI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 317 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = V_x))) # label(fact_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 318 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = V_y))) # label(fact_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 319 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 320 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 321 (all V_z_2 all V_ya_2 all V_xa_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2),V_z_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_z_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_z_2)))) # label(fact_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 322 (all V_ya_2 all V_xa_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2) = V_ya_2))) # label(fact_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 323 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 324 (all V_x all V_y all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 325 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 326 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 327 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2)) = c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2)))) # label(fact_ivl__disj__un_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 328 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OlessThan(T_a,V_u_2)))) # label(fact_ivl__disj__un_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 329 (all V_n all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n)) -> 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].
% 2.24/2.58 330 (all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2)) = c_SetInterval_Oord__class_OatLeast(T_a,V_l_2))) # label(fact_ivl__disj__un_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 331 (all V_a_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2))))) # label(fact_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 332 (all V_a_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2)))) # label(fact_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 333 (all V_a_2 all T_a -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_emptyE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 334 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) # label(fact_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 335 (all V_n 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].
% 2.24/2.58 336 (all V_k_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_k_2) -> c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_greaterThanLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 337 (all T_a c_Set_OPow(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) # label(fact_Pow__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 338 (all V_xa_2 all T_b all T_a (class_Orderings_Obot(T_a) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_xa_2) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 339 (all V_a_2 all T_a all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> -c_member(T_a,V_a_2,V_A_2))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 340 (all V_c_2 all T_a -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 341 (all V_A_2 all T_a ((exists B_x c_member(T_a,B_x,V_A_2)) <-> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 342 (all V_A_2 all T_a ((all B_x -c_member(T_a,B_x,V_A_2)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 343 (all V_A_2 all V_a_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_Set_Oinsert(T_a,V_a_2,V_A_2)) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 344 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 345 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_a_2 = V_c_2 & V_b_2 = V_d_2 | V_a_2 = V_d_2 & V_b_2 = V_c_2)) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 346 (all V_b_2 all V_a_2 all T_a (c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) -> V_a_2 = V_b_2)) # label(fact_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 347 (all V_Pa_2 all T_a (c_Set_OCollect(T_a,V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> (all B_x -hBOOL(hAPP(V_Pa_2,B_x))))) # label(fact_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 348 (all V_Pa_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Set_OCollect(T_a,V_Pa_2) <-> (all B_x -hBOOL(hAPP(V_Pa_2,B_x))))) # label(fact_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 349 (all T_a c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_UNIV__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 350 (all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 351 (all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = V_B_2) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 352 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2) # label(fact_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 353 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 354 (all V_A_2 all T_a c_Set_OPow(T_a,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) # label(fact_Pow__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 355 (all V_A_2 all T_a -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 356 (all V_x all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a),V_x))) # label(fact_bot__least) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 357 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x) = V_x)) # label(fact_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 358 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)) = V_x)) # label(fact_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 359 (all V_ya_2 all V_xa_2 all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> (c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2) = c_Orderings_Obot__class_Obot(T_a) <-> V_xa_2 = c_Orderings_Obot__class_Obot(T_a) & V_ya_2 = c_Orderings_Obot__class_Obot(T_a)))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 360 (all V_a_2 all V_b_2 all T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> V_b_2 = V_a_2)) # label(fact_singletonE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 361 (all V_a_2 all V_b_2 all T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_b_2 = V_a_2)) # label(fact_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.58 362 (all V_xa_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) | V_A_2 = c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 363 (all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) <-> -c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_atLeastatMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 364 (all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> -c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_atLeastatMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 365 (all V_a_2 all V_b_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) -> c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_atLeastatMost__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 366 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 367 (all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (V_a_2 = V_b_2 -> c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_atLeastAtMost__singleton_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 368 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) <-> V_a_2 = V_b_2 & V_b_2 = V_c_2))) # label(fact_atLeastAtMost__singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 369 (all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_atLeastAtMost__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 370 (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].
% 2.24/2.59 371 (all V_n -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].
% 2.24/2.59 372 (all V_B_2 all T_a c_member(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Set_OPow(T_a,V_B_2))) # label(fact_Pow__bottom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 373 (all V_n_2 (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].
% 2.24/2.59 374 (all V_x (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].
% 2.24/2.59 375 (all V_x (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].
% 2.24/2.59 376 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> 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].
% 2.24/2.59 377 (all V_n_2 (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)) <-> 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].
% 2.24/2.59 378 (all V_u_2 all T_a (class_Orderings_Olinorder(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(T_a,V_u_2))) # label(fact_ivl__disj__un_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 379 (all V_xa_2 all T_a c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_xa_2) # label(fact_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 380 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I19_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 381 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 382 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 383 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I18_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 384 (all V_n_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_n_2)) # label(fact_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 385 (all V_m_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) # label(fact_atLeastLessThan0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 386 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) -> V_b_2 = V_d_2))))) # label(fact_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 387 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) -> V_a_2 = V_c_2))))) # label(fact_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 388 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) -> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) <-> V_a_2 = V_c_2 & V_b_2 = V_d_2))))) # label(fact_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 389 (all V_Pa_2 all V_n_2 ((all B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2) -> hBOOL(hAPP(V_Pa_2,B_m)))) <-> (all B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 390 (all V_Pa_2 all V_n_2 ((exists B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2) & hBOOL(hAPP(V_Pa_2,B_m)))) <-> (exists B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 391 (all V_a_2 all V_b_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) -> c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_atLeastLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 392 (all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) <-> -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_atLeastLessThan__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 393 (all V_b_2 all V_a_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_atLeastLessThan__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 394 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2)))) # label(fact_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 395 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 396 (all V_k_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_k_2) -> c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_greaterThanAtMost__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 397 (all V_l_2 all V_k_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) <-> -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2)))) # label(fact_greaterThanAtMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 398 (all V_l_2 all V_k_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2)))) # label(fact_greaterThanAtMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 399 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 400 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 401 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OlessThan(T_a,V_u_2)))) # label(fact_ivl__disj__un_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 402 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2)) = c_SetInterval_Oord__class_OatLeast(T_a,V_l_2)))) # label(fact_ivl__disj__un_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 403 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I22_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 404 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatMost(T_a,V_u_2)))) # label(fact_ivl__disj__un_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 405 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2)) = c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2)))) # label(fact_ivl__disj__un_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 406 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 407 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_m_2) -> (c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 408 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 409 (all V_u_2 all V_l_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 410 (all V_B_2 all V_xa_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2)) <-> (c_member(T_a,V_xa_2,V_B_2) -> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & (-c_member(T_a,V_xa_2,V_B_2) -> (c_member(T_a,V_xa_2,V_A_2) -> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)) & (-c_member(T_a,V_xa_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 411 (all V_n_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_n_2),c_SetInterval_Oord__class_OatLeast(T_a,V_n_2)) = c_Set_Oinsert(T_a,V_n_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_atMost__Int__atLeast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 412 (all V_n_2 c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal))) # label(fact_Nats__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 413 (all T_a (class_GCD_Ogcd(T_a) -> c_GCD_Ogcd__class_OGcd(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_Gcd__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 414 (all V_B_2 all V_xa_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2) -> (c_member(T_a,V_xa_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))))) # label(fact_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 415 (all T_a all V_B_2 all V_xa_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_xa_2)) -> (hBOOL(hAPP(V_B_2,V_xa_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))))) # label(fact_inf1I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 416 (all V_xa_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)) -> -(hBOOL(hAPP(V_A_2,V_xa_2)) -> -hBOOL(hAPP(V_B_2,V_xa_2))))) # label(fact_inf1E) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 417 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -(c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 418 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_IntI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 419 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -(c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_DiffE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 420 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_DiffI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 421 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 422 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2)) # label(fact_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 423 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 424 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Obot__class_Obot(T_a),V_x) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 425 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z),V_x) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_z,V_x)))) # label(fact_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 426 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_z,V_x)))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 427 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 428 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 429 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = V_x)) # label(fact_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 430 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)) = V_x)) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 431 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Otop__class_Otop(T_a),V_x) = V_x)) # label(fact_inf__top__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 432 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)) = V_x)) # label(fact_inf__top__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 433 (all V_ya_2 all V_xa_2 all T_a (class_Lattices_Obounded__lattice__top(T_a) -> (c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2) = c_Orderings_Otop__class_Otop(T_a) <-> V_xa_2 = c_Orderings_Otop__class_Otop(T_a) & V_ya_2 = c_Orderings_Otop__class_Otop(T_a)))) # label(fact_inf__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 434 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) <-> c_member(T_a,V_c_2,V_A_2) & c_member(T_a,V_c_2,V_B_2))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 435 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_A_2))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 436 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_B_2))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 437 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) <-> c_member(T_a,V_c_2,V_A_2) & -c_member(T_a,V_c_2,V_B_2))) # label(fact_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 438 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_A_2))) # label(fact_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 439 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -c_member(T_a,V_c_2,V_B_2))) # label(fact_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 440 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_B_2) -> B_x != B_xa)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 441 (all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 442 (all V_B_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 443 (all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 444 (all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2) # label(fact_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 445 (all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 446 (all V_B_2 all V_A_2 all V_a_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_A_2),c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 447 (all V_B_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = V_B_2) # label(fact_Int__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 448 (all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2) # label(fact_Int__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 449 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 450 (all V_B_2 all V_A_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 451 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 452 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2)) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 453 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)) # label(fact_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 454 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 455 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = V_A_2))) # label(fact_double__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 456 (all V_B_2 all V_D_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_D_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 457 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 458 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 459 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 460 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 461 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 462 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 463 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 464 (all V_A_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 465 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 466 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 467 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 468 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = V_A_2) # label(fact_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 469 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 470 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x) = V_x)) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 471 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 472 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 473 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 474 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 475 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 476 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 477 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 478 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 479 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 480 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 481 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 482 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 483 (all V_xa_2 all V_B_2 all V_A_2 all T_b all T_a (class_Groups_Ominus(T_a) -> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_xa_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_xa_2),hAPP(V_B_2,V_xa_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 484 (all V_xa_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)))) # label(fact_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 485 (all V_B_2 all V_A_2 all T_a c_Set_OPow(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2))) # label(fact_Pow__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 486 (all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) = V_A_2) # label(fact_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 487 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 488 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 489 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 490 (all V_B_2 all V_A_2 all V_C_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2))) # label(fact_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 491 (all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 492 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 493 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 494 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 495 (all V_B_2 all V_C_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),V_B_2)) # label(fact_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 496 (all V_xa_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)) -> hBOOL(hAPP(V_A_2,V_xa_2)))) # label(fact_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 497 (all V_xa_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)) -> hBOOL(hAPP(V_B_2,V_xa_2)))) # label(fact_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 498 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_less__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 499 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_less__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 500 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b))))) # label(fact_le__infE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 501 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d)))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 502 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 503 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 504 (all V_x all V_y all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_y))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 505 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_x))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 506 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 507 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 508 (all V_z_2 all V_ya_2 all V_xa_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_ya_2,V_z_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_z_2)))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 509 (all V_ya_2 all V_xa_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2) = V_xa_2))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 510 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 511 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 512 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 513 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.59 514 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))))) # label(fact_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 515 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))))) # label(fact_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 516 (all V_B_2 all V_C_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 517 (all V_B_2 all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 518 (all V_B_2 all V_C_2 all V_a_2 all T_a (-c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 519 (all V_B_2 all V_A_2 all V_a_2 all T_a (-c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 520 (all V_B_2 all V_C_2 all V_a_2 all T_a ((c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) & (-c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)))) # label(fact_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 521 (all V_B_2 all V_A_2 all V_a_2 all T_a ((c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) & (-c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 522 (all V_A_2 all V_B_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,V_B_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 523 (all V_A_2 all V_B_2 all V_xa_2 all T_a ((c_member(T_a,V_xa_2,V_B_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & (-c_member(T_a,V_xa_2,V_B_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2) = c_Set_Oinsert(T_a,V_xa_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 524 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Set_Oinsert(T_a,V_a_2,V_A_2)) # label(fact_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 525 (all V_B_2 all V_a_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)) # label(fact_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 526 (all V_B_2 all V_a_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 527 (all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Diff__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 528 (all V_m_2 all V_n_2 all V_i_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_i_2,V_n_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_n_2)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2,V_m_2)))) # label(fact_ivl__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 529 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 530 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 531 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) = V_B_2)) # label(fact_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 532 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)))) # label(fact_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 533 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 534 (all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2)) # label(fact_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 535 (all V_A_2 all V_xa_2 all T_a (-c_member(T_a,V_xa_2,V_A_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2)) # label(fact_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 536 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 537 (all V_k_2 all T_a (class_Orderings_Oorder(T_a) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(T_a,V_k_2)) = c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 538 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 539 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 540 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 541 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 542 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 543 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 544 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 545 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 546 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 547 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 548 (all V_u_2 all V_m_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 549 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 550 (all V_u_2 all V_l_2 all T_a (class_Orderings_Oorder(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 551 (all T_a (class_Rings_Osemiring__1(T_a) -> c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_ONats(T_a)))) # label(fact_Nats__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 552 (all V_B_2 all V_xa_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2)) <-> (c_member(T_a,V_xa_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)) & (-c_member(T_a,V_xa_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 553 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 554 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 555 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 556 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 557 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 558 (all V_n all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 559 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 560 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 561 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 562 (all V_n all V_k all V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 563 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 564 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 565 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 566 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 567 (all V_n all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i)) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 568 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 569 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 570 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 571 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 572 (all V_x all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) -> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a))) # label(fact_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 573 (all V_x all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) -> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a))) # label(fact_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 574 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 575 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 576 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 577 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 578 (all V_n_2 all V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 579 (all V_c all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 580 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 581 (all V_xa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_xa_2 <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 582 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (V_a_2 = V_b_2 <-> V_c_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 583 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 584 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 585 (all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_a_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 586 (all V_Q_2 all V_Pa_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> ((all B_x (c_member(T_a,B_x,V_A_2) -> (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Q_2,B_x))))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2)))))) # label(fact_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 587 (all V_ya_2 all V_z_2 all V_f_2 all T_b all V_A_2 all V_xa_2 all T_a (c_member(T_a,V_xa_2,V_A_2) -> (c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_ya_2) -> c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_xa_2),V_ya_2))))) # label(fact_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 588 (all V_p_2 all T_a (class_Groups_Ozero(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 589 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 590 (all V_z_2 all V_f_2 all T_b all T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2)) # label(fact_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 591 (all V_a2_2 all V_a1_2 all T_b all T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2)) # label(fact_fold__graph_H_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 592 (all V_a5_2 all V_a1_2 all V_a2_2 all V_a4_2 all V_a3_2 all T_b all T_a (c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) <-> V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 | (exists B_x exists B_y (hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) & c_member(T_a,B_x,V_a2_2) & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,B_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y))))) # label(fact_fold__graph_H_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 593 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))) # label(fact_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 594 (all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) -> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) = c_Set_Oinsert(tc_Nat_Onat,V_n_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2))) & (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) -> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_atLeastLessThanSuc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 595 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 596 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 597 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 598 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 599 (all V_k all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 600 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 601 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 602 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 603 (all V_nat_H_1 c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 604 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 605 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 606 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 607 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 608 (all V_k_2 c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2)) # label(fact_atLeast__Suc__greaterThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 609 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 610 (all V_y all V_x (c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 611 (all V_nat_H_2 all V_nat_2 (c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 612 (all V_n c_Nat_OSuc(V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 613 (all V_n V_n != c_Nat_OSuc(V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 614 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 615 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> V_m = c_Nat_OSuc(V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 616 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 617 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 618 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = c_Nat_OSuc(V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 619 (all V_n_2 all V_m_2 (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 620 (all V_n -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 621 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 622 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 623 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 624 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 625 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Nat_OSuc(V_m) != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 626 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 627 (all V_m all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m)) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 628 (all V_m_2 all V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> V_n_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 629 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 630 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 631 (all V_n_2 all V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 632 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastSucAtMost__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 633 (all V_xa_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_xa_2 <-> V_xa_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 634 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 635 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 636 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 637 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 638 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = c_Nat_OSuc(B_j) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2))))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 639 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 640 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) <-> (exists B_m V_n_2 = c_Nat_OSuc(B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 641 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 642 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 643 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 644 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 645 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 646 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 647 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 648 (all V_n all V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 649 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 650 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Omonoseq(T_a,V_X_2) <-> (all B_n c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))) | (all B_n c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n)))))) # label(fact_monoseq__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 651 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,c_Nat_OSuc(V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 652 (all V_k_2 c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_greaterThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 653 (all T_a (class_Rings_Osemiring__1(T_a) -> c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_ONats(T_a)))) # label(fact_Nats__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 654 (all V_k_2 c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2))) # label(fact_lessThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 655 (all V_k_2 c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2))) # label(fact_atMost__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 656 (all V_f_2 (c_SEQ_Osubseq(V_f_2) <-> (all B_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_n),hAPP(V_f_2,c_Nat_OSuc(B_n)))))) # label(fact_subseq__Suc__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 657 (all V_k_2 c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2)) # label(fact_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 658 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n)) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 659 (all V_i all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 660 (all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))) # label(fact_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 661 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) = c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_atLeastAtMostSuc__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 662 (all V_m_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_m_2)) = c_Set_Oinsert(tc_Nat_Onat,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_atLeastLessThan__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 663 (all V_k_2 c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2)) = c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_atLeast__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 664 (all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2)) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_j_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) # label(fact_interval__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 665 (all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 666 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 667 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 668 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 669 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 670 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2))) # label(fact_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 671 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 672 (all T_a (class_GCD_Ogcd(T_a) -> c_GCD_Ogcd__class_OLcm(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a))) # label(fact_Lcm__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.60 673 (all V_r (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) -> (exists B_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)))))) # label(fact_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 674 (all V_r (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) -> (exists B_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))))) # label(fact_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 675 (all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) # label(fact_interval__plus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 676 (all V_n all V_z (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) -> 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].
% 2.24/2.61 677 (all V_x all V_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,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].
% 2.24/2.61 678 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 679 (all V_n_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 680 (all V_n_2 all V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 681 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 682 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 683 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i)))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 684 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m)))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 685 (all V_m all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 686 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 687 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 688 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 689 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 690 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2) <-> V_b_2 = V_c_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 691 (all V_c_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2) <-> V_b_2 = V_c_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 692 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 693 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 694 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 695 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 696 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> 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].
% 2.24/2.61 697 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 698 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 699 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 700 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 701 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 702 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 703 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 704 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 705 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 706 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 707 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> 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].
% 2.24/2.61 708 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 709 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)))) # label(fact_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 710 (all V_j all V_i -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 711 (all V_i all V_j -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 712 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 713 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 714 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 715 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 716 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 717 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 718 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 719 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 720 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 721 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 722 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 723 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 724 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 725 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 726 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 727 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 728 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 729 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 730 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 731 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 732 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 733 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 734 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 735 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 736 (all V_k all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 737 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 738 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 739 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = 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].
% 2.24/2.61 740 (all V_n all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 741 (all V_n_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 742 (all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 743 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 744 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 745 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 746 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_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].
% 2.24/2.61 747 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 748 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 749 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = 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].
% 2.24/2.61 750 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = 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].
% 2.24/2.61 751 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 752 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 753 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) <-> 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].
% 2.24/2.61 754 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> 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].
% 2.24/2.61 755 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 756 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 757 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 758 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 759 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 760 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 761 (all V_ya_2 all V_xa_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2) -> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 762 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 763 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> 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].
% 2.24/2.61 764 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) <-> 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].
% 2.24/2.61 765 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m) # label(fact_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 766 (all V_m all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m) # label(fact_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 767 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 768 (all V_n all V_m all V_k c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 769 (all V_n all V_k all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 770 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 771 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 772 (all V_d all V_b all V_c all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)))) # label(fact_Deriv_Oadd__diff__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 773 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 774 (all V_n all V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 775 (all V_n c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 776 (all V_n c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 777 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 778 (all V_i_2 all V_k_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 779 (all V_m all V_n all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 780 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 781 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 782 (all V_i_2 all V_j_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 783 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 784 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2 <-> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2)))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 785 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 786 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 787 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 788 (all V_b_2 all V_a_2 all T_a (class_Rings_Osemiring__1(T_a) -> (c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a)) -> (c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a)) -> c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))))) # label(fact_Nats__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 789 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = 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].
% 2.24/2.61 790 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = 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].
% 2.24/2.61 791 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 792 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 793 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 794 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 795 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 796 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 797 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 798 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,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) = 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].
% 2.24/2.61 799 (all V_b_2 all V_a_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (all B_d (V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) -> hBOOL(hAPP(V_Pa_2,B_d)))))) # label(fact_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 800 (all V_b_2 all V_a_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) & -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) & -hBOOL(hAPP(V_Pa_2,B_d))))))) # label(fact_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 801 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)))) # label(fact_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 802 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 803 (all V_n c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = 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].
% 2.24/2.61 804 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2))))) # label(fact_atLeastLessThan__add__Un) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 805 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 2.24/2.61 806 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 807 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),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].
% 2.24/2.61 808 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,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].
% 2.24/2.61 809 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> 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].
% 2.24/2.61 810 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) <-> (exists B_n V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 811 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (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].
% 2.24/2.61 812 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 813 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 814 (all T_a (class_Rings_Oring__1(T_a) -> c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_OInts(T_a)))) # label(fact_Ints__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 815 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__1(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a)) -> c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)))))) # label(fact_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 816 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__1(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a)) -> c_member(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)))))) # label(fact_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 817 (all T_a (class_Rings_Oring__1(T_a) -> c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Oring__1__class_OInts(T_a)))) # label(fact_Ints__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 818 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 819 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 820 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 821 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 822 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 823 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 824 (all V_n_2 c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal))) # label(fact_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 825 (all V_a_2 all T_a (class_Int_Oring__char__0(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> (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_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 826 (all V_a_2 all T_a (class_Int_Oring__char__0(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 827 (all V_a_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 828 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 829 (all V_n_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_Pa_2,V_n_2)) -> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) & (all B_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) -> -hBOOL(hAPP(V_Pa_2,B_i)))) & hBOOL(hAPP(V_Pa_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 830 (all V_v (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) -> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 831 (all V_w_2 all T_a (class_Int_Onumber__ring(T_a) -> c_member(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Oring__1__class_OInts(T_a)))) # label(fact_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 832 (all V_ya_2 all V_xa_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2)))) # label(fact_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 833 (all V_ya_2 all V_xa_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,V_ya_2)))) # label(fact_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.61 834 (all V_ya_2 all V_xa_2 all T_a (class_Int_Onumber__ring(T_a) & class_Int_Oring__char__0(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_xa_2) = c_Int_Onumber__class_Onumber__of(T_a,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 835 (all V_xa_2 all V_w_2 all T_a (class_Int_Onumber(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_xa_2 <-> V_xa_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))) # label(fact_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 836 (all V_w_2 all V_v_2 all T_a (class_Int_Onumber(T_a) & class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) <-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))))) # label(fact_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 837 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 838 (all V_c all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c))) # label(fact_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 839 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 840 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)))) # label(fact_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 841 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z))) # label(fact_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 842 (all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2) -> c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,V_M_2) = c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_M_2,c_Set_Oinsert(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))) # label(fact_Gcd__remove0__nat) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 843 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a)))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 844 (all V_u_2 all V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2))) # label(fact_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 845 (all V_u_2 all V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) # label(fact_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 846 (all V_k_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2))) # label(fact_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 847 (all V_k_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2))) # label(fact_finite__atMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 848 (all V_u_2 all V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) # label(fact_finite__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 849 (all V_u_2 all V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) # label(fact_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 850 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__1(T_a) -> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a)) -> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a)) -> c_member(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)))))) # label(fact_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 851 (all V_n c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) # label(fact_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 852 (all V_n c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) # label(fact_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 853 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 854 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 855 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z))) # label(fact_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 856 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)))) # label(fact_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 857 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 858 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Oring(T_b) -> c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))))) # label(fact_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 859 (all V_c all V_b all V_v all T_b (class_Int_Onumber(T_b) & class_Rings_Oring(T_b) -> c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)))) # label(fact_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 860 (all V_w all V_v c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))) # label(fact_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 861 (all V_c all V_b all V_v all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)))) # label(fact_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 862 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))))) # label(fact_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 863 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 864 (all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 865 (all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 866 (all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),c_Set_Oinsert(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))) # label(fact_interval__plus__one__int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 867 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 868 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_u_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 869 (all V_z all V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 870 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 871 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 872 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) | V_w_2 = V_z_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 873 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastPlusOneAtMost__greaterThanAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 874 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 875 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 876 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 877 (all V_n all V_m all V_k c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 878 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 879 (all V_z all V_z_H all V_w all V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 880 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 881 (all V_w all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w))) # label(fact_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 882 (all V_w all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 883 (all V_z3 all V_z2 all V_z1 c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 884 (all V_z2 all V_z1 all V_w c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 885 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 886 (all V_w all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 887 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 888 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 889 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 890 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 891 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 892 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) <-> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 893 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) <-> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) = V_d_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 894 (all V_ya_2 all V_xa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 895 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 896 (all V_z2 all V_z1 all V_w c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))) # label(fact_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 897 (all V_w all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))) # label(fact_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 898 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 899 (all V_w c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w)) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 900 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 901 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 902 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 903 (all V_w_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) & V_z_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 904 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) | V_x = V_y | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 905 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) -> (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 906 (all V_z_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 907 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 908 (all V_ya_2 all V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 909 (all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2) -> (V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) -> (c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2))))) # label(fact_Lcm0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 910 (all V_b_2 all V_a_2 all T_a (class_Rings_Osemiring__1(T_a) -> (c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a)) -> (c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a)) -> c_member(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))))) # label(fact_Nats__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 911 (all V_z 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].
% 2.24/2.62 912 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 913 (all V_n c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 914 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 915 (all V_n c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 916 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 917 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 918 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 919 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 920 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 921 (all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2) -> (c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2) -> c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_Lcm__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 922 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 923 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 924 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 925 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 926 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 927 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 928 (all V_ya_2 all V_xa_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 929 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 930 (all V_y all V_x all V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y))))) # label(fact_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 931 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 932 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 933 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 934 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 935 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 936 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 937 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 938 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 939 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 940 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) = V_a)) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 941 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = V_x)) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 942 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 943 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) = 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].
% 2.24/2.62 944 (all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) <-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x,B_m))))) # label(fact_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 945 (all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) <-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,B_m))))) # label(fact_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 946 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a) | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 947 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 948 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (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].
% 2.24/2.62 949 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 950 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 951 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 952 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 953 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 954 (all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 955 (all V_n c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 956 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 957 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 958 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_RComplete_Onatfloor(V_a),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a,V_b)))))) # label(fact_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 959 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 960 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 961 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 962 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 963 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 964 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 965 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 966 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 967 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 968 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 969 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 970 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 971 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 972 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oidom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 973 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 974 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 975 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 976 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 977 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 978 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 979 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 980 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 981 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 982 (all T_2 all T_1 (class_Lattices_Odistrib__lattice(T_1) -> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 983 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 984 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Olattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Olattice) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 985 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 986 (all T_2 all T_1 (class_Orderings_Otop(T_1) -> class_Orderings_Otop(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Otop) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 987 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 988 (all T_2 all T_1 (class_Orderings_Obot(T_1) -> class_Orderings_Obot(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 989 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 990 (all T_1 (class_Rings_Oidom(T_1) -> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 991 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 992 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 993 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 994 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 995 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 996 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 997 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 998 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 999 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.62 1000 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1001 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1002 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1003 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1004 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1005 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1006 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1007 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1008 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1009 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1010 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__idom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1011 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1012 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1013 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__group__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1014 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1015 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1016 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 1017 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.63 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].
% 2.24/2.72 1019 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1020 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 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].
% 2.24/2.72 1022 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1023 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1024 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 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].
% 2.24/2.72 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].
% 2.24/2.72 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].
% 2.24/2.72 1028 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 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].
% 2.24/2.72 1030 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Oring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1031 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Int_Onumber(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Int_Onumber) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1032 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Oone(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oone) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1033 (all V_y_2 all V_x_2 (-hBOOL(hAPP(c_fequal(V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72 1034 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(c_fequal(V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.72
% 2.24/2.72 ============================== end of process non-clausal formulas ===
% 2.24/2.72
% 2.24/2.72 ============================== PROCESS INITIAL CLAUSES ===============
% 2.24/2.72
% 2.24/2.72 ============================== PREDICATE ELIMINATION =================
% 2.24/2.72 1035 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.24/2.72 1036 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom). [clausify(12)].
% 2.24/2.72 1037 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(20)].
% 2.24/2.72 1038 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(20)].
% 2.24/2.72 1039 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(20)].
% 2.24/2.72 1040 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(21)].
% 2.24/2.72 1041 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(21)].
% 2.24/2.72 1042 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | B != C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(21)].
% 2.24/2.72 1043 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__less__linear) # label(axiom). [clausify(22)].
% 2.24/2.72 1044 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | C = B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(23)].
% 2.24/2.72 1045 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) | C != B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(23)].
% 2.24/2.72 1046 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neqE) # label(axiom). [clausify(24)].
% 2.24/2.72 1047 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__cases) # label(axiom). [clausify(39)].
% 2.24/2.72 1048 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,B,C) | B = C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(47)].
% 2.24/2.72 1049 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,C) | B != C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(47)].
% 2.24/2.72 1050 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_leD) # label(axiom). [clausify(49)].
% 2.24/2.72 1051 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B = C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(52)].
% 2.24/2.72 1052 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | B != C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(52)].
% 2.24/2.72 1053 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__leE) # label(axiom). [clausify(53)].
% 2.24/2.72 1054 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_leI) # label(axiom). [clausify(54)].
% 2.24/2.72 1055 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(58)].
% 2.24/2.72 1056 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(59)].
% 2.24/2.72 1057 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(59)].
% 2.24/2.72 1058 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(60)].
% 2.24/2.72 1059 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(60)].
% 2.24/2.72 1060 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom). [clausify(63)].
% 2.24/2.72 1061 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | -c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E)) | c_Orderings_Oord__class_Oless(B,D,E) # label(fact_strict__mono__less) # label(axiom). [clausify(165)].
% 2.24/2.72 1062 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E)) | -c_Orderings_Oord__class_Oless(B,D,E) # label(fact_strict__mono__less) # label(axiom). [clausify(165)].
% 2.24/2.72 1063 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(C,D),hAPP(C,E)) | c_Orderings_Oord__class_Oless__eq(B,D,E) # label(fact_strict__mono__less__eq) # label(axiom). [clausify(167)].
% 2.24/2.72 1064 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(C,D),hAPP(C,E)) | -c_Orderings_Oord__class_Oless__eq(B,D,E) # label(fact_strict__mono__less__eq) # label(axiom). [clausify(167)].
% 2.24/2.72 1065 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | hAPP(C,D) != hAPP(C,E) | D = E # label(fact_strict__mono__eq) # label(axiom). [clausify(173)].
% 2.24/2.72 1066 -class_Orderings_Oorder(A) | -class_Orderings_Olinorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(B,A,C) | hAPP(C,D) = hAPP(C,E) | D != E # label(fact_strict__mono__eq) # label(axiom). [clausify(173)].
% 2.24/2.72 1067 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C)) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_lessThan__strict__subset__iff) # label(axiom). [clausify(221)].
% 2.24/2.72 1068 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C)) | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_lessThan__strict__subset__iff) # label(axiom). [clausify(221)].
% 2.24/2.72 1069 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(A,B),c_SetInterval_Oord__class_OgreaterThan(A,C)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_greaterThan__subset__iff) # label(axiom). [clausify(222)].
% 2.24/2.72 1070 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(A,B),c_SetInterval_Oord__class_OgreaterThan(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_greaterThan__subset__iff) # label(axiom). [clausify(222)].
% 2.24/2.72 1071 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_lessThan__subset__iff) # label(axiom). [clausify(225)].
% 2.24/2.72 1072 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_lessThan__subset__iff) # label(axiom). [clausify(225)].
% 2.24/2.72 1073 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(A,B) != c_SetInterval_Oord__class_OlessThan(A,C) | B = C # label(fact_lessThan__eq__iff) # label(axiom). [clausify(226)].
% 2.24/2.72 1074 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(A,B) = c_SetInterval_Oord__class_OlessThan(A,C) | B != C # label(fact_lessThan__eq__iff) # label(axiom). [clausify(226)].
% 2.24/2.72 1075 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThan(A,B) != c_SetInterval_Oord__class_OgreaterThan(A,C) | B = C # label(fact_greaterThan__eq__iff) # label(axiom). [clausify(227)].
% 2.24/2.72 1076 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThan(A,B) = c_SetInterval_Oord__class_OgreaterThan(A,C) | B != C # label(fact_greaterThan__eq__iff) # label(axiom). [clausify(227)].
% 2.24/2.72 1077 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeast(A,B) != c_SetInterval_Oord__class_OatLeast(A,C) | B = C # label(fact_atLeast__eq__iff) # label(axiom). [clausify(236)].
% 2.24/2.72 1078 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeast(A,B) = c_SetInterval_Oord__class_OatLeast(A,C) | B != C # label(fact_atLeast__eq__iff) # label(axiom). [clausify(236)].
% 2.24/2.72 1079 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatMost(A,B) != c_SetInterval_Oord__class_OatMost(A,C) | B = C # label(fact_atMost__eq__iff) # label(axiom). [clausify(237)].
% 2.24/2.72 1080 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatMost(A,B) = c_SetInterval_Oord__class_OatMost(A,C) | B != C # label(fact_atMost__eq__iff) # label(axiom). [clausify(237)].
% 2.24/2.72 1081 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C)) = c_SetInterval_Oord__class_OatLeast(A,B) # label(fact_ivl__disj__un_I13_J) # label(axiom). [clausify(238)].
% 2.24/2.72 1082 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)) = c_SetInterval_Oord__class_OatMost(A,C) # label(fact_ivl__disj__un_I10_J) # label(axiom). [clausify(239)].
% 2.24/2.72 1083 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C)) = c_SetInterval_Oord__class_OgreaterThan(A,B) # label(fact_ivl__disj__un_I12_J) # label(axiom). [clausify(327)].
% 2.24/2.72 1084 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)) = c_SetInterval_Oord__class_OlessThan(A,C) # label(fact_ivl__disj__un_I7_J) # label(axiom). [clausify(328)].
% 2.24/2.72 1085 -class_Orderings_Olinorder(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(A,B)) = c_SetInterval_Oord__class_OatLeast(A,B) # label(fact_ivl__disj__un_I1_J) # label(axiom). [clausify(330)].
% 2.24/2.72 1086 -class_Orderings_Olinorder(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(A,B) # label(fact_ivl__disj__un_I2_J) # label(axiom). [clausify(378)].
% 2.24/2.72 1087 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D)) # label(fact_ivl__disj__un_I19_J) # label(axiom). [clausify(380)].
% 2.24/2.72 1088 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) # label(fact_ivl__disj__un_I4_J) # label(axiom). [clausify(381)].
% 2.24/2.72 1089 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,C) # label(fact_ivl__disj__un_I5_J) # label(axiom). [clausify(382)].
% 2.24/2.72 1090 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,D) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D)) # label(fact_ivl__disj__un_I18_J) # label(axiom). [clausify(383)].
% 2.24/2.72 1091 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) != c_SetInterval_Oord__class_OatLeastLessThan(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | E = C # label(fact_atLeastLessThan__inj_I2_J) # label(axiom). [clausify(386)].
% 2.24/2.72 1092 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) != c_SetInterval_Oord__class_OatLeastLessThan(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | B = D # label(fact_atLeastLessThan__inj_I1_J) # label(axiom). [clausify(387)].
% 2.24/2.72 1093 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) != c_SetInterval_Oord__class_OatLeastLessThan(A,D,E) | B = D # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(388)].
% 2.24/2.72 1094 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) != c_SetInterval_Oord__class_OatLeastLessThan(A,D,E) | E = C # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(388)].
% 2.24/2.72 1095 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) = c_SetInterval_Oord__class_OatLeastLessThan(A,D,E) | B != D | E != C # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(388)].
% 2.24/2.72 1096 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)) | c_Orderings_Oord__class_Oless__eq(A,C,B) | c_Orderings_Oord__class_Oless__eq(A,D,B) # label(fact_atLeastLessThan__subset__iff) # label(axiom). [clausify(394)].
% 2.24/2.72 1097 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)) | c_Orderings_Oord__class_Oless__eq(A,C,B) | c_Orderings_Oord__class_Oless__eq(A,C,E) # label(fact_atLeastLessThan__subset__iff) # label(axiom). [clausify(394)].
% 2.24/2.72 1098 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D)) # label(fact_ivl__disj__un_I17_J) # label(axiom). [clausify(395)].
% 2.24/2.72 1099 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D)) # label(fact_ivl__disj__un_I20_J) # label(axiom). [clausify(399)].
% 2.24/2.72 1100 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,D) # label(fact_ivl__disj__un_I21_J) # label(axiom). [clausify(400)].
% 2.24/2.72 1101 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)) = c_SetInterval_Oord__class_OlessThan(A,C) # label(fact_ivl__disj__un_I8_J) # label(axiom). [clausify(401)].
% 2.24/2.72 1102 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C)) = c_SetInterval_Oord__class_OatLeast(A,B) # label(fact_ivl__disj__un_I14_J) # label(axiom). [clausify(402)].
% 2.24/2.72 1103 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,D) # label(fact_ivl__disj__un_I22_J) # label(axiom). [clausify(403)].
% 2.24/2.72 1104 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)) = c_SetInterval_Oord__class_OatMost(A,C) # label(fact_ivl__disj__un_I9_J) # label(axiom). [clausify(404)].
% 2.24/2.72 1105 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C)) = c_SetInterval_Oord__class_OgreaterThan(A,B) # label(fact_ivl__disj__un_I11_J) # label(axiom). [clausify(405)].
% 2.24/2.72 1106 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D)) # label(fact_ivl__disj__un_I15_J) # label(axiom). [clausify(406)].
% 2.24/2.72 1107 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,D) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D)) # label(fact_ivl__disj__un_I16_J) # label(axiom). [clausify(407)].
% 2.24/2.72 1108 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,C) # label(fact_ivl__disj__un_I6_J) # label(axiom). [clausify(408)].
% 2.24/2.72 1109 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)) # label(fact_ivl__disj__un_I3_J) # label(axiom). [clausify(409)].
% 2.24/2.72 1110 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,D),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,D) # label(fact_ivl__diff) # label(axiom). [clausify(528)].
% 2.24/2.72 1111 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(836)].
% 2.24/2.72 1112 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(836)].
% 2.24/2.72 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1035,a,1036,a)].
% 2.24/2.73 Derived: A = B | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1035,a,1037,a)].
% 2.24/2.73 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1035,a,1038,a)].
% 2.24/2.73 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1035,a,1039,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1035,a,1041,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | A = B. [resolve(1035,a,1048,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1035,a,1050,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | A != B. [resolve(1035,a,1052,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1035,a,1053,a)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1035,a,1061,b)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1035,a,1062,b)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D). [resolve(1035,a,1063,b)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D). [resolve(1035,a,1064,b)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | hAPP(B,C) != hAPP(B,D) | C = D. [resolve(1035,a,1065,b)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Int_Oint,A,B) | hAPP(B,C) = hAPP(B,D) | C != D. [resolve(1035,a,1066,b)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1035,a,1067,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1035,a,1068,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1035,a,1069,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1035,a,1070,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1035,a,1071,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1035,a,1072,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A) != c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B) | A = B. [resolve(1035,a,1073,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A) = c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B) | A != B. [resolve(1035,a,1074,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A) != c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B) | A = B. [resolve(1035,a,1075,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A) = c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B) | A != B. [resolve(1035,a,1076,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,A) != c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,B) | A = B. [resolve(1035,a,1077,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,A) = c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,B) | A != B. [resolve(1035,a,1078,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatMost(tc_Int_Oint,A) != c_SetInterval_Oord__class_OatMost(tc_Int_Oint,B) | A = B. [resolve(1035,a,1079,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatMost(tc_Int_Oint,A) = c_SetInterval_Oord__class_OatMost(tc_Int_Oint,B) | A != B. [resolve(1035,a,1080,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B)) = c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,A). [resolve(1035,a,1081,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OatMost(tc_Int_Oint,B). [resolve(1035,a,1082,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A). [resolve(1035,a,1083,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Int_Oint,A),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B). [resolve(1035,a,1084,a)].
% 2.24/2.73 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_Set_Oinsert(tc_Int_Oint,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A)) = c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,A). [resolve(1035,a,1085,a)].
% 2.24/2.73 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_Set_Oinsert(tc_Int_Oint,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(tc_Int_Oint,A). [resolve(1035,a,1086,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,C)). [resolve(1035,a,1087,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B),c_Set_Oinsert(tc_Int_Oint,B,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))). [resolve(1035,a,1088,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_Set_Oinsert(tc_Int_Oint,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B). [resolve(1035,a,1089,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,C)). [resolve(1035,a,1090,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | D = B. [resolve(1035,a,1091,a)].
% 2.24/2.73 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | A = C. [resolve(1035,a,1092,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C,D) | A != C | D != B. [resolve(1035,a,1095,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,A). [resolve(1035,a,1096,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,D). [resolve(1035,a,1097,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B,C)). [resolve(1035,a,1098,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,B,C)). [resolve(1035,a,1099,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C). [resolve(1035,a,1100,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,A),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_Int_Oint,B). [resolve(1035,a,1101,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,B)) = c_SetInterval_Oord__class_OatLeast(tc_Int_Oint,A). [resolve(1035,a,1102,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C). [resolve(1035,a,1103,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Int_Oint,A),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OatMost(tc_Int_Oint,B). [resolve(1035,a,1104,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint,A). [resolve(1035,a,1105,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B,C)). [resolve(1035,a,1106,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,C)). [resolve(1035,a,1107,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B),c_Set_Oinsert(tc_Int_Oint,B,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B). [resolve(1035,a,1108,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_Set_Oinsert(tc_Int_Oint,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)). [resolve(1035,a,1109,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A,B)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B,C). [resolve(1035,a,1110,a)].
% 2.24/2.73 1113 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1113,a,1036,a)].
% 2.24/2.73 Derived: A = B | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1113,a,1037,a)].
% 2.24/2.73 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1113,a,1038,a)].
% 2.24/2.73 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1113,a,1039,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1113,a,1041,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | A = B. [resolve(1113,a,1048,a)].
% 2.24/2.73 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1113,a,1050,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | A != B. [resolve(1113,a,1052,a)].
% 2.24/2.73 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1113,a,1053,a)].
% 2.24/2.73 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). [resolve(1113,a,1061,b)].
% 2.24/2.74 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). [resolve(1113,a,1062,b)].
% 2.24/2.74 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D). [resolve(1113,a,1063,b)].
% 2.24/2.74 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D). [resolve(1113,a,1064,b)].
% 2.24/2.74 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | hAPP(B,C) != hAPP(B,D) | C = D. [resolve(1113,a,1065,b)].
% 2.24/2.74 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Nat_Onat,A,B) | hAPP(B,C) = hAPP(B,D) | C != D. [resolve(1113,a,1066,b)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1113,a,1067,a)].
% 2.24/2.74 Derived: c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1113,a,1068,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1113,a,1069,a)].
% 2.24/2.74 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1113,a,1070,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(1113,a,1071,a)].
% 2.24/2.74 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(1113,a,1072,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A) != c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B) | A = B. [resolve(1113,a,1073,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A) = c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B) | A != B. [resolve(1113,a,1074,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A) != c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B) | A = B. [resolve(1113,a,1075,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A) = c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B) | A != B. [resolve(1113,a,1076,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,A) != c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,B) | A = B. [resolve(1113,a,1077,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,A) = c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,B) | A != B. [resolve(1113,a,1078,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,A) != c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,B) | A = B. [resolve(1113,a,1079,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,A) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,B) | A != B. [resolve(1113,a,1080,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B)) = c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,A). [resolve(1113,a,1081,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,B). [resolve(1113,a,1082,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A). [resolve(1113,a,1083,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,A),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B). [resolve(1113,a,1084,a)].
% 2.24/2.74 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A)) = c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,A). [resolve(1113,a,1085,a)].
% 2.24/2.74 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,A). [resolve(1113,a,1086,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)). [resolve(1113,a,1087,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B),c_Set_Oinsert(tc_Nat_Onat,B,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). [resolve(1113,a,1088,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B). [resolve(1113,a,1089,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,B,C)). [resolve(1113,a,1090,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | D = B. [resolve(1113,a,1091,a)].
% 2.24/2.74 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | A = C. [resolve(1113,a,1092,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D) | A != C | D != B. [resolve(1113,a,1095,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,A). [resolve(1113,a,1096,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,D). [resolve(1113,a,1097,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,C)). [resolve(1113,a,1098,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,C)). [resolve(1113,a,1099,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C). [resolve(1113,a,1100,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,A),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,B). [resolve(1113,a,1101,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,B)) = c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,A). [resolve(1113,a,1102,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C). [resolve(1113,a,1103,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,A),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,B). [resolve(1113,a,1104,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,A). [resolve(1113,a,1105,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,C)). [resolve(1113,a,1106,a)].
% 2.24/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,B,C)). [resolve(1113,a,1107,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B),c_Set_Oinsert(tc_Nat_Onat,B,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B). [resolve(1113,a,1108,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)). [resolve(1113,a,1109,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,C). [resolve(1113,a,1110,a)].
% 2.24/2.75 1114 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1114,a,1036,a)].
% 2.24/2.75 Derived: A = B | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1114,a,1037,a)].
% 2.24/2.75 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1114,a,1038,a)].
% 2.24/2.75 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1114,a,1039,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1114,a,1041,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | A = B. [resolve(1114,a,1048,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1114,a,1050,a)].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | A != B. [resolve(1114,a,1052,a)].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1114,a,1053,a)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1114,a,1061,b)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1114,a,1062,b)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D). [resolve(1114,a,1063,b)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D). [resolve(1114,a,1064,b)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | hAPP(B,C) != hAPP(B,D) | C = D. [resolve(1114,a,1065,b)].
% 2.24/2.75 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oorder__class_Ostrict__mono(tc_RealDef_Oreal,A,B) | hAPP(B,C) = hAPP(B,D) | C != D. [resolve(1114,a,1066,b)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1114,a,1067,a)].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1114,a,1068,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1114,a,1069,a)].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1114,a,1070,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1114,a,1071,a)].
% 2.24/2.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1114,a,1072,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A) != c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B) | A = B. [resolve(1114,a,1073,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A) = c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B) | A != B. [resolve(1114,a,1074,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A) != c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B) | A = B. [resolve(1114,a,1075,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A) = c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B) | A != B. [resolve(1114,a,1076,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,A) != c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,B) | A = B. [resolve(1114,a,1077,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,A) = c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,B) | A != B. [resolve(1114,a,1078,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,A) != c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,B) | A = B. [resolve(1114,a,1079,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,A) = c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,B) | A != B. [resolve(1114,a,1080,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B)) = c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,A). [resolve(1114,a,1081,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,B). [resolve(1114,a,1082,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A). [resolve(1114,a,1083,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B). [resolve(1114,a,1084,a)].
% 2.24/2.75 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_Set_Oinsert(tc_RealDef_Oreal,A,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A)) = c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,A). [resolve(1114,a,1085,a)].
% 2.24/2.75 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_Set_Oinsert(tc_RealDef_Oreal,A,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,A). [resolve(1114,a,1086,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1087,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B),c_Set_Oinsert(tc_RealDef_Oreal,B,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)))). [resolve(1114,a,1088,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_Set_Oinsert(tc_RealDef_Oreal,A,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B). [resolve(1114,a,1089,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1090,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | D = B. [resolve(1114,a,1091,a)].
% 2.24/2.75 Derived: c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B) != c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | A = C. [resolve(1114,a,1092,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B) = c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,C,D) | A != C | D != B. [resolve(1114,a,1095,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,A). [resolve(1114,a,1096,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,C,D)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,D). [resolve(1114,a,1097,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1098,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1099,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,C). [resolve(1114,a,1100,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OlessThan(tc_RealDef_Oreal,B). [resolve(1114,a,1101,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,B)) = c_SetInterval_Oord__class_OatLeast(tc_RealDef_Oreal,A). [resolve(1114,a,1102,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,C). [resolve(1114,a,1103,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,A),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OatMost(tc_RealDef_Oreal,B). [resolve(1114,a,1104,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,B)) = c_SetInterval_Oord__class_OgreaterThan(tc_RealDef_Oreal,A). [resolve(1114,a,1105,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1106,a)].
% 2.24/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_RealDef_Oreal,A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,B,C)). [resolve(1114,a,1107,a)].
% 2.24/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B),c_Set_Oinsert(tc_RealDef_Oreal,B,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_RealDef_Oreal,A,B). [resolve(1114,a,1108,a)].
% 2.24/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_Set_Oinsert(tc_RealDef_Oreal,A,c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_RealDef_Oreal,A,B)). [resolve(1114,a,1109,a)].
% 2.24/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Groups_Ominus__class_Ominus(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,A,B)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_RealDef_Oreal,B,C). [resolve(1114,a,1110,a)].
% 2.24/2.76 1115 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1016)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1036,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | B = C | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1037,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | B != C | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1038,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | B != C | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1039,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1041,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | B = C. [resolve(1115,b,1048,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1050,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | B != C. [resolve(1115,b,1052,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1053,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(B,hAPP(C,D),hAPP(C,E)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1115,b,1061,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(B,hAPP(C,D),hAPP(C,E)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1115,b,1062,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(B,hAPP(C,D),hAPP(C,E)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1115,b,1063,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(B,hAPP(C,D),hAPP(C,E)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1115,b,1064,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | hAPP(C,D) != hAPP(C,E) | D = E. [resolve(1115,b,1065,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -class_Orderings_Oorder(B) | -c_Orderings_Oorder__class_Ostrict__mono(tc_Polynomial_Opoly(A),B,C) | hAPP(C,D) = hAPP(C,E) | D != E. [resolve(1115,b,1066,b)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1067,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1068,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1069,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1115,b,1070,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1071,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1072,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B) != c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1115,b,1073,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B) = c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1115,b,1074,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B) != c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1115,b,1075,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B) = c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1115,b,1076,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),B) != c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1115,b,1077,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),B) = c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1115,b,1078,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),B) != c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1115,b,1079,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),B) = c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1115,b,1080,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C)) = c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1081,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),C). [resolve(1115,b,1082,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),C)) = c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1083,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C). [resolve(1115,b,1084,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_Set_Oinsert(tc_Polynomial_Opoly(A),B,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B)) = c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1085,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_Set_Oinsert(tc_Polynomial_Opoly(A),B,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1086,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1087,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C),c_Set_Oinsert(tc_Polynomial_Opoly(A),C,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool)))). [resolve(1115,b,1088,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_Set_Oinsert(tc_Polynomial_Opoly(A),B,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1089,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1090,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | E = C. [resolve(1115,b,1091,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | B = D. [resolve(1115,b,1092,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),D,E) | B != D | E != C. [resolve(1115,b,1095,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,B). [resolve(1115,b,1096,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,E). [resolve(1115,b,1097,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1098,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1099,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),C,D)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,D). [resolve(1115,b,1100,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OlessThan(tc_Polynomial_Opoly(A),C). [resolve(1115,b,1101,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),C)) = c_SetInterval_Oord__class_OatLeast(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1102,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),C,D)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,D). [resolve(1115,b,1103,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),B),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OatMost(tc_Polynomial_Opoly(A),C). [resolve(1115,b,1104,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),C)) = c_SetInterval_Oord__class_OgreaterThan(tc_Polynomial_Opoly(A),B). [resolve(1115,b,1105,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1106,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Polynomial_Opoly(A),B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),C,D)). [resolve(1115,b,1107,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C),c_Set_Oinsert(tc_Polynomial_Opoly(A),C,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Polynomial_Opoly(A),B,C). [resolve(1115,b,1108,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_Set_Oinsert(tc_Polynomial_Opoly(A),B,c_Orderings_Obot__class_Obot(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Polynomial_Opoly(A),B,C)). [resolve(1115,b,1109,a)].
% 2.24/2.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ominus__class_Ominus(tc_fun(tc_Polynomial_Opoly(A),tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,D),c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),B,C)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Polynomial_Opoly(A),C,D). [resolve(1115,b,1110,a)].
% 2.66/2.96 1116 class_Orderings_Odense__linorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Odense__linorder) # label(axiom). [assumption].
% 2.66/2.96 1117 -class_Orderings_Odense__linorder(A) | c_Orderings_Oord__class_Oless(A,f4(B,C,A),C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_dense__le) # label(axiom). [clausify(78)].
% 2.66/2.96 1118 -class_Orderings_Odense__linorder(A) | -c_Orderings_Oord__class_Oless__eq(A,f4(B,C,A),B) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_dense__le) # label(axiom). [clausify(78)].
% 2.66/2.96 1119 -class_Orderings_Odense__linorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,B,f5(D,C,B,A)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_dense__le__bounded) # label(axiom). [clausify(79)].
% 2.66/2.96 1120 -class_Orderings_Odense__linorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,f5(D,C,B,A),C) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_dense__le__bounded) # label(axiom). [clausify(79)].
% 2.66/2.96 1121 -class_Orderings_Odense__linorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,f5(D,C,B,A),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_dense__le__bounded) # label(axiom). [clausify(79)].
% 2.66/2.96 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,f4(A,B,tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1116,a,1117,a)].
% 2.66/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,f4(A,B,tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1116,a,1118,a)].
% 2.66/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,f5(C,B,A,tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1116,a,1119,a)].
% 2.66/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,f5(C,B,A,tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1116,a,1120,a)].
% 2.66/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,f5(C,B,A,tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1116,a,1121,a)].
% 2.66/2.96 1122 -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)) | c_Lubs_Osetle(A,C,D) # label(fact_isUb__def) # label(axiom). [clausify(142)].
% 2.66/2.96 1123 -class_Orderings_Oord(A) | -c_Lubs_Osetle(A,B,C) | -c_member(A,C,D) | hBOOL(hAPP(c_Lubs_OisUb(A,D,B),C)) # label(fact_isUbI) # label(axiom). [clausify(141)].
% 2.66/2.96 Derived: -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)) | -class_Orderings_Oord(A) | -c_member(A,D,E) | hBOOL(hAPP(c_Lubs_OisUb(A,E,C),D)). [resolve(1122,c,1123,b)].
% 2.66/2.96 1124 -class_Orderings_Oord(A) | hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)) | -c_Lubs_Osetle(A,C,D) | -c_member(A,D,B) # label(fact_isUb__def) # label(axiom). [clausify(142)].
% 2.66/2.96 1125 -class_Orderings_Oord(A) | -c_Lubs_Osetle(A,B,C) | -c_member(A,D,B) | c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_setle__def) # label(axiom). [clausify(148)].
% 2.66/2.96 Derived: -class_Orderings_Oord(A) | -c_member(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,D) | -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Lubs_OisUb(A,E,C),D)). [resolve(1125,b,1122,c)].
% 2.66/2.96 1126 -class_Orderings_Oord(A) | c_Lubs_Osetle(A,B,C) | c_member(A,f24(C,B,A),B) # label(fact_setle__def) # label(axiom). [clausify(148)].
% 2.66/2.96 Derived: -class_Orderings_Oord(A) | c_member(A,f24(B,C,A),C) | -class_Orderings_Oord(A) | -c_member(A,B,D) | hBOOL(hAPP(c_Lubs_OisUb(A,D,C),B)). [resolve(1126,b,1123,b)].
% 2.66/2.96 Derived: -class_Orderings_Oord(A) | c_member(A,f24(B,C,A),C) | -class_Orderings_Oord(A) | -c_member(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,D,B). [resolve(1126,b,1125,b)].
% 2.86/3.12 1127 -class_Orderings_Oord(A) | c_Lubs_Osetle(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,f24(C,B,A),C) # label(fact_setle__def) # label(axiom). [clausify(148)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,f24(B,C,A),B) | -class_Orderings_Oord(A) | -c_member(A,B,D) | hBOOL(hAPP(c_Lubs_OisUb(A,D,C),B)). [resolve(1127,b,1123,b)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,f24(B,C,A),B) | -class_Orderings_Oord(A) | -c_member(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,D,B). [resolve(1127,b,1125,b)].
% 2.86/3.12 1128 -class_Orderings_Oord(A) | -c_Lubs_OisLub(A,B,C,D) | c_Lubs_Osetle(A,C,D) # label(fact_isLubD1) # label(axiom). [clausify(150)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Lubs_OisLub(A,B,C,D) | -class_Orderings_Oord(A) | -c_member(A,D,E) | hBOOL(hAPP(c_Lubs_OisUb(A,E,C),D)). [resolve(1128,c,1123,b)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Lubs_OisLub(A,B,C,D) | -class_Orderings_Oord(A) | -c_member(A,E,C) | c_Orderings_Oord__class_Oless__eq(A,E,D). [resolve(1128,c,1125,b)].
% 2.86/3.12 1129 -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)) | c_Lubs_Osetle(A,C,D) # label(fact_isUbD2) # label(axiom). [clausify(151)].
% 2.86/3.12 1130 -class_Orderings_Oord(A) | -c_Lubs_Osetle(A,B,C) | -c_member(A,D,B) | c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_setleD) # label(axiom). [clausify(152)].
% 2.86/3.12 1131 -class_Orderings_Oord(A) | c_member(A,f28(B,C,A),C) | c_Lubs_Osetle(A,C,B) # label(fact_setleI) # label(axiom). [clausify(156)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | c_member(A,f28(B,C,A),C) | -class_Orderings_Oord(A) | -c_member(A,B,D) | hBOOL(hAPP(c_Lubs_OisUb(A,D,C),B)). [resolve(1131,c,1123,b)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | c_member(A,f28(B,C,A),C) | -class_Orderings_Oord(A) | -c_member(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,D,B). [resolve(1131,c,1125,b)].
% 2.86/3.12 1132 -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,f28(B,C,A),B) | c_Lubs_Osetle(A,C,B) # label(fact_setleI) # label(axiom). [clausify(156)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,f28(B,C,A),B) | -class_Orderings_Oord(A) | -c_member(A,B,D) | hBOOL(hAPP(c_Lubs_OisUb(A,D,C),B)). [resolve(1132,c,1123,b)].
% 2.86/3.12 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,f28(B,C,A),B) | -class_Orderings_Oord(A) | -c_member(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,D,B). [resolve(1132,c,1125,b)].
% 2.86/3.12 1133 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)) # label(fact_decseq__def) # label(axiom). [clausify(161)].
% 2.86/3.12 1134 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)) # label(fact_decseq__def) # label(axiom). [clausify(161)].
% 2.86/3.12 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)). [resolve(1133,b,1134,b)].
% 2.86/3.12 1135 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))) # label(fact_decseq__def) # label(axiom). [clausify(161)].
% 2.86/3.12 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)). [resolve(1135,b,1134,b)].
% 2.86/3.12 1136 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_decseq__imp__monoseq) # label(axiom). [clausify(213)].
% 2.86/3.12 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)). [resolve(1136,b,1133,b)].
% 2.86/3.12 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))). [resolve(1136,b,1135,b)].
% 3.08/3.40 1137 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)) # label(fact_incseq__def) # label(axiom). [clausify(162)].
% 3.08/3.40 1138 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) # label(fact_incseq__def) # label(axiom). [clausify(162)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)). [resolve(1137,b,1138,b)].
% 3.08/3.40 1139 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))) # label(fact_incseq__def) # label(axiom). [clausify(162)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)). [resolve(1139,b,1138,b)].
% 3.08/3.40 1140 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_incseq__imp__monoseq) # label(axiom). [clausify(212)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)). [resolve(1140,b,1137,b)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))). [resolve(1140,b,1139,b)].
% 3.08/3.40 1141 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f37(B,A),f38(B,A)) # label(fact_monoseq__def) # label(axiom). [clausify(198)].
% 3.08/3.40 1142 -class_Orderings_Oorder(A) | -c_SEQ_Omonoseq(A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)) # label(fact_monoseq__def) # label(axiom). [clausify(198)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f37(B,A),f38(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1141,b,1142,b)].
% 3.08/3.40 1143 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f37(B,A)),hAPP(B,f38(B,A))) # label(fact_monoseq__def) # label(axiom). [clausify(198)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f37(B,A)),hAPP(B,f38(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1143,b,1142,b)].
% 3.08/3.40 1144 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f39(B,A),f40(B,A)) # label(fact_monoseq__def) # label(axiom). [clausify(198)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f39(B,A),f40(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1144,b,1142,b)].
% 3.08/3.40 1145 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f40(B,A)),hAPP(B,f39(B,A))) # label(fact_monoseq__def) # label(axiom). [clausify(198)].
% 3.08/3.40 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f40(B,A)),hAPP(B,f39(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1145,b,1142,b)].
% 3.19/3.42 1146 -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f41(B,A),f42(B,A)) | c_SEQ_Omonoseq(A,B) # label(fact_monoI2) # label(axiom). [clausify(219)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f41(B,A),f42(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1146,c,1142,b)].
% 3.19/3.42 1147 -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f42(B,A)),hAPP(B,f41(B,A))) | c_SEQ_Omonoseq(A,B) # label(fact_monoI2) # label(axiom). [clausify(219)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f42(B,A)),hAPP(B,f41(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1147,c,1142,b)].
% 3.19/3.42 1148 -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f43(B,A),f44(B,A)) | c_SEQ_Omonoseq(A,B) # label(fact_monoI1) # label(axiom). [clausify(220)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f43(B,A),f44(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1148,c,1142,b)].
% 3.19/3.42 1149 -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f43(B,A)),hAPP(B,f44(B,A))) | c_SEQ_Omonoseq(A,B) # label(fact_monoI1) # label(axiom). [clausify(220)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f43(B,A)),hAPP(B,f44(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1149,c,1142,b)].
% 3.19/3.42 1150 -class_Orderings_Oorder(A) | -c_SEQ_Omonoseq(A,B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) # label(fact_monoseq__Suc) # label(axiom). [clausify(650)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f37(B,A),f38(B,A)). [resolve(1150,b,1141,b)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f37(B,A)),hAPP(B,f38(B,A))). [resolve(1150,b,1143,b)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f39(B,A),f40(B,A)). [resolve(1150,b,1144,b)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f40(B,A)),hAPP(B,f39(B,A))). [resolve(1150,b,1145,b)].
% 3.19/3.42 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f41(B,A),f42(B,A)). [resolve(1150,b,1146,c)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f42(B,A)),hAPP(B,f41(B,A))). [resolve(1150,b,1147,c)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f43(B,A),f44(B,A)). [resolve(1150,b,1148,c)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f43(B,A)),hAPP(B,f44(B,A))). [resolve(1150,b,1149,c)].
% 3.19/3.50 1151 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f78(B,A)),hAPP(B,c_Nat_OSuc(f78(B,A)))) # label(fact_monoseq__Suc) # label(axiom). [clausify(650)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f78(B,A)),hAPP(B,c_Nat_OSuc(f78(B,A)))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1151,b,1142,b)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f78(B,A)),hAPP(B,c_Nat_OSuc(f78(B,A)))) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1151,b,1150,b)].
% 3.19/3.50 1152 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(f79(B,A))),hAPP(B,f79(B,A))) # label(fact_monoseq__Suc) # label(axiom). [clausify(650)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(f79(B,A))),hAPP(B,f79(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1152,b,1142,b)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(f79(B,A))),hAPP(B,f79(B,A))) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1152,b,1150,b)].
% 3.19/3.50 1153 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)). [resolve(1136,b,1133,b)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1153,b,1142,b)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(B,A),f34(B,A)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1153,b,1150,b)].
% 3.19/3.50 1154 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))). [resolve(1136,b,1135,b)].
% 3.19/3.50 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1154,b,1142,b)].
% 3.28/3.57 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f34(B,A)),hAPP(B,f33(B,A))) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1154,b,1150,b)].
% 3.28/3.57 1155 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)). [resolve(1140,b,1137,b)].
% 3.28/3.57 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1155,b,1142,b)].
% 3.28/3.57 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f35(B,A),f36(B,A)) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1155,b,1150,b)].
% 3.28/3.57 1156 -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))). [resolve(1140,b,1139,b)].
% 3.28/3.57 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,E,F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,F),hAPP(B,E)). [resolve(1156,b,1142,b)].
% 3.28/3.57 Derived: -class_Orderings_Oorder(A) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f35(B,A)),hAPP(B,f36(B,A))) | -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,c_Nat_OSuc(D)),hAPP(B,D)). [resolve(1156,b,1150,b)].
% 3.28/3.57 1157 c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f57(A),f58(A)) # label(fact_subseq__def) # label(axiom). [clausify(291)].
% 3.28/3.57 1158 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)) # label(fact_seq__suble) # label(axiom). [clausify(243)].
% 3.28/3.57 1159 -c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)) # label(fact_subseq__def) # label(axiom). [clausify(291)].
% 3.28/3.57 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f57(A),f58(A)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1157,a,1158,a)].
% 3.28/3.57 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f57(A),f58(A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). [resolve(1157,a,1159,a)].
% 3.28/3.57 1160 c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f57(A)),hAPP(A,f58(A))) # label(fact_subseq__def) # label(axiom). [clausify(291)].
% 3.28/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f57(A)),hAPP(A,f58(A))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1160,a,1158,a)].
% 3.28/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f57(A)),hAPP(A,f58(A))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). [resolve(1160,a,1159,a)].
% 3.28/3.57 1161 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(656)].
% 3.49/3.75 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f57(A),f58(A)). [resolve(1161,a,1157,a)].
% 3.49/3.75 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f57(A)),hAPP(A,f58(A))). [resolve(1161,a,1160,a)].
% 3.49/3.75 1162 c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f80(A)),hAPP(A,c_Nat_OSuc(f80(A)))) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(656)].
% 3.49/3.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f80(A)),hAPP(A,c_Nat_OSuc(f80(A)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1162,a,1158,a)].
% 3.49/3.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f80(A)),hAPP(A,c_Nat_OSuc(f80(A)))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). [resolve(1162,a,1159,a)].
% 3.49/3.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f80(A)),hAPP(A,c_Nat_OSuc(f80(A)))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))). [resolve(1162,a,1161,a)].
% 3.49/3.75 1163 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__top(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom). [clausify(978)].
% 3.49/3.75 1164 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Otop__class_Otop(A)) = c_Orderings_Otop__class_Otop(A) # label(fact_sup__top__right) # label(axiom). [clausify(293)].
% 3.49/3.75 1165 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Otop__class_Otop(A),B) = c_Orderings_Otop__class_Otop(A) # label(fact_sup__top__left) # label(axiom). [clausify(294)].
% 3.49/3.75 1166 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Otop__class_Otop(A),B) = B # label(fact_inf__top__left) # label(axiom). [clausify(431)].
% 3.49/3.75 1167 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Otop__class_Otop(A)) = B # label(fact_inf__top__right) # label(axiom). [clausify(432)].
% 3.49/3.75 1168 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != c_Orderings_Otop__class_Otop(A) | c_Orderings_Otop__class_Otop(A) = B # label(fact_inf__eq__top__iff) # label(axiom). [clausify(433)].
% 3.49/3.75 1169 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != c_Orderings_Otop__class_Otop(A) | c_Orderings_Otop__class_Otop(A) = C # label(fact_inf__eq__top__iff) # label(axiom). [clausify(433)].
% 3.49/3.75 1170 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Orderings_Otop__class_Otop(A) | c_Orderings_Otop__class_Otop(A) != B | c_Orderings_Otop__class_Otop(A) != C # label(fact_inf__eq__top__iff) # label(axiom). [clausify(433)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Orderings_Otop__class_Otop(tc_fun(B,A))) = c_Orderings_Otop__class_Otop(tc_fun(B,A)). [resolve(1163,b,1164,a)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),c_Orderings_Otop__class_Otop(tc_fun(B,A)),C) = c_Orderings_Otop__class_Otop(tc_fun(B,A)). [resolve(1163,b,1165,a)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Orderings_Otop__class_Otop(tc_fun(B,A)),C) = C. [resolve(1163,b,1166,a)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Orderings_Otop__class_Otop(tc_fun(B,A))) = C. [resolve(1163,b,1167,a)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) != c_Orderings_Otop__class_Otop(tc_fun(B,A)) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = C. [resolve(1163,b,1168,a)].
% 3.49/3.75 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) != c_Orderings_Otop__class_Otop(tc_fun(B,A)) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = D. [resolve(1163,b,1169,a)].
% 3.66/3.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = c_Orderings_Otop__class_Otop(tc_fun(B,A)) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != C | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != D. [resolve(1163,b,1170,a)].
% 3.66/3.89 1171 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__top) # label(axiom). [assumption].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Orderings_Otop__class_Otop(tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_HOL_Obool). [resolve(1171,a,1164,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Otop__class_Otop(tc_HOL_Obool),A) = c_Orderings_Otop__class_Otop(tc_HOL_Obool). [resolve(1171,a,1165,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Orderings_Otop__class_Otop(tc_HOL_Obool),A) = A. [resolve(1171,a,1166,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Orderings_Otop__class_Otop(tc_HOL_Obool)) = A. [resolve(1171,a,1167,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != c_Orderings_Otop__class_Otop(tc_HOL_Obool) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = A. [resolve(1171,a,1168,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != c_Orderings_Otop__class_Otop(tc_HOL_Obool) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = B. [resolve(1171,a,1169,a)].
% 3.66/3.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = c_Orderings_Otop__class_Otop(tc_HOL_Obool) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != A | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != B. [resolve(1171,a,1170,a)].
% 3.66/3.89 1172 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__sup(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom). [clausify(980)].
% 3.66/3.89 1173 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)) # label(fact_less__supI2) # label(axiom). [clausify(297)].
% 3.66/3.89 1174 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_less__supI1) # label(axiom). [clausify(298)].
% 3.66/3.89 1175 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup_Oidem) # label(axiom). [clausify(299)].
% 3.66/3.89 1176 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup__idem) # label(axiom). [clausify(300)].
% 3.66/3.89 1177 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup_Ocommute) # label(axiom). [clausify(301)].
% 3.66/3.89 1178 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup__commute) # label(axiom). [clausify(303)].
% 3.66/3.89 1179 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup_Oleft__idem) # label(axiom). [clausify(304)].
% 3.66/3.89 1180 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup__left__idem) # label(axiom). [clausify(306)].
% 3.66/3.89 1181 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup_Oleft__commute) # label(axiom). [clausify(307)].
% 3.66/3.89 1182 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup__left__commute) # label(axiom). [clausify(309)].
% 3.66/3.89 1183 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup_Oassoc) # label(axiom). [clausify(310)].
% 3.66/3.89 1184 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup__assoc) # label(axiom). [clausify(312)].
% 3.66/3.89 1185 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__supE) # label(axiom). [clausify(313)].
% 3.66/3.89 1186 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__supE) # label(axiom). [clausify(313)].
% 3.66/3.89 1187 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),c_Lattices_Osemilattice__sup__class_Osup(A,C,E)) # label(fact_sup__mono) # label(axiom). [clausify(314)].
% 3.66/3.89 1188 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_sup__least) # label(axiom). [clausify(315)].
% 3.66/3.89 1189 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_le__supI) # label(axiom). [clausify(316)].
% 3.66/3.89 1190 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) = C # label(fact_sup__absorb1) # label(axiom). [clausify(317)].
% 3.66/3.89 1191 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C # label(fact_sup__absorb2) # label(axiom). [clausify(318)].
% 3.66/3.89 1192 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)) # label(fact_le__supI2) # label(axiom). [clausify(319)].
% 3.66/3.89 1193 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_le__supI1) # label(axiom). [clausify(320)].
% 3.66/3.89 1194 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__sup__iff) # label(axiom). [clausify(321)].
% 3.66/3.89 1195 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__sup__iff) # label(axiom). [clausify(321)].
% 3.66/3.89 1196 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__sup__iff) # label(axiom). [clausify(321)].
% 3.66/3.89 1197 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C # label(fact_le__iff__sup) # label(axiom). [clausify(322)].
% 3.66/3.89 1198 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) != C # label(fact_le__iff__sup) # label(axiom). [clausify(322)].
% 3.66/3.90 1199 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)) # label(fact_sup__ge2) # label(axiom). [clausify(323)].
% 3.66/3.90 1200 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) # label(fact_sup__ge1) # label(axiom). [clausify(325)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),E,D)). [resolve(1172,b,1173,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)). [resolve(1172,b,1174,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,C) = C. [resolve(1172,b,1175,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C). [resolve(1172,b,1177,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D). [resolve(1172,b,1179,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E)). [resolve(1172,b,1181,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)). [resolve(1172,b,1183,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(1172,b,1185,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),D,E). [resolve(1172,b,1186,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,F)). [resolve(1172,b,1187,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E),D). [resolve(1172,b,1188,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C) = D. [resolve(1172,b,1190,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) = D. [resolve(1172,b,1191,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),E,D)). [resolve(1172,b,1192,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)). [resolve(1172,b,1193,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) != D. [resolve(1172,b,1198,a)].
% 3.66/3.90 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C)). [resolve(1172,b,1199,a)].
% 3.66/3.91 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D)). [resolve(1172,b,1200,a)].
% 3.66/3.91 1201 class_Lattices_Osemilattice__sup(tc_Int_Oint) # label(arity_Int__Oint__Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,C,B)). [resolve(1201,a,1173,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,C)). [resolve(1201,a,1174,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,A) = A. [resolve(1201,a,1175,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,A). [resolve(1201,a,1177,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B). [resolve(1201,a,1179,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,C)). [resolve(1201,a,1181,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,C)). [resolve(1201,a,1183,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1201,a,1185,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1201,a,1186,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,D)). [resolve(1201,a,1187,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,C),B). [resolve(1201,a,1188,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,A) = B. [resolve(1201,a,1190,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B) = B. [resolve(1201,a,1191,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,C,B)). [resolve(1201,a,1192,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,C)). [resolve(1201,a,1193,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B) != B. [resolve(1201,a,1198,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,B,A)). [resolve(1201,a,1199,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint,A,B)). [resolve(1201,a,1200,a)].
% 3.66/3.91 1202 class_Lattices_Osemilattice__sup(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,C,B)). [resolve(1202,a,1173,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)). [resolve(1202,a,1174,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,A) = A. [resolve(1202,a,1175,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A). [resolve(1202,a,1177,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B). [resolve(1202,a,1179,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,C)). [resolve(1202,a,1181,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)). [resolve(1202,a,1183,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1202,a,1185,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1202,a,1186,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,D)). [resolve(1202,a,1187,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,C),B). [resolve(1202,a,1188,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A) = B. [resolve(1202,a,1190,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) = B. [resolve(1202,a,1191,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,C,B)). [resolve(1202,a,1192,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)). [resolve(1202,a,1193,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) != B. [resolve(1202,a,1198,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A)). [resolve(1202,a,1199,a)].
% 3.66/3.91 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B)). [resolve(1202,a,1200,a)].
% 3.66/3.91 1203 class_Lattices_Osemilattice__sup(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,C,B)). [resolve(1203,a,1173,a)].
% 3.66/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(1203,a,1174,a)].
% 3.66/3.91 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,A) = A. [resolve(1203,a,1175,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A). [resolve(1203,a,1177,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B). [resolve(1203,a,1179,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C)). [resolve(1203,a,1181,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(1203,a,1183,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(1203,a,1185,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,B,C). [resolve(1203,a,1186,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,D)). [resolve(1203,a,1187,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C),B). [resolve(1203,a,1188,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) = B. [resolve(1203,a,1190,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = B. [resolve(1203,a,1191,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,C,B)). [resolve(1203,a,1192,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(1203,a,1193,a)].
% 3.66/3.92 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) != B. [resolve(1203,a,1198,a)].
% 3.66/3.92 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A)). [resolve(1203,a,1199,a)].
% 3.66/3.92 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)). [resolve(1203,a,1200,a)].
% 3.66/3.92 1204 class_Lattices_Osemilattice__sup(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,C,B)). [resolve(1204,a,1173,a)].
% 3.66/3.92 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,C)). [resolve(1204,a,1174,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,A) = A. [resolve(1204,a,1175,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,A). [resolve(1204,a,1177,a)].
% 3.66/3.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B). [resolve(1204,a,1179,a)].
% 3.80/4.06 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,C)). [resolve(1204,a,1181,a)].
% 3.80/4.06 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,C)). [resolve(1204,a,1183,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1204,a,1185,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1204,a,1186,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,D)). [resolve(1204,a,1187,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,C),B). [resolve(1204,a,1188,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,A) = B. [resolve(1204,a,1190,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B) = B. [resolve(1204,a,1191,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,C,B)). [resolve(1204,a,1192,a)].
% 3.80/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,C)). [resolve(1204,a,1193,a)].
% 3.80/4.06 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B) != B. [resolve(1204,a,1198,a)].
% 3.80/4.06 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,B,A)). [resolve(1204,a,1199,a)].
% 3.80/4.06 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__sup__class_Osup(tc_RealDef_Oreal,A,B)). [resolve(1204,a,1200,a)].
% 3.80/4.06 1205 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(979)].
% 3.80/4.06 1206 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Obot__class_Obot(A),B) = B # label(fact_sup__bot__left) # label(axiom). [clausify(357)].
% 3.80/4.06 1207 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Obot__class_Obot(A)) = B # label(fact_sup__bot__right) # label(axiom). [clausify(358)].
% 3.80/4.06 1208 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != c_Lattices_Osemilattice__sup__class_Osup(A,B,C) | c_Orderings_Obot__class_Obot(A) = B # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(359)].
% 3.80/4.06 1209 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != c_Lattices_Osemilattice__sup__class_Osup(A,B,C) | c_Orderings_Obot__class_Obot(A) = C # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(359)].
% 3.80/4.06 1210 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) | c_Orderings_Obot__class_Obot(A) != B | c_Orderings_Obot__class_Obot(A) != C # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(359)].
% 3.95/4.22 1211 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Obot__class_Obot(A)) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__right) # label(axiom). [clausify(423)].
% 3.95/4.22 1212 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Obot__class_Obot(A),B) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__left) # label(axiom). [clausify(424)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),c_Orderings_Obot__class_Obot(tc_fun(B,A)),C) = C. [resolve(1205,b,1206,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = C. [resolve(1205,b,1207,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C. [resolve(1205,b,1208,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = D. [resolve(1205,b,1209,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != C | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != D. [resolve(1205,b,1210,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(1205,b,1211,a)].
% 3.95/4.22 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Orderings_Obot__class_Obot(tc_fun(B,A)),C) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(1205,b,1212,a)].
% 3.95/4.22 1213 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 3.95/4.22 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = A. [resolve(1213,a,1206,a)].
% 3.95/4.22 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(1213,a,1207,a)].
% 3.95/4.22 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A. [resolve(1213,a,1208,a)].
% 3.95/4.22 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = B. [resolve(1213,a,1209,a)].
% 3.95/4.22 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != A | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != B. [resolve(1213,a,1210,a)].
% 3.95/4.22 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(1213,a,1211,a)].
% 3.95/4.22 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(1213,a,1212,a)].
% 3.95/4.22 1214 class_GCD_Ogcd(tc_Int_Oint) # label(arity_Int__Oint__GCD_Ogcd) # label(axiom). [assumption].
% 3.95/4.22 1215 -class_GCD_Ogcd(A) | c_GCD_Ogcd__class_OGcd(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(A) # label(fact_Gcd__empty) # label(axiom). [clausify(413)].
% 3.95/4.22 1216 -class_GCD_Ogcd(A) | c_GCD_Ogcd__class_OLcm(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(A) # label(fact_Lcm__empty) # label(axiom). [clausify(672)].
% 3.95/4.22 Derived: c_GCD_Ogcd__class_OGcd(tc_Int_Oint,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1214,a,1215,a)].
% 4.10/4.37 Derived: c_GCD_Ogcd__class_OLcm(tc_Int_Oint,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1214,a,1216,a)].
% 4.10/4.37 1217 class_GCD_Ogcd(tc_Nat_Onat) # label(arity_Nat__Onat__GCD_Ogcd) # label(axiom). [assumption].
% 4.10/4.37 Derived: c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1217,a,1215,a)].
% 4.10/4.37 Derived: c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1217,a,1216,a)].
% 4.10/4.37 1218 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(981)].
% 4.10/4.37 1219 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(469)].
% 4.10/4.37 1220 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf__idem) # label(axiom). [clausify(470)].
% 4.10/4.37 1221 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf_Ocommute) # label(axiom). [clausify(471)].
% 4.10/4.37 1222 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf__commute) # label(axiom). [clausify(473)].
% 4.10/4.37 1223 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf_Oleft__idem) # label(axiom). [clausify(474)].
% 4.10/4.37 1224 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf__left__idem) # label(axiom). [clausify(476)].
% 4.10/4.37 1225 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf_Oleft__commute) # label(axiom). [clausify(477)].
% 4.10/4.37 1226 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf__left__commute) # label(axiom). [clausify(479)].
% 4.10/4.37 1227 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf_Oassoc) # label(axiom). [clausify(480)].
% 4.10/4.37 1228 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__assoc) # label(axiom). [clausify(482)].
% 4.10/4.38 1229 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_less__infI1) # label(axiom). [clausify(498)].
% 4.10/4.38 1230 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_less__infI2) # label(axiom). [clausify(499)].
% 4.10/4.38 1231 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__infE) # label(axiom). [clausify(500)].
% 4.10/4.38 1232 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__infE) # label(axiom). [clausify(500)].
% 4.10/4.38 1233 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),c_Lattices_Osemilattice__inf__class_Oinf(A,C,E)) # label(fact_inf__mono) # label(axiom). [clausify(501)].
% 4.10/4.38 1234 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__greatest) # label(axiom). [clausify(502)].
% 4.10/4.38 1235 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__infI) # label(axiom). [clausify(503)].
% 4.10/4.38 1236 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) = B # label(fact_inf__absorb2) # label(axiom). [clausify(504)].
% 4.10/4.38 1237 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_inf__absorb1) # label(axiom). [clausify(505)].
% 4.10/4.38 1238 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_le__infI2) # label(axiom). [clausify(506)].
% 4.10/4.38 1239 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_le__infI1) # label(axiom). [clausify(507)].
% 4.10/4.38 1240 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__inf__iff) # label(axiom). [clausify(508)].
% 4.10/4.38 1241 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__inf__iff) # label(axiom). [clausify(508)].
% 4.10/4.38 1242 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__inf__iff) # label(axiom). [clausify(508)].
% 4.10/4.38 1243 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_le__iff__inf) # label(axiom). [clausify(509)].
% 4.10/4.38 1244 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != B # label(fact_le__iff__inf) # label(axiom). [clausify(509)].
% 4.10/4.38 1245 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C) # label(fact_inf__le2) # label(axiom). [clausify(510)].
% 4.10/4.38 1246 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B) # label(fact_inf__le1) # label(axiom). [clausify(512)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,C) = C. [resolve(1218,b,1219,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C). [resolve(1218,b,1221,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D). [resolve(1218,b,1223,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E)). [resolve(1218,b,1225,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),E) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(1218,b,1227,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),D). [resolve(1218,b,1229,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),E,C),D). [resolve(1218,b,1230,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(1218,b,1231,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(1218,b,1232,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,F)). [resolve(1218,b,1233,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(1218,b,1234,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C) = C. [resolve(1218,b,1236,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = C. [resolve(1218,b,1237,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),E,C),D). [resolve(1218,b,1238,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),D). [resolve(1218,b,1239,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) != C. [resolve(1218,b,1244,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),D). [resolve(1218,b,1245,a)].
% 4.10/4.38 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),C). [resolve(1218,b,1246,a)].
% 4.10/4.38 1247 class_Lattices_Osemilattice__inf(tc_Int_Oint) # label(arity_Int__Oint__Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 4.10/4.38 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,A) = A. [resolve(1247,a,1219,a)].
% 4.10/4.38 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,A). [resolve(1247,a,1221,a)].
% 4.10/4.38 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B). [resolve(1247,a,1223,a)].
% 4.10/4.38 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,C)). [resolve(1247,a,1225,a)].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,C)). [resolve(1247,a,1227,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,C),B). [resolve(1247,a,1229,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,C,A),B). [resolve(1247,a,1230,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1247,a,1231,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1247,a,1232,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,D)). [resolve(1247,a,1233,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,C)). [resolve(1247,a,1234,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,B,A) = A. [resolve(1247,a,1236,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B) = A. [resolve(1247,a,1237,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,C,A),B). [resolve(1247,a,1238,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,C),B). [resolve(1247,a,1239,a)].
% 4.10/4.39 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B) != A. [resolve(1247,a,1244,a)].
% 4.10/4.39 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B),B). [resolve(1247,a,1245,a)].
% 4.10/4.39 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint,A,B),A). [resolve(1247,a,1246,a)].
% 4.10/4.39 1248 class_Lattices_Osemilattice__inf(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,A) = A. [resolve(1248,a,1219,a)].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A). [resolve(1248,a,1221,a)].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B). [resolve(1248,a,1223,a)].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C)). [resolve(1248,a,1225,a)].
% 4.10/4.39 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(1248,a,1227,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),B). [resolve(1248,a,1229,a)].
% 4.10/4.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,C,A),B). [resolve(1248,a,1230,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(1248,a,1231,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1248,a,1232,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,D)). [resolve(1248,a,1233,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(1248,a,1234,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A) = A. [resolve(1248,a,1236,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = A. [resolve(1248,a,1237,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,C,A),B). [resolve(1248,a,1238,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),B). [resolve(1248,a,1239,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) != A. [resolve(1248,a,1244,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),B). [resolve(1248,a,1245,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),A). [resolve(1248,a,1246,a)].
% 4.10/4.40 1249 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,A) = A. [resolve(1249,a,1219,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A). [resolve(1249,a,1221,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B). [resolve(1249,a,1223,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C)). [resolve(1249,a,1225,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(1249,a,1227,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(1249,a,1229,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(1249,a,1230,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(1249,a,1231,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(1249,a,1232,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,D)). [resolve(1249,a,1233,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(1249,a,1234,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A) = A. [resolve(1249,a,1236,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = A. [resolve(1249,a,1237,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(1249,a,1238,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(1249,a,1239,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != A. [resolve(1249,a,1244,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),B). [resolve(1249,a,1245,a)].
% 4.10/4.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),A). [resolve(1249,a,1246,a)].
% 4.10/4.40 1250 class_Lattices_Osemilattice__inf(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,A) = A. [resolve(1250,a,1219,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,A). [resolve(1250,a,1221,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B). [resolve(1250,a,1223,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,C)). [resolve(1250,a,1225,a)].
% 4.10/4.40 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,C)). [resolve(1250,a,1227,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,C),B). [resolve(1250,a,1229,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,C,A),B). [resolve(1250,a,1230,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1250,a,1231,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1250,a,1232,a)].
% 4.10/4.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,D)). [resolve(1250,a,1233,a)].
% 4.25/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,C)). [resolve(1250,a,1234,a)].
% 4.25/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,B,A) = A. [resolve(1250,a,1236,a)].
% 4.25/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B) = A. [resolve(1250,a,1237,a)].
% 4.25/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,C,A),B). [resolve(1250,a,1238,a)].
% 4.25/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,C),B). [resolve(1250,a,1239,a)].
% 4.25/4.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B) != A. [resolve(1250,a,1244,a)].
% 4.25/4.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B),B). [resolve(1250,a,1245,a)].
% 4.25/4.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Lattices_Osemilattice__inf__class_Oinf(tc_RealDef_Oreal,A,B),A). [resolve(1250,a,1246,a)].
% 4.25/4.57 1251 class_Rings_Osemiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__1) # label(axiom). [assumption].
% 4.25/4.57 1252 -class_Rings_Osemiring__1(A) | c_member(A,c_Groups_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_ONats(A)) # label(fact_Nats__0) # label(axiom). [clausify(551)].
% 4.25/4.57 1253 -class_Rings_Osemiring__1(A) | c_member(A,c_Groups_Oone__class_Oone(A),c_Nat_Osemiring__1__class_ONats(A)) # label(fact_Nats__1) # label(axiom). [clausify(653)].
% 4.25/4.57 1254 -class_Rings_Osemiring__1(A) | -c_member(A,B,c_Nat_Osemiring__1__class_ONats(A)) | -c_member(A,C,c_Nat_Osemiring__1__class_ONats(A)) | c_member(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Nat_Osemiring__1__class_ONats(A)) # label(fact_Nats__add) # label(axiom). [clausify(788)].
% 4.25/4.57 1255 -class_Rings_Osemiring__1(A) | -c_member(A,B,c_Nat_Osemiring__1__class_ONats(A)) | -c_member(A,C,c_Nat_Osemiring__1__class_ONats(A)) | c_member(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Nat_Osemiring__1__class_ONats(A)) # label(fact_Nats__mult) # label(axiom). [clausify(910)].
% 4.25/4.57 Derived: c_member(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)). [resolve(1251,a,1252,a)].
% 4.25/4.57 Derived: c_member(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)). [resolve(1251,a,1253,a)].
% 4.25/4.57 Derived: -c_member(tc_Int_Oint,A,c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)) | -c_member(tc_Int_Oint,B,c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)) | c_member(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)). [resolve(1251,a,1254,a)].
% 4.25/4.57 Derived: -c_member(tc_Int_Oint,A,c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)) | -c_member(tc_Int_Oint,B,c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)) | c_member(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint)). [resolve(1251,a,1255,a)].
% 4.25/4.57 1256 class_Rings_Osemiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__1) # label(axiom). [assumption].
% 4.25/4.57 Derived: c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)). [resolve(1256,a,1252,a)].
% 4.25/4.57 Derived: c_member(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)). [resolve(1256,a,1253,a)].
% 4.25/4.57 Derived: -c_member(tc_Nat_Onat,A,c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)) | -c_member(tc_Nat_Onat,B,c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)) | c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)). [resolve(1256,a,1254,a)].
% 4.50/4.73 Derived: -c_member(tc_Nat_Onat,A,c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)) | -c_member(tc_Nat_Onat,B,c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)) | c_member(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat)). [resolve(1256,a,1255,a)].
% 4.50/4.73 1257 class_Rings_Osemiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__1) # label(axiom). [assumption].
% 4.50/4.73 Derived: c_member(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)). [resolve(1257,a,1252,a)].
% 4.50/4.73 Derived: c_member(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)). [resolve(1257,a,1253,a)].
% 4.50/4.73 Derived: -c_member(tc_RealDef_Oreal,A,c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)) | -c_member(tc_RealDef_Oreal,B,c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)) | c_member(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)). [resolve(1257,a,1254,a)].
% 4.50/4.73 Derived: -c_member(tc_RealDef_Oreal,A,c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)) | -c_member(tc_RealDef_Oreal,B,c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)) | c_member(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)). [resolve(1257,a,1255,a)].
% 4.50/4.73 1258 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Osemiring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__1) # label(axiom). [clausify(1019)].
% 4.50/4.73 Derived: -class_Rings_Ocomm__semiring__1(A) | c_member(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))). [resolve(1258,b,1252,a)].
% 4.50/4.73 Derived: -class_Rings_Ocomm__semiring__1(A) | c_member(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))). [resolve(1258,b,1253,a)].
% 4.50/4.73 Derived: -class_Rings_Ocomm__semiring__1(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))) | -c_member(tc_Polynomial_Opoly(A),C,c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))) | c_member(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))). [resolve(1258,b,1254,a)].
% 4.50/4.73 Derived: -class_Rings_Ocomm__semiring__1(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))) | -c_member(tc_Polynomial_Opoly(A),C,c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))) | c_member(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Nat_Osemiring__1__class_ONats(tc_Polynomial_Opoly(A))). [resolve(1258,b,1255,a)].
% 4.50/4.73 1259 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 4.50/4.73 1260 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(553)].
% 4.50/4.73 1261 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(553)].
% 4.50/4.73 1262 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(554)].
% 4.50/4.73 1263 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(554)].
% 4.50/4.74 1264 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(555)].
% 4.50/4.74 1265 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(555)].
% 4.50/4.74 1266 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(556)].
% 4.50/4.74 1267 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(556)].
% 4.50/4.74 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1259,a,1260,a)].
% 4.50/4.74 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1259,a,1261,a)].
% 4.50/4.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1259,a,1262,a)].
% 4.50/4.74 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1259,a,1263,a)].
% 4.50/4.74 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1259,a,1264,a)].
% 4.50/4.74 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1259,a,1265,a)].
% 4.50/4.74 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D). [resolve(1259,a,1266,a)].
% 4.50/4.74 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D). [resolve(1259,a,1267,a)].
% 4.50/4.74 1268 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 4.50/4.74 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1268,a,1260,a)].
% 4.50/4.74 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1268,a,1261,a)].
% 4.50/4.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1268,a,1262,a)].
% 4.50/4.74 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1268,a,1263,a)].
% 4.64/4.89 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1268,a,1264,a)].
% 4.64/4.89 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1268,a,1265,a)].
% 4.64/4.89 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D). [resolve(1268,a,1266,a)].
% 4.64/4.89 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D). [resolve(1268,a,1267,a)].
% 4.64/4.89 1269 -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(1002)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1269,b,1260,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1269,b,1261,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1269,b,1262,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1269,b,1263,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1269,b,1264,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1269,b,1265,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1269,b,1266,a)].
% 4.64/4.89 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1269,b,1267,a)].
% 4.64/4.89 1270 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 4.64/4.89 1271 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | C = B # label(fact_right__minus__eq) # label(axiom). [clausify(557)].
% 4.64/4.89 1272 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | C != B # label(fact_right__minus__eq) # label(axiom). [clausify(557)].
% 4.80/5.05 1273 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(583)].
% 4.80/5.05 1274 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_diff__self) # label(axiom). [clausify(584)].
% 4.80/5.05 1275 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(770)].
% 4.80/5.05 1276 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(771)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B = A. [resolve(1270,a,1271,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B != A. [resolve(1270,a,1272,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1270,a,1273,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1270,a,1274,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = A. [resolve(1270,a,1275,a)].
% 4.80/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),B) = A. [resolve(1270,a,1276,a)].
% 4.80/5.05 1277 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B = A. [resolve(1277,a,1271,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B != A. [resolve(1277,a,1272,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1277,a,1273,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1277,a,1274,a)].
% 4.80/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1277,a,1275,a)].
% 4.80/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1277,a,1276,a)].
% 4.80/5.05 1278 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1020)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = B. [resolve(1278,b,1271,a)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C != B. [resolve(1278,b,1272,a)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1278,b,1273,a)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1278,b,1274,a)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),C) = B. [resolve(1278,b,1275,a)].
% 4.80/5.05 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),C) = B. [resolve(1278,b,1276,a)].
% 4.80/5.05 1279 class_Rings_Ozero__neq__one(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.80/5.05 1280 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_one__neq__zero) # label(axiom). [clausify(606)].
% 4.99/5.22 1281 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_zero__neq__one) # label(axiom). [clausify(607)].
% 4.99/5.22 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1279,a,1280,a)].
% 4.99/5.22 1282 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.99/5.22 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1282,a,1280,a)].
% 4.99/5.22 1283 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.99/5.22 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1283,a,1280,a)].
% 4.99/5.22 1284 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom). [clausify(1014)].
% 4.99/5.22 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1284,b,1280,a)].
% 4.99/5.22 1285 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.99/5.22 1286 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__le__one) # label(axiom). [clausify(634)].
% 4.99/5.22 1287 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__le__zero) # label(axiom). [clausify(635)].
% 4.99/5.22 1288 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__less__one) # label(axiom). [clausify(636)].
% 4.99/5.22 1289 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__less__zero) # label(axiom). [clausify(637)].
% 4.99/5.22 1290 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_less__add__one) # label(axiom). [clausify(678)].
% 4.99/5.22 1291 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_pos__add__strict) # label(axiom). [clausify(757)].
% 4.99/5.22 1292 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__two) # label(axiom). [clausify(797)].
% 4.99/5.22 1293 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_less__1__mult) # label(axiom). [clausify(920)].
% 4.99/5.22 Derived: 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(1285,a,1286,a)].
% 4.99/5.22 Derived: -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(1285,a,1287,a)].
% 4.99/5.22 Derived: 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(1285,a,1288,a)].
% 4.99/5.22 Derived: -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(1285,a,1289,a)].
% 4.99/5.22 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1285,a,1290,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1285,a,1291,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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(1285,a,1292,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1285,a,1293,a)].
% 4.99/5.23 1294 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1294,a,1286,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1294,a,1287,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1294,a,1288,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1294,a,1289,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1294,a,1290,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1294,a,1291,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1294,a,1292,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1294,a,1293,a)].
% 4.99/5.23 1295 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.99/5.23 Derived: 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(1295,a,1286,a)].
% 4.99/5.23 Derived: -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(1295,a,1287,a)].
% 4.99/5.23 Derived: 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(1295,a,1288,a)].
% 4.99/5.23 Derived: -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(1295,a,1289,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1295,a,1290,a)].
% 4.99/5.23 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1295,a,1291,a)].
% 4.99/5.23 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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(1295,a,1292,a)].
% 5.15/5.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1295,a,1293,a)].
% 5.15/5.40 1296 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(1004)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1296,b,1286,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1296,b,1287,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1296,b,1288,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1296,b,1289,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1296,b,1290,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1296,b,1291,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1296,b,1292,a)].
% 5.15/5.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1296,b,1293,a)].
% 5.15/5.40 1297 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.15/5.40 1298 -class_Groups_Oab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(689)].
% 5.15/5.40 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)). [resolve(1297,a,1298,a)].
% 5.15/5.40 1299 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.15/5.40 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1299,a,1298,a)].
% 5.15/5.40 1300 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)). [resolve(1300,a,1298,a)].
% 5.30/5.56 1301 -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(1007)].
% 5.30/5.56 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,D)). [resolve(1301,b,1298,a)].
% 5.30/5.56 1302 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.30/5.56 1303 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(690)].
% 5.30/5.56 1304 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(690)].
% 5.30/5.56 1305 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__cancel) # label(axiom). [clausify(691)].
% 5.30/5.56 1306 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,D,C) | B != D # label(fact_add__right__cancel) # label(axiom). [clausify(691)].
% 5.30/5.56 1307 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(692)].
% 5.30/5.56 1308 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(694)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B = C. [resolve(1302,a,1303,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B != C. [resolve(1302,a,1304,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A = C. [resolve(1302,a,1305,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A != C. [resolve(1302,a,1306,a)].
% 5.30/5.56 1309 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B = C. [resolve(1309,a,1303,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B != C. [resolve(1309,a,1304,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A = C. [resolve(1309,a,1305,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A != C. [resolve(1309,a,1306,a)].
% 5.30/5.56 1310 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B = C. [resolve(1310,a,1303,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B != C. [resolve(1310,a,1304,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A = C. [resolve(1310,a,1305,a)].
% 5.30/5.56 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A != C. [resolve(1310,a,1306,a)].
% 5.30/5.56 1311 -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(1003)].
% 5.59/5.88 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C = D. [resolve(1311,b,1303,a)].
% 5.59/5.88 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C != D. [resolve(1311,b,1304,a)].
% 5.59/5.88 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B = D. [resolve(1311,b,1305,a)].
% 5.59/5.88 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B != D. [resolve(1311,b,1306,a)].
% 5.59/5.88 1312 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.59/5.88 1313 -class_Groups_Ocancel__ab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(693)].
% 5.59/5.88 1314 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.59/5.88 1315 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.59/5.88 1316 -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(999)].
% 5.59/5.88 1317 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].
% 5.59/5.88 1318 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(695)].
% 5.59/5.88 1319 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(695)].
% 5.59/5.88 1320 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(696)].
% 5.59/5.88 1321 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(696)].
% 5.59/5.88 1322 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(700)].
% 5.59/5.88 1323 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(701)].
% 5.59/5.88 1324 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(702)].
% 5.59/5.88 1325 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(703)].
% 5.59/5.88 1326 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(707)].
% 5.59/5.88 1327 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(707)].
% 5.59/5.88 1328 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(708)].
% 5.59/5.88 1329 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(708)].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1317,a,1318,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1317,a,1319,a)].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1317,a,1320,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1317,a,1321,a)].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1317,a,1324,a)].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1317,a,1325,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1317,a,1327,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1317,a,1329,a)].
% 5.59/5.88 1330 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].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1330,a,1318,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1330,a,1319,a)].
% 5.59/5.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1330,a,1320,a)].
% 5.59/5.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1330,a,1321,a)].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1330,a,1324,a)].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1330,a,1325,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1330,a,1327,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1330,a,1329,a)].
% 5.59/5.89 1331 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].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1331,a,1318,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1331,a,1319,a)].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1331,a,1320,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1331,a,1321,a)].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1331,a,1324,a)].
% 5.59/5.89 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1331,a,1325,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1331,a,1327,a)].
% 5.59/5.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1331,a,1329,a)].
% 5.59/5.89 1332 -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(992)].
% 5.59/5.89 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1332,b,1318,a)].
% 5.59/5.89 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1332,b,1319,a)].
% 5.59/5.89 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1332,b,1320,a)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1332,b,1321,a)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1332,b,1324,a)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1332,b,1325,a)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1332,b,1327,a)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1332,b,1329,a)].
% 5.75/6.07 1333 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.75/6.07 1334 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__right__mono) # label(axiom). [clausify(697)].
% 5.75/6.07 1335 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__left__mono) # label(axiom). [clausify(698)].
% 5.75/6.07 1336 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__mono) # label(axiom). [clausify(699)].
% 5.75/6.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1333,a,1336,a)].
% 5.75/6.07 1337 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.75/6.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1337,a,1336,a)].
% 5.75/6.07 1338 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.75/6.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1338,a,1336,a)].
% 5.75/6.07 1339 -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(996)].
% 5.75/6.07 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1339,b,1336,a)].
% 5.98/6.22 1340 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.98/6.22 1341 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__strict__mono) # label(axiom). [clausify(704)].
% 5.98/6.22 1342 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__strict__left__mono) # label(axiom). [clausify(705)].
% 5.98/6.22 1343 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__strict__right__mono) # label(axiom). [clausify(706)].
% 5.98/6.22 1344 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__le__less__mono) # label(axiom). [clausify(751)].
% 5.98/6.22 1345 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__less__le__mono) # label(axiom). [clausify(752)].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1340,a,1341,a)].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1340,a,1344,a)].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1340,a,1345,a)].
% 5.98/6.22 1346 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1346,a,1341,a)].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1346,a,1344,a)].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1346,a,1345,a)].
% 5.98/6.22 1347 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.98/6.22 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1347,a,1341,a)].
% 6.16/6.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1347,a,1344,a)].
% 6.16/6.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1347,a,1345,a)].
% 6.16/6.40 1348 -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(991)].
% 6.16/6.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1348,b,1341,a)].
% 6.16/6.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1348,b,1344,a)].
% 6.16/6.40 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1348,b,1345,a)].
% 6.16/6.40 1349 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 6.16/6.40 1350 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_add__0__left) # label(axiom). [clausify(744)].
% 6.16/6.40 1351 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(747)].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A. [resolve(1349,a,1350,a)].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1349,a,1351,a)].
% 6.16/6.40 1352 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A. [resolve(1352,a,1350,a)].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1352,a,1351,a)].
% 6.16/6.40 1353 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = A. [resolve(1353,a,1350,a)].
% 6.16/6.40 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1353,a,1351,a)].
% 6.16/6.40 1354 -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)].
% 6.16/6.40 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = B. [resolve(1354,b,1350,a)].
% 6.16/6.40 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1354,b,1351,a)].
% 6.28/6.56 1355 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 6.28/6.56 1356 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(746)].
% 6.28/6.56 1357 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(746)].
% 6.28/6.56 1358 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(753)].
% 6.28/6.56 1359 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(753)].
% 6.28/6.56 1360 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(754)].
% 6.28/6.56 1361 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(754)].
% 6.28/6.56 1362 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(763)].
% 6.28/6.56 1363 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(763)].
% 6.28/6.56 1364 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(764)].
% 6.28/6.56 1365 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(764)].
% 6.28/6.56 1366 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(811)].
% 6.28/6.56 1367 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(811)].
% 6.28/6.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1355,a,1356,a)].
% 6.28/6.56 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1355,a,1357,a)].
% 6.28/6.56 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1355,a,1358,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1355,a,1360,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1355,a,1361,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1355,a,1362,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1355,a,1363,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1355,a,1364,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1355,a,1365,a)].
% 6.28/6.57 1368 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 6.28/6.57 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1368,a,1356,a)].
% 6.28/6.57 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1368,a,1357,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1368,a,1358,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1368,a,1360,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1368,a,1361,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1368,a,1362,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1368,a,1363,a)].
% 6.28/6.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1368,a,1364,a)].
% 6.28/6.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1368,a,1365,a)].
% 6.49/6.74 1369 -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(998)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1369,b,1356,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1369,b,1357,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1369,b,1358,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1369,b,1360,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1369,b,1361,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1369,b,1362,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1369,b,1363,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1369,b,1364,a)].
% 6.49/6.74 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1369,b,1365,a)].
% 6.49/6.74 1370 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.49/6.74 1371 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__pos) # label(axiom). [clausify(755)].
% 6.49/6.74 1372 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__neg) # label(axiom). [clausify(756)].
% 6.49/6.74 1373 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(758)].
% 6.49/6.74 1374 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,D,B)) # label(fact_add__increasing2) # label(axiom). [clausify(759)].
% 6.49/6.74 1375 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__increasing) # label(axiom). [clausify(760)].
% 6.49/6.74 1376 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(761)].
% 6.49/6.74 1377 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(761)].
% 6.49/6.74 1378 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(761)].
% 6.49/6.74 1379 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(762)].
% 6.49/6.74 1380 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__nonneg) # label(axiom). [clausify(791)].
% 6.49/6.74 1381 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__pos) # label(axiom). [clausify(792)].
% 6.49/6.74 1382 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing) # label(axiom). [clausify(793)].
% 6.49/6.74 1383 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing2) # label(axiom). [clausify(794)].
% 6.49/6.74 1384 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__nonpos) # label(axiom). [clausify(795)].
% 6.49/6.75 1385 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__neg) # label(axiom). [clausify(796)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1370,a,1372,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1370,a,1373,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A)). [resolve(1370,a,1374,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1370,a,1375,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1370,a,1376,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1370,a,1377,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,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(1370,a,1378,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(1370,a,1380,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(1370,a,1381,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1370,a,1382,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1370,a,1383,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1370,a,1384,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1370,a,1385,a)].
% 6.49/6.75 1386 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1386,a,1372,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1386,a,1373,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)). [resolve(1386,a,1374,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1386,a,1375,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1386,a,1376,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1386,a,1377,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1386,a,1378,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)). [resolve(1386,a,1380,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)). [resolve(1386,a,1381,a)].
% 6.49/6.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1386,a,1382,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1386,a,1383,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1386,a,1384,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1386,a,1385,a)].
% 6.49/6.76 1387 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1387,a,1372,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1387,a,1373,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A)). [resolve(1387,a,1374,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1387,a,1375,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1387,a,1376,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1387,a,1377,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,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(1387,a,1378,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)). [resolve(1387,a,1380,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)). [resolve(1387,a,1381,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1387,a,1382,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1387,a,1383,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1387,a,1384,a)].
% 6.49/6.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1387,a,1385,a)].
% 6.49/6.76 1388 -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(997)].
% 6.49/6.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1388,b,1372,a)].
% 6.49/6.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1388,b,1373,a)].
% 6.49/6.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,B)). [resolve(1388,b,1374,a)].
% 6.49/6.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1388,b,1375,a)].
% 6.49/6.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1388,b,1376,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1388,b,1377,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1388,b,1378,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)). [resolve(1388,b,1380,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)). [resolve(1388,b,1381,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1388,b,1382,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1388,b,1383,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1388,b,1384,a)].
% 6.69/6.93 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1388,b,1385,a)].
% 6.69/6.93 1389 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 6.69/6.93 1390 -class_Rings_Oring__1(A) | c_member(A,c_Groups_Ozero__class_Ozero(A),c_Int_Oring__1__class_OInts(A)) # label(fact_Ints__0) # label(axiom). [clausify(814)].
% 6.69/6.93 1391 -class_Rings_Oring__1(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | -c_member(A,C,c_Int_Oring__1__class_OInts(A)) | c_member(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Int_Oring__1__class_OInts(A)) # label(fact_Ints__add) # label(axiom). [clausify(815)].
% 6.69/6.94 1392 -class_Rings_Oring__1(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | -c_member(A,C,c_Int_Oring__1__class_OInts(A)) | c_member(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Int_Oring__1__class_OInts(A)) # label(fact_Ints__diff) # label(axiom). [clausify(816)].
% 6.69/6.94 1393 -class_Rings_Oring__1(A) | c_member(A,c_Groups_Oone__class_Oone(A),c_Int_Oring__1__class_OInts(A)) # label(fact_Ints__1) # label(axiom). [clausify(817)].
% 6.69/6.94 1394 -class_Rings_Oring__1(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | -c_member(A,C,c_Int_Oring__1__class_OInts(A)) | c_member(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Int_Oring__1__class_OInts(A)) # label(fact_Ints__mult) # label(axiom). [clausify(850)].
% 6.69/6.94 Derived: c_member(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Oring__1__class_OInts(tc_Int_Oint)). [resolve(1389,a,1390,a)].
% 6.69/6.94 Derived: -c_member(tc_Int_Oint,A,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | -c_member(tc_Int_Oint,B,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | c_member(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Int_Oring__1__class_OInts(tc_Int_Oint)). [resolve(1389,a,1391,a)].
% 6.69/6.94 Derived: -c_member(tc_Int_Oint,A,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | -c_member(tc_Int_Oint,B,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | c_member(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Int_Oring__1__class_OInts(tc_Int_Oint)). [resolve(1389,a,1392,a)].
% 6.69/6.94 Derived: c_member(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Oring__1__class_OInts(tc_Int_Oint)). [resolve(1389,a,1393,a)].
% 6.69/6.94 Derived: -c_member(tc_Int_Oint,A,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | -c_member(tc_Int_Oint,B,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | c_member(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Int_Oring__1__class_OInts(tc_Int_Oint)). [resolve(1389,a,1394,a)].
% 6.69/6.94 1395 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption].
% 6.69/6.94 Derived: c_member(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)). [resolve(1395,a,1390,a)].
% 6.69/6.94 Derived: -c_member(tc_RealDef_Oreal,A,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | -c_member(tc_RealDef_Oreal,B,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | c_member(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)). [resolve(1395,a,1391,a)].
% 6.69/6.94 Derived: -c_member(tc_RealDef_Oreal,A,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | -c_member(tc_RealDef_Oreal,B,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | c_member(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)). [resolve(1395,a,1392,a)].
% 6.69/6.94 Derived: c_member(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)). [resolve(1395,a,1393,a)].
% 6.69/6.94 Derived: -c_member(tc_RealDef_Oreal,A,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | -c_member(tc_RealDef_Oreal,B,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | c_member(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)). [resolve(1395,a,1394,a)].
% 6.69/6.94 1396 -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)].
% 6.69/6.94 Derived: -class_Rings_Ocomm__ring__1(A) | c_member(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))). [resolve(1396,b,1390,a)].
% 6.69/6.94 Derived: -class_Rings_Ocomm__ring__1(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | -c_member(tc_Polynomial_Opoly(A),C,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | c_member(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))). [resolve(1396,b,1391,a)].
% 6.89/7.12 Derived: -class_Rings_Ocomm__ring__1(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | -c_member(tc_Polynomial_Opoly(A),C,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | c_member(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))). [resolve(1396,b,1392,a)].
% 6.89/7.12 Derived: -class_Rings_Ocomm__ring__1(A) | c_member(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))). [resolve(1396,b,1393,a)].
% 6.89/7.12 Derived: -class_Rings_Ocomm__ring__1(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | -c_member(tc_Polynomial_Opoly(A),C,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | c_member(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))). [resolve(1396,b,1394,a)].
% 6.89/7.12 1397 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 6.89/7.12 1398 -class_Int_Oring__char__0(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_Ints__double__eq__0__iff) # label(axiom). [clausify(825)].
% 6.89/7.12 1399 -class_Int_Oring__char__0(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_Ints__double__eq__0__iff) # label(axiom). [clausify(825)].
% 6.89/7.12 1400 -class_Int_Oring__char__0(A) | -c_member(A,B,c_Int_Oring__1__class_OInts(A)) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),B),B) != c_Groups_Ozero__class_Ozero(A) # label(fact_Ints__odd__nonzero) # label(axiom). [clausify(826)].
% 6.89/7.12 1401 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Int_Onumber__class_Onumber__of(A,C) | B = C # label(fact_eq__number__of) # label(axiom). [clausify(834)].
% 6.89/7.12 1402 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Int_Onumber__class_Onumber__of(A,C) | B != C # label(fact_eq__number__of) # label(axiom). [clausify(834)].
% 6.89/7.12 Derived: -c_member(tc_Int_Oint,A,c_Int_Oring__1__class_OInts(tc_Int_Oint)) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1397,a,1400,a)].
% 6.89/7.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | A = B. [resolve(1397,a,1401,b)].
% 6.89/7.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | A != B. [resolve(1397,a,1402,b)].
% 6.89/7.12 1403 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Oring__char__0) # label(axiom). [assumption].
% 6.89/7.12 Derived: -c_member(tc_RealDef_Oreal,A,c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A),A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1403,a,1400,a)].
% 6.89/7.12 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | A = B. [resolve(1403,a,1401,b)].
% 6.89/7.12 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | A != B. [resolve(1403,a,1402,b)].
% 6.89/7.12 1404 -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(1023)].
% 6.89/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_member(tc_Polynomial_Opoly(A),B,c_Int_Oring__1__class_OInts(tc_Polynomial_Opoly(A))) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B),B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1404,b,1400,a)].
% 7.21/7.47 Derived: -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B) != c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1404,b,1401,b)].
% 7.21/7.47 Derived: -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B) = c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1404,b,1402,b)].
% 7.21/7.47 1405 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].
% 7.21/7.47 1406 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(827)].
% 7.21/7.47 1407 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(827)].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1405,a,1406,a)].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1405,a,1407,a)].
% 7.21/7.47 1408 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].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1408,a,1406,a)].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1408,a,1407,a)].
% 7.21/7.47 1409 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].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1409,a,1406,a)].
% 7.21/7.47 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1409,a,1407,a)].
% 7.21/7.47 1410 -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(990)].
% 7.21/7.47 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1410,b,1406,a)].
% 7.21/7.47 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1410,b,1407,a)].
% 7.21/7.47 1411 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 7.21/7.47 1412 -class_Rings_Olinordered__semiring__1__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oplus__class_Oplus(A,E,F) != c_Groups_Oone__class_Oone(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C) # label(fact_convex__bound__lt) # label(axiom). [clausify(843)].
% 7.35/7.65 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,E) != c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,E,C)),B). [resolve(1411,a,1412,a)].
% 7.35/7.65 1413 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 7.35/7.65 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,E) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E,C)),B). [resolve(1413,a,1412,a)].
% 7.35/7.65 1414 -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(994)].
% 7.35/7.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),E,F) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),F,D)),C). [resolve(1414,b,1412,a)].
% 7.35/7.65 1415 class_Int_Onumber(tc_Int_Oint) # label(arity_Int__Oint__Int_Onumber) # label(axiom). [assumption].
% 7.35/7.65 1416 -class_Int_Onumber(A) | -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_left__diff__distrib__number__of) # label(axiom). [clausify(858)].
% 7.35/7.65 1417 -class_Int_Onumber(A) | -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,C,D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C),c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) # label(fact_right__diff__distrib__number__of) # label(axiom). [clausify(859)].
% 7.35/7.65 1418 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oplus__class_Oplus(A,C,D)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C),c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) # label(fact_right__distrib__number__of) # label(axiom). [clausify(861)].
% 7.35/7.65 1419 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_left__distrib__number__of) # label(axiom). [clausify(862)].
% 7.35/7.65 Derived: -class_Rings_Oring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))). [resolve(1415,a,1416,a)].
% 7.35/7.65 Derived: -class_Rings_Oring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)). [resolve(1415,a,1417,a)].
% 7.35/7.65 Derived: -class_Rings_Osemiring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)). [resolve(1415,a,1418,a)].
% 7.35/7.65 Derived: -class_Rings_Osemiring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))). [resolve(1415,a,1419,a)].
% 7.35/7.65 1420 class_Int_Onumber(tc_Nat_Onat) # label(arity_Nat__Onat__Int_Onumber) # label(axiom). [assumption].
% 7.35/7.65 Derived: -class_Rings_Oring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))). [resolve(1420,a,1416,a)].
% 7.35/7.65 Derived: -class_Rings_Oring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)). [resolve(1420,a,1417,a)].
% 7.35/7.65 Derived: -class_Rings_Osemiring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)). [resolve(1420,a,1418,a)].
% 7.35/7.65 Derived: -class_Rings_Osemiring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))). [resolve(1420,a,1419,a)].
% 7.35/7.65 1421 class_Int_Onumber(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Onumber) # label(axiom). [assumption].
% 7.35/7.65 Derived: -class_Rings_Oring(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))). [resolve(1421,a,1416,a)].
% 7.35/7.66 Derived: -class_Rings_Oring(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)). [resolve(1421,a,1417,a)].
% 7.35/7.66 Derived: -class_Rings_Osemiring(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)). [resolve(1421,a,1418,a)].
% 7.35/7.66 Derived: -class_Rings_Osemiring(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))). [resolve(1421,a,1419,a)].
% 7.35/7.66 1422 -class_Rings_Ocomm__ring__1(A) | class_Int_Onumber(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Int_Onumber) # label(axiom). [clausify(1031)].
% 7.35/7.66 Derived: -class_Rings_Ocomm__ring__1(A) | -class_Rings_Oring(tc_Polynomial_Opoly(A)) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D))). [resolve(1422,b,1416,a)].
% 7.35/7.66 Derived: -class_Rings_Ocomm__ring__1(A) | -class_Rings_Oring(tc_Polynomial_Opoly(A)) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,D)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),D)). [resolve(1422,b,1417,a)].
% 7.35/7.66 Derived: -class_Rings_Ocomm__ring__1(A) | -class_Rings_Osemiring(tc_Polynomial_Opoly(A)) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,D)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),B),D)). [resolve(1422,b,1418,a)].
% 7.35/7.66 Derived: -class_Rings_Ocomm__ring__1(A) | -class_Rings_Osemiring(tc_Polynomial_Opoly(A)) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,c_Int_Onumber__class_Onumber__of(tc_Polynomial_Opoly(A),D))). [resolve(1422,b,1419,a)].
% 7.78/8.02 1423 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 7.78/8.02 1424 -class_Rings_Ocomm__semiring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(887)].
% 7.78/8.02 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1423,a,1424,a)].
% 7.78/8.02 1425 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 7.78/8.02 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1425,a,1424,a)].
% 7.78/8.02 1426 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 7.78/8.02 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1426,a,1424,a)].
% 7.78/8.02 1427 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1012)].
% 7.78/8.02 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1427,b,1424,a)].
% 7.78/8.02 1428 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 7.78/8.02 1429 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(894)].
% 7.78/8.02 1430 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(894)].
% 7.78/8.02 1431 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(894)].
% 7.78/8.02 1432 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(959)].
% 7.78/8.02 1433 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(960)].
% 7.78/8.02 1434 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__neg__neg) # label(axiom). [clausify(964)].
% 7.78/8.02 1435 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(966)].
% 7.78/8.02 1436 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(966)].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),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(1428,a,1429,a)].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),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(1428,a,1430,a)].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),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(1428,a,1431,a)].
% 7.78/8.02 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A)). [resolve(1428,a,1432,a)].
% 7.78/8.02 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1428,a,1433,a)].
% 7.78/8.02 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1428,a,1434,a)].
% 7.78/8.02 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B). [resolve(1428,a,1435,a)].
% 7.78/8.02 1437 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),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(1437,a,1429,a)].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),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(1437,a,1430,a)].
% 7.78/8.02 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),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(1437,a,1431,a)].
% 7.78/8.02 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1437,a,1432,a)].
% 7.78/8.03 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1437,a,1433,a)].
% 7.78/8.03 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1437,a,1434,a)].
% 7.78/8.03 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B). [resolve(1437,a,1435,a)].
% 7.78/8.03 1438 -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(1000)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1438,b,1429,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1438,b,1430,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1438,b,1431,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,B)). [resolve(1438,b,1432,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)). [resolve(1438,b,1433,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1438,b,1434,a)].
% 7.78/8.03 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1438,b,1435,a)].
% 8.11/8.40 1439 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 8.11/8.40 1440 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(916)].
% 8.11/8.40 1441 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1) # label(axiom). [clausify(918)].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1439,a,1440,a)].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) = A. [resolve(1439,a,1441,a)].
% 8.11/8.40 1442 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1442,a,1440,a)].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) = A. [resolve(1442,a,1441,a)].
% 8.11/8.40 1443 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1443,a,1440,a)].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) = A. [resolve(1443,a,1441,a)].
% 8.11/8.40 1444 -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(1006)].
% 8.11/8.40 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1444,b,1440,a)].
% 8.11/8.40 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) = B. [resolve(1444,b,1441,a)].
% 8.11/8.40 1445 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 8.11/8.40 1446 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(917)].
% 8.11/8.40 1447 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(919)].
% 8.11/8.40 1448 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 8.11/8.40 1449 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption].
% 8.11/8.40 1450 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1017)].
% 8.11/8.40 1451 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 8.11/8.40 1452 -class_Groups_Oab__semigroup__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(934)].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1451,a,1452,a)].
% 8.11/8.40 1453 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 8.11/8.40 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1453,a,1452,a)].
% 8.49/8.74 1454 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 8.49/8.74 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1454,a,1452,a)].
% 8.49/8.74 1455 -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(1005)].
% 8.49/8.74 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1455,b,1452,a)].
% 8.49/8.74 1456 class_Rings_Ono__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 8.49/8.74 1457 -class_Rings_Ono__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divisors__zero) # label(axiom). [clausify(946)].
% 8.49/8.74 1458 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_no__zero__divisors) # label(axiom). [clausify(947)].
% 8.49/8.74 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,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(1456,a,1457,a)].
% 8.49/8.74 1459 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 8.49/8.74 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1459,a,1457,a)].
% 8.49/8.74 1460 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 8.49/8.74 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,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(1460,a,1457,a)].
% 8.49/8.74 1461 -class_Rings_Oidom(A) | class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom). [clausify(1008)].
% 8.49/8.74 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1461,b,1457,a)].
% 8.49/8.74 1462 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 8.49/8.74 1463 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(948)].
% 8.49/8.74 1464 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(948)].
% 8.49/8.74 1465 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(948)].
% 8.49/8.74 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1462,a,1464,a)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1462,a,1465,a)].
% 8.72/8.97 1466 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1466,a,1464,a)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1466,a,1465,a)].
% 8.72/8.97 1467 -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(1001)].
% 8.72/8.97 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1467,b,1464,a)].
% 8.72/8.97 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1467,b,1465,a)].
% 8.72/8.97 1468 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom). [assumption].
% 8.72/8.97 1469 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__right) # label(axiom). [clausify(949)].
% 8.72/8.97 1470 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__left) # label(axiom). [clausify(950)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1468,a,1469,a)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1468,a,1470,a)].
% 8.72/8.97 1471 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1471,a,1469,a)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1471,a,1470,a)].
% 8.72/8.97 1472 class_Rings_Omult__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Omult__zero) # label(axiom). [assumption].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1472,a,1469,a)].
% 8.72/8.97 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1472,a,1470,a)].
% 8.72/8.97 1473 -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)].
% 8.72/8.97 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1473,b,1469,a)].
% 8.72/8.97 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1473,b,1470,a)].
% 8.72/8.97 1474 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 8.72/8.97 1475 -class_Rings_Olinordered__comm__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(961)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)). [resolve(1474,a,1475,a)].
% 8.80/9.09 1476 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)). [resolve(1476,a,1475,a)].
% 8.80/9.09 1477 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1477,a,1475,a)].
% 8.80/9.09 1478 -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(993)].
% 8.80/9.09 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)). [resolve(1478,b,1475,a)].
% 8.80/9.09 1479 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 8.80/9.09 1480 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(962)].
% 8.80/9.09 1481 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(963)].
% 8.80/9.09 1482 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom). [clausify(965)].
% 8.80/9.09 1483 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(967)].
% 8.80/9.09 1484 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(968)].
% 8.80/9.09 1485 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom). [clausify(969)].
% 8.80/9.09 1486 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom). [clausify(970)].
% 8.80/9.09 1487 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__pos__pos) # label(axiom). [clausify(971)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1479,a,1481,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1479,a,1482,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1479,a,1483,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1479,a,1484,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1479,a,1486,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1479,a,1487,a)].
% 8.80/9.09 1488 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1488,a,1481,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1488,a,1482,a)].
% 8.80/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). [resolve(1488,a,1483,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). [resolve(1488,a,1484,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1488,a,1486,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1488,a,1487,a)].
% 8.88/9.09 1489 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1489,a,1481,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1489,a,1482,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1489,a,1483,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1489,a,1484,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1489,a,1486,a)].
% 8.88/9.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1489,a,1487,a)].
% 8.88/9.09 1490 -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(995)].
% 8.88/9.09 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1490,b,1481,a)].
% 9.40/9.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1490,b,1482,a)].
% 9.40/9.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1490,b,1483,a)].
% 9.40/9.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1490,b,1484,a)].
% 9.40/9.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1490,b,1486,a)].
% 9.40/9.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1490,b,1487,a)].
% 9.40/9.64
% 9.40/9.64 ============================== end predicate elimination =============
% 9.40/9.64
% 9.40/9.64 Auto_denials: (non-Horn, no changes).
% 9.40/9.64
% 9.40/9.64 Term ordering decisions:
% 9.40/9.64 Function symbol KB weights: tc_Nat_Onat=1. tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_HOL_Obool=1. v_P=1. v_L____=1. v_Y____=1. v_y____=1. v_x____=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. tc_fun=1. hAPP=1. c_Int_Onumber__class_Onumber__of=1. c_SetInterval_Oord__class_OlessThan=1. c_RealDef_Oreal=1. c_SetInterval_Oord__class_OgreaterThan=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OatLeast=1. c_Set_OCollect=1. c_Set_OPow=1. c_GCD_Ogcd__class_OLcm=1. c_GCD_Ogcd__class_OGcd=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Predicate_OPowp=1. c_Set_Othe__elem=1. f1=1. f31=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f76=1. f78=1. f79=1. f83=1. f84=1. f87=1. f88=1. f90=1. f92=1. tc_Polynomial_Opoly=1. c_Groups_Ozero__class_Ozero=1. c_Nat_OSuc=1. c_Orderings_Obot__class_Obot=1. c_Groups_Oone__class_Oone=1. c_Orderings_Otop__class_Otop=1. c_Int_Oring__1__class_OInts=1. c_Nat_Osemiring__1__class_ONats=1. c_RComplete_Onatfloor=1. c_RComplete_Onatceiling=1. c_fequal=1. f22=1. f23=1. f32=1. f57=1. f58=1. f77=1. f80=1. f81=1. f82=1. f89=1. f91=1. c_Groups_Oplus__class_Oplus=1. c_Lattices_Osemilattice__sup__class_Osup=1. c_Groups_Otimes__class_Otimes=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_Groups_Ominus__class_Ominus=1. c_Set_Oinsert=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetIntervalCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------