TSTP Solution File: SWV582-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV582-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 : Wed Jul 20 21:13:58 EDT 2022
% Result : Unsatisfiable 4.46s 4.77s
% Output : Refutation 4.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV582-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 23:50:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.14/1.55 ============================== Prover9 ===============================
% 1.14/1.55 Prover9 (32) version 2009-11A, November 2009.
% 1.14/1.55 Process 30448 was started by sandbox2 on n028.cluster.edu,
% 1.14/1.55 Tue Jun 14 23:50:10 2022
% 1.14/1.55 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30295_n028.cluster.edu".
% 1.14/1.55 ============================== end of head ===========================
% 1.14/1.55
% 1.14/1.55 ============================== INPUT =================================
% 1.14/1.55
% 1.14/1.55 % Reading from file /tmp/Prover9_30295_n028.cluster.edu
% 1.14/1.55
% 1.14/1.55 set(prolog_style_variables).
% 1.14/1.55 set(auto2).
% 1.14/1.55 % set(auto2) -> set(auto).
% 1.14/1.55 % set(auto) -> set(auto_inference).
% 1.14/1.55 % set(auto) -> set(auto_setup).
% 1.14/1.55 % set(auto_setup) -> set(predicate_elim).
% 1.14/1.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.14/1.55 % set(auto) -> set(auto_limits).
% 1.14/1.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.14/1.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.14/1.55 % set(auto) -> set(auto_denials).
% 1.14/1.55 % set(auto) -> set(auto_process).
% 1.14/1.55 % set(auto2) -> assign(new_constants, 1).
% 1.14/1.55 % set(auto2) -> assign(fold_denial_max, 3).
% 1.14/1.55 % set(auto2) -> assign(max_weight, "200.000").
% 1.14/1.55 % set(auto2) -> assign(max_hours, 1).
% 1.14/1.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.14/1.55 % set(auto2) -> assign(max_seconds, 0).
% 1.14/1.55 % set(auto2) -> assign(max_minutes, 5).
% 1.14/1.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.14/1.55 % set(auto2) -> set(sort_initial_sos).
% 1.14/1.55 % set(auto2) -> assign(sos_limit, -1).
% 1.14/1.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.14/1.55 % set(auto2) -> assign(max_megs, 400).
% 1.14/1.55 % set(auto2) -> assign(stats, some).
% 1.14/1.55 % set(auto2) -> clear(echo_input).
% 1.14/1.55 % set(auto2) -> set(quiet).
% 1.14/1.55 % set(auto2) -> clear(print_initial_clauses).
% 1.14/1.55 % set(auto2) -> clear(print_given).
% 1.14/1.55 assign(lrs_ticks,-1).
% 1.14/1.55 assign(sos_limit,10000).
% 1.14/1.55 assign(order,kbo).
% 1.14/1.55 set(lex_order_vars).
% 1.14/1.55 clear(print_given).
% 1.14/1.55
% 1.14/1.55 % formulas(sos). % not echoed (1088 formulas)
% 1.14/1.55
% 1.14/1.55 ============================== end of input ==========================
% 1.14/1.55
% 1.14/1.55 % From the command line: assign(max_seconds, 300).
% 1.14/1.55
% 1.14/1.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.14/1.55
% 1.14/1.55 % Formulas that are not ordinary clauses:
% 1.14/1.55
% 1.14/1.55 ============================== end of process non-clausal formulas ===
% 1.14/1.55
% 1.14/1.55 ============================== PROCESS INITIAL CLAUSES ===============
% 1.14/1.55
% 1.14/1.55 ============================== PREDICATE ELIMINATION =================
% 1.14/1.55 1 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.14/1.55 2 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 1.14/1.55 3 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 1.14/1.55 4 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I21_J_0) # label(axiom). [assumption].
% 1.14/1.55 5 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I22_J_0) # label(axiom). [assumption].
% 1.14/1.55 6 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 1.14/1.55 7 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B),A),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 1.14/1.55 8 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 1.14/1.55 9 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 1.14/1.55 10 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 1.14/1.55 11 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I20_J_0) # label(axiom). [assumption].
% 1.14/1.55 12 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I19_J_0) # label(axiom). [assumption].
% 1.14/1.55 13 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 1.14/1.55 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)). [resolve(1,a,2,a)].
% 1.14/1.55 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B). [resolve(1,a,3,a)].
% 1.14/1.55 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(1,a,4,a)].
% 1.14/1.55 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(1,a,5,a)].
% 1.14/1.55 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B). [resolve(1,a,6,a)].
% 1.14/1.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),D). [resolve(1,a,7,a)].
% 1.14/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C)). [resolve(1,a,8,a)].
% 1.14/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C) = E. [resolve(1,a,9,a)].
% 1.14/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E). [resolve(1,a,10,a)].
% 1.14/1.65 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(1,a,11,a)].
% 1.14/1.65 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(1,a,12,a)].
% 1.14/1.65 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)). [resolve(1,a,13,a)].
% 1.14/1.65 14 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.14/1.65 15 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) # label(cls_le__eq__neg_0) # label(axiom). [assumption].
% 1.14/1.65 16 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__eq__neg_1) # label(axiom). [assumption].
% 1.14/1.65 17 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sup__eq__if_1) # label(axiom). [assumption].
% 1.14/1.65 18 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sup__0__imp__0_0) # label(axiom). [assumption].
% 1.14/1.65 19 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.14/1.65 20 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.14/1.65 21 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.14/1.65 22 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.14/1.65 23 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sup__eq__if_0) # label(axiom). [assumption].
% 1.14/1.65 24 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.14/1.65 25 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.14/1.65 26 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.14/1.65 27 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.14/1.65 28 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.14/1.65 29 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.14/1.65 30 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.14/1.65 31 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.14/1.65 32 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.14/1.65 33 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.14/1.65 34 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) # label(axiom). [assumption].
% 1.14/1.65 35 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) # label(axiom). [assumption].
% 1.14/1.65 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))). [resolve(14,a,15,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,16,a)].
% 1.14/1.65 Derived: -class_Orderings_Olinorder(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,17,b)].
% 1.14/1.65 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(14,a,18,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))). [resolve(14,a,19,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(14,a,20,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,21,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,22,a)].
% 1.14/1.65 Derived: -class_Orderings_Olinorder(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,23,b)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))). [resolve(14,a,24,a)].
% 1.14/1.65 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(14,a,25,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(14,a,26,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,27,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),A)). [resolve(14,a,28,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(14,a,29,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,30,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(14,a,31,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(14,a,32,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(14,a,33,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(14,a,34,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal)),C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(14,a,35,a)].
% 1.46/1.74 36 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.46/1.74 37 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.46/1.74 38 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.46/1.74 39 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I27_J_1) # label(axiom). [assumption].
% 1.46/1.74 40 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I27_J_0) # label(axiom). [assumption].
% 1.46/1.74 41 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I28_J_1) # label(axiom). [assumption].
% 1.46/1.74 42 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I28_J_0) # label(axiom). [assumption].
% 1.46/1.74 43 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I26_J_0) # label(axiom). [assumption].
% 1.46/1.74 44 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I26_J_1) # label(axiom). [assumption].
% 1.46/1.74 45 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I25_J_0) # label(axiom). [assumption].
% 1.46/1.74 46 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I25_J_1) # label(axiom). [assumption].
% 1.46/1.74 47 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.46/1.74 48 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.46/1.74 49 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.46/1.74 50 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.46/1.74 51 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 1.46/1.74 52 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 1.46/1.74 53 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.46/1.74 54 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.46/1.74 55 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.46/1.74 56 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.46/1.74 57 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 1.46/1.74 58 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.46/1.74 59 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I23_J_1) # label(axiom). [assumption].
% 1.46/1.74 60 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I23_J_0) # label(axiom). [assumption].
% 1.46/1.74 61 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I24_J_1) # label(axiom). [assumption].
% 1.46/1.74 62 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I24_J_0) # label(axiom). [assumption].
% 1.46/1.74 63 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 1.46/1.74 64 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 1.46/1.74 65 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I20_J_0) # label(axiom). [assumption].
% 1.46/1.74 66 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I20_J_1) # label(axiom). [assumption].
% 1.46/1.74 67 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I19_J_0) # label(axiom). [assumption].
% 1.46/1.74 68 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I19_J_1) # label(axiom). [assumption].
% 1.46/1.74 69 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.46/1.74 70 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.46/1.74 71 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.46/1.74 72 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.46/1.74 73 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.46/1.74 74 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.46/1.74 75 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.46/1.74 76 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.46/1.74 77 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.46/1.74 78 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.46/1.74 79 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E))) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.46/1.74 80 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_1) # label(axiom). [assumption].
% 1.46/1.74 81 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_0) # label(axiom). [assumption].
% 1.46/1.74 82 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_1) # label(axiom). [assumption].
% 1.46/1.74 83 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_0) # label(axiom). [assumption].
% 1.46/1.74 84 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.46/1.74 85 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 1.46/1.74 86 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_0) # label(axiom). [assumption].
% 1.46/1.74 87 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_1) # label(axiom). [assumption].
% 1.46/1.74 88 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_0) # label(axiom). [assumption].
% 1.46/1.74 89 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_1) # label(axiom). [assumption].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,37,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(36,a,38,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,39,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,40,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,41,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,42,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,43,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,44,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,45,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10). [resolve(36,a,46,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)). [resolve(36,a,47,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,48,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),D)). [resolve(36,a,49,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)). [resolve(36,a,50,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)). [resolve(36,a,51,a)].
% 1.46/1.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)). [resolve(36,a,52,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,53,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)). [resolve(36,a,54,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,55,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,56,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(36,a,57,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,58,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,59,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,60,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,61,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,62,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)). [resolve(36,a,63,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,64,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,65,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,66,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,67,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,68,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)). [resolve(36,a,69,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,70,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)). [resolve(36,a,71,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,73,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)). [resolve(36,a,75,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,77,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))). [resolve(36,a,79,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,80,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,81,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,82,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(36,a,83,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(36,a,84,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(36,a,85,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,86,a)].
% 1.46/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,87,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,88,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(36,a,89,a)].
% 1.54/1.79 90 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.54/1.79 91 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.54/1.79 92 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.54/1.79 93 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.54/1.79 94 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.54/1.79 95 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 1.54/1.79 96 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 1.54/1.79 97 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.54/1.79 98 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B))) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.54/1.79 99 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.54/1.79 100 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.54/1.79 101 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.54/1.79 102 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.54/1.79 103 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.54/1.79 104 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.54/1.79 105 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))))) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.54/1.79 106 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.54/1.79 107 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.54/1.79 108 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.54/1.79 109 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.54/1.79 110 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.54/1.79 111 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.54/1.79 112 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.54/1.79 113 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.54/1.79 114 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.54/1.79 115 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.54/1.79 116 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.54/1.79 117 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.54/1.79 118 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.54/1.79 119 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.54/1.79 120 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.54/1.79 121 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.54/1.79 122 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.54/1.79 123 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.54/1.79 124 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.54/1.79 125 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.54/1.79 126 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.54/1.79 127 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.54/1.79 128 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.54/1.79 129 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.54/1.79 130 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.54/1.79 131 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.54/1.79 132 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.54/1.79 133 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.54/1.79 134 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 1.54/1.79 135 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.54/1.79 136 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.54/1.79 137 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.54/1.79 138 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,91,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,92,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,93,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,94,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(90,a,95,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(90,a,96,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,97,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A))). [resolve(90,a,98,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(90,a,99,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,100,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))). [resolve(90,a,101,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))). [resolve(90,a,102,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))). [resolve(90,a,103,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))). [resolve(90,a,104,a)].
% 1.54/1.79 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))))). [resolve(90,a,105,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))). [resolve(90,a,106,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))). [resolve(90,a,107,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))). [resolve(90,a,108,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))). [resolve(90,a,109,a)].
% 1.54/1.79 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,110,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,111,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))). [resolve(90,a,112,a)].
% 1.54/1.79 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,113,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(90,a,114,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,115,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(90,a,116,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(90,a,117,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,118,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,119,a)].
% 1.54/1.79 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,120,a)].
% 1.54/1.79 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,121,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(90,a,122,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(90,a,123,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,124,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(90,a,125,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,127,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(90,a,128,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(90,a,131,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(90,a,133,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(90,a,134,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))). [resolve(90,a,135,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))). [resolve(90,a,136,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))). [resolve(90,a,137,a)].
% 1.54/1.79 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))). [resolve(90,a,138,a)].
% 1.57/1.83 139 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.57/1.83 140 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.57/1.83 141 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.57/1.83 142 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.57/1.83 143 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.57/1.83 144 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.57/1.83 145 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.57/1.83 146 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.57/1.83 147 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.57/1.83 148 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.57/1.83 149 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.57/1.83 150 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.57/1.83 151 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.57/1.83 152 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.57/1.83 153 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.57/1.83 154 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.57/1.83 155 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.57/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(139,a,140,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(139,a,141,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(139,a,143,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))). [resolve(139,a,144,a)].
% 1.57/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A))). [resolve(139,a,145,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(139,a,146,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C))). [resolve(139,a,147,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))). [resolve(139,a,148,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(139,a,149,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C))). [resolve(139,a,150,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))). [resolve(139,a,151,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(139,a,152,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(139,a,153,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(139,a,154,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(139,a,155,a)].
% 1.57/1.84 156 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(156,a,140,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(156,a,141,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(156,a,143,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))). [resolve(156,a,144,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))). [resolve(156,a,145,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(156,a,146,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))). [resolve(156,a,147,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(156,a,148,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(156,a,149,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))). [resolve(156,a,150,a)].
% 1.57/1.84 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(156,a,154,a)].
% 1.66/1.96 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(156,a,155,a)].
% 1.66/1.96 157 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.66/1.96 158 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.66/1.96 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(157,a,158,a)].
% 1.66/1.96 159 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.66/1.96 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(159,a,158,a)].
% 1.66/1.96 160 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.66/1.96 161 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.66/1.96 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(160,a,161,a)].
% 1.66/1.96 162 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.66/1.96 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)). [resolve(162,a,161,a)].
% 1.66/1.96 163 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.66/1.96 164 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.66/1.96 165 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.66/1.96 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(163,a,165,a)].
% 1.74/1.99 166 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(166,a,165,a)].
% 1.74/1.99 167 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.74/1.99 168 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 1.74/1.99 169 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 1.74/1.99 170 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 1.74/1.99 171 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 1.74/1.99 172 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.74/1.99 173 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_lessequals(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F))) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 1.74/1.99 174 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A),E)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)),F))) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 1.74/1.99 175 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 1.74/1.99 176 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)),E),A),F)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),F))) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 1.74/1.99 177 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)),E),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),F))) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 1.74/1.99 178 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D),A),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 1.74/1.99 179 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A),E)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)),F))) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 1.74/1.99 180 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F))) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)). [resolve(167,a,168,a)].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),A)). [resolve(167,a,169,a)].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E))). [resolve(167,a,173,a)].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal),D)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)),E))). [resolve(167,a,174,a)].
% 1.74/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),E)). [resolve(167,a,175,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),E)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)),E))). [resolve(167,a,176,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)),E))). [resolve(167,a,177,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),E)). [resolve(167,a,178,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal),D)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)),E))). [resolve(167,a,179,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E))). [resolve(167,a,180,a)].
% 1.74/2.02 181 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.74/2.02 182 -class_RealVector_Oreal__normed__algebra(A) | c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(B,A),A,A) # label(cls_mult_Oadditive__right_0) # label(axiom). [assumption].
% 1.74/2.02 183 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 1.74/2.02 184 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 1.74/2.02 185 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 1.74/2.02 186 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 1.74/2.02 187 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 1.74/2.02 188 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 1.74/2.02 189 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 1.74/2.02 190 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 1.74/2.02 191 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 1.74/2.02 192 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),E))),hAPP(c_HOL_Otimes__class_Otimes(D,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 1.74/2.02 193 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 1.74/2.02 194 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 1.74/2.02 195 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 1.74/2.02 196 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 1.74/2.02 197 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.74/2.02 198 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.74/2.02 199 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.74/2.02 200 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.74/2.02 201 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 1.74/2.02 202 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 1.74/2.02 203 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 1.74/2.02 204 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 1.74/2.02 Derived: c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(181,a,182,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)). [resolve(181,a,183,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)). [resolve(181,a,185,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal). [resolve(181,a,187,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(181,a,188,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(181,a,190,a)].
% 1.74/2.02 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D))),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),D))),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D))). [resolve(181,a,192,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(181,a,193,a)].
% 1.74/2.02 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(181,a,195,a)].
% 1.74/2.05 Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(181,a,197,a)].
% 1.74/2.05 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(181,a,199,a)].
% 1.74/2.05 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(181,a,201,a)].
% 1.74/2.05 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(181,a,203,a)].
% 1.74/2.05 205 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.74/2.05 206 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.74/2.05 207 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 1.74/2.05 208 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.74/2.05 209 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),B) != hAPP(c_HOL_Otimes__class_Otimes(C,A),C) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 1.74/2.05 210 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.74/2.05 211 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.74/2.05 212 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.74/2.05 213 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.74/2.05 214 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.74/2.07 215 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.74/2.07 216 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.74/2.07 217 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(205,a,206,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(205,a,208,a)].
% 1.74/2.07 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A) != hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B. [resolve(205,a,209,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(205,a,210,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)) | B = D | A = C. [resolve(205,a,211,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(205,a,213,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)). [resolve(205,a,214,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(205,a,216,a)].
% 1.74/2.07 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(205,a,217,a)].
% 1.74/2.07 218 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom). [assumption].
% 1.74/2.07 219 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,D,A),A),C)) # label(cls_divide__less__eq_0) # label(axiom). [assumption].
% 1.74/2.07 220 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_6) # label(axiom). [assumption].
% 1.74/2.07 221 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_less__divide__eq_0) # label(axiom). [assumption].
% 1.74/2.07 222 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_6) # label(axiom). [assumption].
% 1.74/2.07 223 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__imp__div__pos__less_0) # label(axiom). [assumption].
% 1.74/2.07 224 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__imp__less__div__pos_0) # label(axiom). [assumption].
% 1.74/2.07 225 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__less__divide__iff_0) # label(axiom). [assumption].
% 1.74/2.07 226 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__less__divide__iff_1) # label(axiom). [assumption].
% 1.74/2.07 227 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__less__divide__iff_2) # label(axiom). [assumption].
% 1.74/2.07 228 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__less__divide__iff_3) # label(axiom). [assumption].
% 1.74/2.07 229 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__nonneg__neg_0) # label(axiom). [assumption].
% 1.74/2.07 230 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__nonpos__pos_0) # label(axiom). [assumption].
% 1.74/2.07 231 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_8) # label(axiom). [assumption].
% 1.74/2.07 232 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_8) # label(axiom). [assumption].
% 1.74/2.07 233 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_divide__right__mono_0) # label(axiom). [assumption].
% 1.74/2.07 234 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_divide__right__mono__neg_0) # label(axiom). [assumption].
% 1.74/2.07 235 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_lessequals(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__less_0) # label(axiom). [assumption].
% 1.74/2.07 236 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__less__eq_2) # label(axiom). [assumption].
% 1.74/2.07 237 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__less__eq_3) # label(axiom). [assumption].
% 1.74/2.07 238 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_8) # label(axiom). [assumption].
% 1.74/2.07 239 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_9) # label(axiom). [assumption].
% 1.74/2.07 240 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_less__divide__eq_2) # label(axiom). [assumption].
% 1.74/2.07 241 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_less__divide__eq_3) # label(axiom). [assumption].
% 1.74/2.07 242 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_8) # label(axiom). [assumption].
% 1.74/2.07 243 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_9) # label(axiom). [assumption].
% 1.74/2.07 244 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__neg__neg_0) # label(axiom). [assumption].
% 1.74/2.07 245 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__pos__pos_0) # label(axiom). [assumption].
% 1.74/2.07 246 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__divide__iff_4) # label(axiom). [assumption].
% 1.74/2.07 247 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__divide__iff_5) # label(axiom). [assumption].
% 1.74/2.07 248 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__imp__le__div__pos_0) # label(axiom). [assumption].
% 1.74/2.07 249 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__imp__div__pos__le_0) # label(axiom). [assumption].
% 1.74/2.07 250 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_6) # label(axiom). [assumption].
% 1.74/2.07 251 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_le__divide__eq_0) # label(axiom). [assumption].
% 1.74/2.07 252 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_6) # label(axiom). [assumption].
% 1.74/2.07 253 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,D,A),A),C)) # label(cls_divide__le__eq_0) # label(axiom). [assumption].
% 1.74/2.07 254 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_5) # label(axiom). [assumption].
% 1.74/2.07 255 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__le__0__iff_4) # label(axiom). [assumption].
% 1.74/2.07 256 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_divide__strict__right__mono_0) # label(axiom). [assumption].
% 1.74/2.07 257 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_divide__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.74/2.07 258 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__nonneg__pos_0) # label(axiom). [assumption].
% 1.74/2.07 259 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__nonpos__neg_0) # label(axiom). [assumption].
% 1.74/2.07 260 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__le__eq_5) # label(axiom). [assumption].
% 1.74/2.07 261 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_7) # label(axiom). [assumption].
% 1.74/2.07 262 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_le__divide__eq_5) # label(axiom). [assumption].
% 1.74/2.07 263 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_7) # label(axiom). [assumption].
% 1.74/2.07 264 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_0) # label(axiom). [assumption].
% 1.74/2.07 265 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_1) # label(axiom). [assumption].
% 1.74/2.07 266 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_divide__left__mono__neg_0) # label(axiom). [assumption].
% 1.74/2.07 267 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_divide__left__mono_0) # label(axiom). [assumption].
% 1.74/2.07 268 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__less2_0) # label(axiom). [assumption].
% 1.74/2.07 269 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__le__divide__iff_3) # label(axiom). [assumption].
% 1.74/2.07 270 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__le__divide__iff_2) # label(axiom). [assumption].
% 1.74/2.07 271 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__le__divide__iff_1) # label(axiom). [assumption].
% 1.74/2.08 272 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__le__divide__iff_0) # label(axiom). [assumption].
% 1.74/2.08 273 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_2) # label(axiom). [assumption].
% 1.74/2.08 274 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_3) # label(axiom). [assumption].
% 1.74/2.08 275 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__less__eq_1) # label(axiom). [assumption].
% 1.74/2.08 276 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__less__eq_4) # label(axiom). [assumption].
% 1.74/2.08 277 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__less__eq_5) # label(axiom). [assumption].
% 1.74/2.08 278 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_7) # label(axiom). [assumption].
% 1.74/2.08 279 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Oinverse__class_Odivide(B,D,A))) # label(cls_less__divide__eq_1) # label(axiom). [assumption].
% 1.74/2.08 280 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_less__divide__eq_4) # label(axiom). [assumption].
% 1.74/2.08 281 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_less__divide__eq_5) # label(axiom). [assumption].
% 1.74/2.08 282 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_7) # label(axiom). [assumption].
% 1.74/2.08 283 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__divide__iff_4) # label(axiom). [assumption].
% 1.74/2.08 284 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__divide__iff_5) # label(axiom). [assumption].
% 1.74/2.08 285 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_lessequals(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__le_0) # label(axiom). [assumption].
% 1.74/2.08 286 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_3) # label(axiom). [assumption].
% 1.74/2.08 287 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_2) # label(axiom). [assumption].
% 1.74/2.08 288 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_1) # label(axiom). [assumption].
% 1.74/2.08 289 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_0) # label(axiom). [assumption].
% 1.74/2.08 290 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_9) # label(axiom). [assumption].
% 1.74/2.08 291 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_le__divide__eq_3) # label(axiom). [assumption].
% 1.74/2.08 292 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_le__divide__eq_2) # label(axiom). [assumption].
% 1.74/2.08 293 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_9) # label(axiom). [assumption].
% 1.74/2.08 294 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__le__eq_3) # label(axiom). [assumption].
% 1.74/2.08 295 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__le__eq_2) # label(axiom). [assumption].
% 1.74/2.08 296 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_divide__strict__left__mono_0) # label(axiom). [assumption].
% 1.74/2.08 297 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_divide__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.74/2.08 298 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__le__eq_1) # label(axiom). [assumption].
% 1.74/2.08 299 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__le__eq_4) # label(axiom). [assumption].
% 1.74/2.08 300 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oinverse__class_Odivide(B,D,A))) # label(cls_le__divide__eq_1) # label(axiom). [assumption].
% 1.74/2.08 301 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_le__divide__eq_4) # label(axiom). [assumption].
% 1.74/2.08 302 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__neg__pos_0) # label(axiom). [assumption].
% 1.74/2.08 303 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__pos__neg_0) # label(axiom). [assumption].
% 1.74/2.08 304 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__less__0__iff_4) # label(axiom). [assumption].
% 1.74/2.08 305 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_5) # label(axiom). [assumption].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,219,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,220,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))). [resolve(218,a,221,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,222,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,223,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,224,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))). [resolve(218,a,225,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))). [resolve(218,a,226,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))). [resolve(218,a,227,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))). [resolve(218,a,228,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,229,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,230,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,231,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,232,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(218,a,233,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),A)). [resolve(218,a,234,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,235,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,236,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,237,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,238,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,239,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))). [resolve(218,a,240,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,241,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,242,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,243,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,244,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,245,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,248,a)].
% 1.74/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,249,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))). [resolve(218,a,251,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,253,a)].
% 1.74/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,254,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,255,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(218,a,256,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),A)). [resolve(218,a,257,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,258,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,259,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,260,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,261,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,262,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,263,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,264,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,265,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)). [resolve(218,a,266,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)). [resolve(218,a,267,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,268,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))). [resolve(218,a,269,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))). [resolve(218,a,270,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))). [resolve(218,a,271,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))). [resolve(218,a,272,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,273,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,274,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,275,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,276,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,277,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,278,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))). [resolve(218,a,279,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,280,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,281,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,282,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,283,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,284,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,285,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,286,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,287,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,288,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,289,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)). [resolve(218,a,290,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,291,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))). [resolve(218,a,292,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))). [resolve(218,a,293,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,294,a)].
% 1.84/2.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,295,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),B)). [resolve(218,a,296,a)].
% 1.84/2.08 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)). [resolve(218,a,297,a)].
% 1.85/2.11 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,298,a)].
% 1.85/2.11 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(218,a,299,a)].
% 1.85/2.11 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))). [resolve(218,a,300,a)].
% 1.85/2.11 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(218,a,301,a)].
% 1.87/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(218,a,302,a)].
% 1.87/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(218,a,303,a)].
% 1.87/2.11 306 class_OrderedGroup_Osemigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__mult) # label(axiom). [assumption].
% 1.87/2.11 307 -class_OrderedGroup_Osemigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I33_J_0) # label(axiom). [assumption].
% 1.87/2.11 308 -class_OrderedGroup_Osemigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I37_J_0) # label(axiom). [assumption].
% 1.87/2.11 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(306,a,307,a)].
% 1.87/2.11 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(306,a,308,a)].
% 1.87/2.14 309 class_OrderedGroup_Osemigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__mult) # label(axiom). [assumption].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(309,a,307,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(309,a,308,a)].
% 1.87/2.14 310 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.87/2.14 311 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I31_J_0) # label(axiom). [assumption].
% 1.87/2.14 312 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I35_J_0) # label(axiom). [assumption].
% 1.87/2.14 313 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.87/2.14 314 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I32_J_0) # label(axiom). [assumption].
% 1.87/2.14 315 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I36_J_0) # label(axiom). [assumption].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(310,a,311,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(310,a,312,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)). [resolve(310,a,313,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7). [resolve(310,a,314,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10). [resolve(310,a,315,a)].
% 1.87/2.14 316 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(316,a,311,a)].
% 1.87/2.14 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(316,a,312,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(316,a,313,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7). [resolve(316,a,314,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10). [resolve(316,a,315,a)].
% 1.87/2.16 317 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.87/2.16 318 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I18_J_0) # label(axiom). [assumption].
% 1.87/2.16 319 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I17_J_0) # label(axiom). [assumption].
% 1.87/2.16 320 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I21_J_0) # label(axiom). [assumption].
% 1.87/2.16 321 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I22_J_0) # label(axiom). [assumption].
% 1.87/2.16 322 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(317,a,318,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(317,a,319,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(317,a,320,a)].
% 1.87/2.16 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(317,a,321,a)].
% 1.87/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),B)),D). [resolve(317,a,322,a)].
% 1.87/2.19 323 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.87/2.19 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)),D). [resolve(323,a,322,a)].
% 1.87/2.19 324 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.87/2.19 325 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.87/2.19 326 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.87/2.19 327 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.87/2.19 328 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.87/2.19 329 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.87/2.19 330 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.87/2.19 331 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.87/2.19 332 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.87/2.19 333 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.87/2.19 334 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.87/2.19 335 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,B,A))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.87/2.19 336 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.87/2.19 337 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.87/2.19 338 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.87/2.19 339 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.87/2.19 340 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.87/2.19 341 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.87/2.19 342 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.87/2.19 343 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.87/2.19 344 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.87/2.19 345 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(C,A)),tc_fun(C,A)),D)). [resolve(324,a,325,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(C,A)),tc_fun(C,A)),D)). [resolve(324,a,326,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)). [resolve(324,a,327,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),E)). [resolve(324,a,328,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),D)). [resolve(324,a,331,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),E)). [resolve(324,a,332,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),E)). [resolve(324,a,333,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,A)))). [resolve(324,a,334,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,A)))). [resolve(324,a,335,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(324,a,338,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(324,a,339,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(324,a,340,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(324,a,341,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(324,a,342,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),B)). [resolve(324,a,343,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(324,a,344,a)].
% 1.87/2.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(324,a,345,a)].
% 1.87/2.19 346 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat),B)). [resolve(346,a,325,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),tc_nat),B)). [resolve(346,a,326,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(346,a,327,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(346,a,328,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(346,a,331,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(346,a,332,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(346,a,333,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))). [resolve(346,a,334,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))). [resolve(346,a,335,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(346,a,338,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(346,a,339,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(346,a,340,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(346,a,341,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(346,a,342,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(346,a,343,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(346,a,344,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(346,a,345,a)].
% 1.87/2.19 347 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool),B)). [resolve(347,a,325,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),tc_bool),B)). [resolve(347,a,326,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(347,a,327,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)). [resolve(347,a,328,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),B)). [resolve(347,a,331,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),C)). [resolve(347,a,332,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(B,tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)). [resolve(347,a,333,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(347,a,334,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(347,a,335,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(347,a,338,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(347,a,339,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(347,a,340,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(347,a,341,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(347,a,342,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)). [resolve(347,a,343,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(347,a,344,a)].
% 1.87/2.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(347,a,345,a)].
% 1.87/2.19 348 class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(348,a,325,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(348,a,326,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)). [resolve(348,a,327,a)].
% 1.87/2.19 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(348,a,328,a)].
% 1.97/2.25 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)). [resolve(348,a,331,a)].
% 1.97/2.25 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(348,a,332,a)].
% 1.97/2.25 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(348,a,333,a)].
% 1.97/2.25 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal))). [resolve(348,a,334,a)].
% 1.97/2.25 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal))). [resolve(348,a,335,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_RealDef_Oreal) = A. [resolve(348,a,338,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(348,a,339,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(348,a,340,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = B | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)). [resolve(348,a,341,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) != B | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)). [resolve(348,a,342,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = A | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)). [resolve(348,a,343,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal). [resolve(348,a,344,a)].
% 1.97/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal). [resolve(348,a,345,a)].
% 1.97/2.25 349 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.97/2.25 350 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.97/2.25 351 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),B,A) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.97/2.25 352 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.97/2.25 353 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.97/2.25 354 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.97/2.25 355 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 1.97/2.25 356 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 1.97/2.25 357 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 1.97/2.25 358 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.97/2.25 359 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oinverse__class_Odivide(C,D,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.97/2.25 360 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),D) = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_1) # label(axiom). [assumption].
% 1.97/2.25 361 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(B)) = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_2) # label(axiom). [assumption].
% 1.97/2.25 362 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(B)),D) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__zero__left_0) # label(axiom). [assumption].
% 1.97/2.25 363 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(c_HOL_Ouminus__class_Ouminus(B),D)),E) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(C,D),E)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__minus__left_0) # label(axiom). [assumption].
% 1.97/2.25 364 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__zero__right_0) # label(axiom). [assumption].
% 1.97/2.25 365 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),D) = hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),E) # label(cls_vector__space_Oscale__cancel__left_1) # label(axiom). [assumption].
% 1.97/2.25 366 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(c_HOL_Ouminus__class_Ouminus(A),E)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(C,D),E)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__minus__right_0) # label(axiom). [assumption].
% 1.97/2.25 367 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(B)) = hAPP(hAPP(C,E),c_HOL_Ozero__class_Ozero(B)) # label(cls_vector__space_Oscale__cancel__right_1) # label(axiom). [assumption].
% 1.97/2.25 368 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 369 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 1.97/2.25 370 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.97/2.25 371 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 1.97/2.25 372 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,F),E) | E = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) | D = F # label(cls_vector__space_Oscale__right__imp__eq_0) # label(axiom). [assumption].
% 1.97/2.25 373 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,F),E) | -c_RealVector_Ovector__space(C,B,A) | E = c_HOL_Ozero__class_Ozero(A) | D = F # label(cls_vector__space_Oscale__cancel__right_0) # label(axiom). [assumption].
% 1.97/2.25 374 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,D),F) | D = c_HOL_Ozero__class_Ozero(B) | -c_RealVector_Ovector__space(C,B,A) | E = F # label(cls_vector__space_Oscale__left__imp__eq_0) # label(axiom). [assumption].
% 1.97/2.25 375 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,D),F) | -c_RealVector_Ovector__space(C,B,A) | D = c_HOL_Ozero__class_Ozero(B) | E = F # label(cls_vector__space_Oscale__cancel__left_0) # label(axiom). [assumption].
% 1.97/2.25 376 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) | E = c_HOL_Ozero__class_Ozero(A) | D = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_0) # label(axiom). [assumption].
% 1.97/2.25 377 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 1.97/2.25 378 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.97/2.25 379 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.97/2.25 380 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.97/2.25 381 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B),B,A) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.97/2.25 382 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(C,E),F)) = hAPP(hAPP(C,E),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__commute_0) # label(axiom). [assumption].
% 1.97/2.25 383 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.97/2.25 384 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.97/2.25 385 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.97/2.25 386 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.97/2.25 387 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.97/2.25 388 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),D) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),C,A) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.97/2.25 389 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(C,E),F)) = hAPP(hAPP(C,hAPP(c_HOL_Otimes__class_Otimes(D,B),E)),F) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__scale_0) # label(axiom). [assumption].
% 1.97/2.25 390 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),D),E)),F) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(C,D),F)),hAPP(hAPP(C,E),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__diff__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 391 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(C,D),E)),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__right__diff__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 392 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.97/2.25 393 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),E) = hAPP(c_HOL_Otimes__class_Otimes(D,A),C) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.97/2.25 394 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != hAPP(c_HOL_Otimes__class_Otimes(D,A),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.97/2.25 395 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.97/2.25 396 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(C,D),E)),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__right__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 397 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(B),D),E)),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(C,D),F)),hAPP(hAPP(C,E),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 398 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal). [resolve(349,a,350,a)].
% 1.97/2.25 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),A,tc_RealDef_Oreal). [resolve(349,a,351,a)].
% 1.97/2.25 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),A,tc_RealDef_Oreal) = B. [resolve(349,a,352,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(349,a,355,a)].
% 1.97/2.25 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(349,a,356,a)].
% 1.97/2.25 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,357,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,358,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),C,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,359,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),C) = c_HOL_Ozero__class_Ozero(A). [resolve(349,a,360,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,C),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A). [resolve(349,a,361,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),C)),D) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(B,C),D)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,363,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),C) = hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),D). [resolve(349,a,365,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(c_HOL_Ouminus__class_Ouminus(A),D)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(B,C),D)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,366,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,C),c_HOL_Ozero__class_Ozero(A)) = hAPP(hAPP(B,D),c_HOL_Ozero__class_Ozero(A)). [resolve(349,a,367,a)].
% 1.97/2.25 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)). [resolve(349,a,368,a)].
% 1.97/2.25 Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,369,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,370,a)].
% 1.97/2.25 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,371,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != hAPP(hAPP(B,E),D) | D = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | C = E. [resolve(349,a,372,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != hAPP(hAPP(B,C),E) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | D = E. [resolve(349,a,374,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | D = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,376,b)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal). [resolve(349,a,377,a)].
% 1.97/2.25 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,378,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,379,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A),A,tc_RealDef_Oreal). [resolve(349,a,381,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(B,D),E)) = hAPP(hAPP(B,D),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,382,b)].
% 1.97/2.25 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,383,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | A = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,384,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B) = A | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,385,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,386,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,387,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),B,tc_RealDef_Oreal). [resolve(349,a,388,a)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(B,D),E)) = hAPP(hAPP(B,hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),E) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,389,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D)),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(B,C),E)),hAPP(hAPP(B,D),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,390,b)].
% 1.97/2.25 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,391,b)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(349,a,392,a)].
% 1.97/2.25 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B). [resolve(349,a,393,a)].
% 1.97/2.25 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) != hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,D,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal). [resolve(349,a,394,a)].
% 1.97/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,395,a)].
% 2.06/2.31 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,396,b)].
% 2.06/2.31 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(B,C),E)),hAPP(hAPP(B,D),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A). [resolve(349,a,397,b)].
% 2.06/2.31 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)). [resolve(349,a,398,a)].
% 2.06/2.31 399 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 2.06/2.31 400 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_Odiff_0) # label(axiom). [assumption].
% 2.06/2.31 401 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR__minus__right_0) # label(axiom). [assumption].
% 2.06/2.31 402 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__left__commute_0) # label(axiom). [assumption].
% 2.06/2.31 403 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom). [assumption].
% 2.06/2.31 404 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,E),D,E,A) # label(cls_scaleR__right_Osetsum_0) # label(axiom). [assumption].
% 2.06/2.31 405 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),c_HOL_Ozero__class_Ozero(A)) # label(cls_scaleR__cancel__right_1) # label(axiom). [assumption].
% 2.06/2.31 406 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),C) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom). [assumption].
% 2.06/2.31 407 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_Oadd_0) # label(axiom). [assumption].
% 2.06/2.31 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(399,a,400,a)].
% 2.06/2.31 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)). [resolve(399,a,401,a)].
% 2.06/2.31 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(399,a,402,a)].
% 2.06/2.35 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(399,a,403,a)].
% 2.06/2.35 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal). [resolve(399,a,404,a)].
% 2.06/2.35 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(399,a,405,a)].
% 2.06/2.35 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C. [resolve(399,a,406,a)].
% 2.06/2.35 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(399,a,407,a)].
% 2.06/2.35 408 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.06/2.35 409 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_Odiff__right_0) # label(axiom). [assumption].
% 2.06/2.35 410 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR_Oadditive__right_0) # label(axiom). [assumption].
% 2.06/2.35 411 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR_Ominus__right_0) # label(axiom). [assumption].
% 2.06/2.35 412 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_OscaleR__right_0) # label(axiom). [assumption].
% 2.06/2.35 413 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_OscaleR_0) # label(axiom). [assumption].
% 2.06/2.35 414 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__right_0) # label(axiom). [assumption].
% 2.06/2.35 415 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_Oadd__right_0) # label(axiom). [assumption].
% 2.06/2.35 Derived: c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(408,a,410,a)].
% 2.06/2.35 416 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 2.06/2.35 417 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 2.06/2.38 418 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 2.06/2.38 419 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 2.06/2.38 420 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 2.06/2.38 421 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 2.06/2.38 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | B = A. [resolve(416,a,417,a)].
% 2.06/2.38 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))). [resolve(416,a,420,a)].
% 2.06/2.38 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(416,a,421,a)].
% 2.06/2.38 422 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.06/2.38 423 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 2.06/2.38 424 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 2.06/2.38 425 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I30_J_0) # label(axiom). [assumption].
% 2.06/2.38 426 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Ozero__class_Ozero(A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_group__add__class_Odiff__0_0) # label(axiom). [assumption].
% 2.06/2.38 427 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 2.06/2.38 428 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 2.06/2.38 429 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 2.06/2.38 430 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 2.06/2.38 431 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I34_J_0) # label(axiom). [assumption].
% 2.06/2.38 432 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 2.06/2.38 433 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 2.06/2.38 434 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 2.06/2.38 435 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 2.06/2.38 436 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 2.06/2.38 437 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 2.06/2.38 438 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 2.06/2.38 439 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 2.06/2.38 440 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 2.06/2.38 441 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 2.06/2.38 442 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 2.06/2.38 443 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 2.06/2.38 444 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 2.06/2.38 445 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 2.06/2.38 446 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 2.06/2.38 447 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 2.06/2.38 448 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 2.06/2.38 449 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 2.06/2.38 450 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 2.06/2.38 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B. [resolve(422,a,423,a)].
% 2.06/2.38 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(422,a,424,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7). [resolve(422,a,425,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A). [resolve(422,a,426,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(422,a,427,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(422,a,428,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)). [resolve(422,a,430,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10). [resolve(422,a,431,a)].
% 2.06/2.38 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(422,a,432,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(422,a,433,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(422,a,434,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(422,a,436,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) = B. [resolve(422,a,437,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B). [resolve(422,a,438,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B). [resolve(422,a,439,a)].
% 2.06/2.38 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = A. [resolve(422,a,440,a)].
% 2.06/2.38 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). [resolve(422,a,441,a)].
% 2.06/2.38 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). [resolve(422,a,444,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = B. [resolve(422,a,445,a)].
% 2.06/2.38 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(422,a,446,a)].
% 2.06/2.38 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(422,a,447,a)].
% 2.06/2.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),B)) = B. [resolve(422,a,448,a)].
% 2.15/2.40 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),B) = A. [resolve(422,a,449,a)].
% 2.15/2.40 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),B) = A. [resolve(422,a,450,a)].
% 2.15/2.40 451 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.15/2.40 452 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(D,A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.15/2.40 453 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.15/2.40 454 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.15/2.40 455 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.15/2.40 456 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.15/2.40 457 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.15/2.40 458 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.15/2.40 459 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.15/2.40 460 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.15/2.40 461 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.15/2.40 462 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.15/2.40 463 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.15/2.40 464 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.15/2.40 465 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.15/2.40 466 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.15/2.40 467 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.15/2.40 468 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.15/2.40 469 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.15/2.40 470 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.15/2.40 471 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 2.15/2.40 472 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 2.15/2.40 473 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.15/2.40 474 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.15/2.40 475 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.15/2.40 476 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.15/2.40 477 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.15/2.40 478 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),D)). [resolve(451,a,452,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),D)). [resolve(451,a,454,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),B). [resolve(451,a,455,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C). [resolve(451,a,457,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)). [resolve(451,a,458,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A). [resolve(451,a,460,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(451,a,462,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(451,a,463,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),B). [resolve(451,a,465,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)). [resolve(451,a,466,a)].
% 2.15/2.41 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)). [resolve(451,a,467,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(451,a,468,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(451,a,469,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(451,a,471,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(451,a,473,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(451,a,474,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(451,a,476,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(451,a,477,a)].
% 2.15/2.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(451,a,478,a)].
% 2.15/2.41 479 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),D)). [resolve(479,a,452,a)].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)). [resolve(479,a,454,a)].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B). [resolve(479,a,455,a)].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C). [resolve(479,a,457,a)].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(479,a,458,a)].
% 2.15/2.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A). [resolve(479,a,460,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B). [resolve(479,a,465,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(479,a,468,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(479,a,469,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),A). [resolve(479,a,471,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(479,a,473,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C). [resolve(479,a,474,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B). [resolve(479,a,476,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(479,a,477,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(479,a,478,a)].
% 2.15/2.43 480 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.15/2.43 481 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.15/2.43 482 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.15/2.43 483 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.15/2.43 484 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.15/2.43 485 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.15/2.43 486 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.15/2.43 487 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.15/2.43 488 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 2.15/2.43 489 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.15/2.43 490 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.15/2.43 491 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(480,a,481,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(480,a,482,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(480,a,483,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(480,a,484,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(480,a,485,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(480,a,486,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(480,a,487,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(480,a,489,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(480,a,491,a)].
% 2.15/2.43 492 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(492,a,481,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(492,a,482,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(492,a,483,a)].
% 2.15/2.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(492,a,484,a)].
% 2.15/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(492,a,485,a)].
% 2.15/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(492,a,486,a)].
% 2.15/2.46 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)). [resolve(492,a,487,a)].
% 2.15/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(492,a,489,a)].
% 2.15/2.46 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(492,a,491,a)].
% 2.15/2.46 493 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.15/2.46 494 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.15/2.46 495 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.15/2.46 496 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.15/2.46 497 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.15/2.46 498 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.26/2.50 499 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.26/2.50 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(493,a,494,a)].
% 2.26/2.50 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(493,a,495,a)].
% 2.26/2.50 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(493,a,496,a)].
% 2.26/2.50 500 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.26/2.50 501 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.26/2.50 502 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 2.26/2.50 503 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 2.26/2.50 504 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 2.26/2.50 505 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 2.26/2.50 506 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 2.26/2.50 507 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 2.26/2.50 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(501,a,502,a)].
% 2.26/2.50 508 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.26/2.50 509 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.26/2.50 510 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.26/2.58 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(508,a,509,a)].
% 2.26/2.58 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(508,a,510,a)].
% 2.26/2.58 511 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.26/2.58 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(511,a,509,a)].
% 2.26/2.58 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(511,a,510,a)].
% 2.26/2.58 512 c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(181,a,182,a)].
% 2.26/2.58 513 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),hAPP(C,D)),hAPP(C,E)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Odiff_0) # label(axiom). [assumption].
% 2.26/2.58 514 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_Finite__Set_Osetsum(D,E,F,B)) = c_Finite__Set_Osetsum(c_COMBB(C,D,B,A,F),E,F,A) | -c_RealVector_Oadditive(C,B,A) # label(cls_additive_Osetsum_0) # label(axiom). [assumption].
% 2.26/2.58 515 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),D)) = hAPP(c_HOL_Ouminus__class_Ouminus(B),hAPP(C,D)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Ominus_0) # label(axiom). [assumption].
% 2.26/2.58 516 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_HOL_Ozero__class_Ozero(B)) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Oadditive(C,B,A) # label(cls_additive_Ozero_0) # label(axiom). [assumption].
% 2.26/2.58 517 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(B),hAPP(C,D)),hAPP(C,E)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Oadd_0) # label(axiom). [assumption].
% 2.26/2.58 518 c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(408,a,410,a)].
% 2.26/2.58 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(518,a,513,d)].
% 2.36/2.63 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal). [resolve(518,a,514,d)].
% 2.36/2.63 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)). [resolve(518,a,515,d)].
% 2.36/2.63 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(518,a,516,d)].
% 2.36/2.63 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(518,a,517,d)].
% 2.36/2.63 519 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.36/2.63 520 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.36/2.63 521 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.36/2.63 522 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.36/2.63 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(519,a,520,a)].
% 2.36/2.63 523 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.36/2.63 524 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom). [assumption].
% 2.36/2.63 525 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom). [assumption].
% 2.36/2.63 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(523,a,524,a)].
% 2.36/2.63 526 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.36/2.63 527 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 2.36/2.63 528 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 2.36/2.66 529 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),D,A) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_OscaleR_0) # label(axiom). [assumption].
% 2.36/2.66 530 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 2.36/2.66 531 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 2.36/2.66 532 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 2.36/2.66 Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),C,tc_RealDef_Oreal) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)). [resolve(527,a,529,a)].
% 2.36/2.66 Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)). [resolve(527,a,530,a)].
% 2.36/2.66 533 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.36/2.66 534 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 2.36/2.66 535 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 2.36/2.66 536 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.36/2.66 537 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.36/2.66 538 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 2.36/2.66 539 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 2.36/2.66 540 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.36/2.66 541 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.36/2.67 542 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 2.36/2.67 543 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 2.36/2.67 544 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 2.36/2.67 545 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 2.36/2.67 546 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 2.36/2.67 547 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 2.36/2.67 548 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 2.36/2.67 549 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(537,a,538,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(537,a,539,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(537,a,540,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(537,a,541,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(537,a,542,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(537,a,543,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(537,a,544,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(537,a,545,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(537,a,546,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(537,a,547,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(537,a,548,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(537,a,549,a)].
% 2.36/2.67 550 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)). [resolve(550,a,538,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(550,a,539,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(550,a,540,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)). [resolve(550,a,541,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(550,a,542,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))). [resolve(550,a,543,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)). [resolve(550,a,544,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))). [resolve(550,a,545,a)].
% 2.36/2.69 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(550,a,546,a)].
% 2.36/2.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))). [resolve(550,a,547,a)].
% 2.36/2.69 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)). [resolve(550,a,548,a)].
% 2.36/2.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))). [resolve(550,a,549,a)].
% 2.36/2.69 551 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.36/2.69 552 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),A),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 2.36/2.69 553 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 2.36/2.69 554 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 2.36/2.69 555 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 2.36/2.69 556 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 2.36/2.69 557 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),A),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 2.36/2.69 558 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(E,A),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(F,A),D),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 2.36/2.69 559 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 2.36/2.69 560 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),A),C),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 2.36/2.69 561 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 2.36/2.69 562 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 2.36/2.69 563 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 2.36/2.69 564 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 2.36/2.69 565 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 2.36/2.69 566 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Divides_Odiv__class_Omod(C,D,A)) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 2.36/2.69 567 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) = hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),A),C) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 2.36/2.69 568 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 2.36/2.69 569 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 2.36/2.69 570 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 2.36/2.69 571 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 2.36/2.69 572 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 2.36/2.69 573 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 2.36/2.69 574 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),B,tc_nat). [resolve(551,a,552,a)].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(551,a,553,a)].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(551,a,554,a)].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(551,a,555,a)].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(551,a,556,a)].
% 2.36/2.69 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(551,a,557,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(D,tc_nat),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(E,tc_nat),C),B,tc_nat). [resolve(551,a,558,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(551,a,559,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),B),C,tc_nat). [resolve(551,a,560,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(551,a,561,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(551,a,562,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat). [resolve(551,a,563,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(551,a,564,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(551,a,565,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)). [resolve(551,a,566,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),B). [resolve(551,a,567,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat). [resolve(551,a,568,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat). [resolve(551,a,569,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(551,a,570,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(551,a,571,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(551,a,572,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(551,a,573,a)].
% 2.46/2.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(551,a,574,a)].
% 2.46/2.71 575 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.55/2.80 576 -class_Ring__and__Field_Osemiring__0(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 2.55/2.80 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_nat),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(575,a,576,a)].
% 2.55/2.80 577 class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.55/2.80 578 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 2.55/2.80 579 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 2.55/2.80 580 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 2.55/2.80 581 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.55/2.80 582 -class_RealVector_Oreal__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),F,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E),F,A))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),F,A),A),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 2.55/2.80 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),E,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D),E,tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),E,tc_RealDef_Oreal),tc_RealDef_Oreal),D)). [resolve(581,a,582,a)].
% 2.55/2.80 583 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.55/2.80 584 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 2.55/2.80 585 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 2.55/2.80 586 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.55/2.80 587 -class_OrderedGroup_Osemigroup__add(A) | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A) # label(cls_semigroup__add__class_Oaxioms_0) # label(axiom). [assumption].
% 2.55/2.80 588 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_OrderedGroup_Osemigroup__add(A,E) # label(cls_semigroup__add_Oadd__assoc_0) # label(axiom). [assumption].
% 2.55/2.80 Derived: -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)). [resolve(587,b,588,b)].
% 2.55/2.80 589 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.55/2.82 590 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.55/2.82 591 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.55/2.82 592 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.82 593 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.55/2.82 594 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.55/2.82 595 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.55/2.82 596 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.55/2.82 597 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.55/2.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(592,a,593,a)].
% 2.55/2.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(592,a,594,a)].
% 2.55/2.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(592,a,597,a)].
% 2.55/2.82 598 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(598,a,593,a)].
% 2.55/2.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(598,a,594,a)].
% 2.55/2.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)). [resolve(598,a,597,a)].
% 2.55/2.86 599 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.86 600 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I39_J_0) # label(axiom). [assumption].
% 2.55/2.86 601 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I38_J_0) # label(axiom). [assumption].
% 2.55/2.86 602 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.55/2.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(599,b,600,a)].
% 2.55/2.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12). [resolve(599,b,601,a)].
% 2.55/2.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)). [resolve(599,b,602,a)].
% 2.55/2.86 603 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.86 604 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.86 605 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.55/2.86 606 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.55/2.86 607 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.55/2.86 608 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.55/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(605,a,606,a)].
% 2.55/2.86 609 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.94 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)). [resolve(609,a,606,a)].
% 2.67/2.94 610 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.67/2.94 611 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.67/2.94 612 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.67/2.94 613 class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 2.67/2.94 614 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__sup__distrib__right_0) # label(axiom). [assumption].
% 2.67/2.94 615 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__sup__distrib__left_0) # label(axiom). [assumption].
% 2.67/2.94 616 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.67/2.94 617 -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I40_J_0) # label(axiom). [assumption].
% 2.67/2.94 618 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.67/2.94 619 class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.67/2.94 620 -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)). [resolve(587,b,588,b)].
% 2.67/2.94 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(620,a,618,a)].
% 2.67/2.94 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(620,a,619,a)].
% 2.67/2.94 621 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.94 622 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(A),A) # label(cls_cancel__ab__semigroup__add__class_Oaxioms_0) # label(axiom). [assumption].
% 2.67/2.94 623 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.67/2.94 Derived: c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat). [resolve(621,a,622,a)].
% 2.79/3.09 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(621,a,623,a)].
% 2.79/3.09 624 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.79/3.09 Derived: c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(624,a,622,a)].
% 2.79/3.09 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(624,a,623,a)].
% 2.79/3.09 625 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Omonoid__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.79/3.09 626 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.79/3.09 627 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.79/3.09 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B. [resolve(625,b,626,a)].
% 2.79/3.09 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B. [resolve(625,b,627,a)].
% 2.79/3.09 628 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.79/3.09 629 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.79/3.09 630 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.79/3.09 631 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.79/3.09 632 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.79/3.09 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(630,a,631,a)].
% 2.79/3.09 633 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.79/3.09 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C. [resolve(633,a,631,a)].
% 2.79/3.09 634 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.79/3.09 635 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.79/3.09 Derived: A = A. [resolve(634,b,635,a)].
% 2.79/3.09
% 2.79/3.09 ============================== end predicate elimination =============
% 2.79/3.09
% 2.79/3.09 Auto_denials: (non-Horn, no changes).
% 2.79/3.09
% 2.79/3.09 Term ordering decisions:
% 2.79/3.09 Function symbol KB weights: tc_RealDef_Oreal=1. tc_nat=1. c_Suc=1. tc_bool=1. t_a=1. v_k=1. v_f=1. v_g=1. v_x=1. t_b=1. v_n=1. v_m=1. t_c=1. v_h=1. hAPP=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_HOL_Otimes__class_Otimes=1. tc_fun=1. c_RealVector_OscaleR__class_OscaleR=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OlessThan=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Ominus__class_Ominus=1. c_Option_Ooption_ONone=1. tc_Option_Ooption=1. c_HOL_Oinverse__class_Odivide=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Divides_Odiv__class_Omod=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanLessThan=1. c_Finite__Set_Osetsum=1. v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1=1. c_Fun_Ocomp=1. c_COMBB=1. c_Fun_Ofcomp=1. c_Option_Ooption_Ooption__case=1. c_COMBS=1. c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1=1. c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1=1. c_Map_Omap__comp=1.
% 4.46/4.77
% 4.46/4.77 ============================== end of process initial clauses ========
% 4.46/4.77
% 4.46/4.77 ============================== CLAUSES FOR SEARCH ====================
% 4.46/4.77
% 4.46/4.77 ============================== end of clauses for search =============
% 4.46/4.77
% 4.46/4.77 ============================== SEARCH ================================
% 4.46/4.77
% 4.46/4.77 % Starting search at 1.71 seconds.
% 4.46/4.77
% 4.46/4.77 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 1.91 sec).
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=75.000, iters=3722
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=62.000, iters=3652
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=60.000, iters=3620
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=59.000, iters=3595
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=57.000, iters=3520
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=56.000, iters=3538
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=52.000, iters=3386
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=50.000, iters=3367
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=48.000, iters=3557
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=47.000, iters=3422
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=45.000, iters=3404
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=44.000, iters=3344
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=43.000, iters=3656
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=42.000, iters=3553
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=41.000, iters=3502
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=40.000, iters=3398
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=39.000, iters=3385
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=38.000, iters=3365
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=37.000, iters=3354
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=36.000, iters=3351
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=35.000, iters=3371
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=33.000, iters=3335
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=32.000, iters=3438
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=31.000, iters=3593
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=30.000, iters=3515
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=29.000, iters=3388
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=28.000, iters=3442
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=27.000, iters=3371
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=26.000, iters=3340
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=25.000, iters=3645
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=24.000, iters=3607
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=23.000, iters=3354
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=18.000, iters=3343
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3634, wt=83.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3661, wt=79.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=2898, wt=77.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3672, wt=76.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=4996, wt=74.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3674, wt=72.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=2287, wt=70.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=4928, wt=68.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3612, wt=66.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=4972, wt=65.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=3942, wt=63.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=12844, wt=14.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=12851, wt=13.000
% 4.46/4.77
% 4.46/4.77 Low Water (displace): id=12990, wt=12.000
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=16.000, iters=3492
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=15.000, iters=3415
% 4.46/4.77
% 4.46/4.77 Low Water (keep): wt=14.000, iters=3334
% 4.46/4.77
% 4.46/4.77 ============================== PROOF =================================
% 4.46/4.77 % SZS status Unsatisfiable
% 4.46/4.77 % SZS output start Refutation
% 4.46/4.77
% 4.46/4.77 % Proof 1 at 3.37 (+ 0.03) seconds.
% 4.46/4.77 % Length of proof is 14.
% 4.46/4.77 % Level of proof is 5.
% 4.46/4.77 % Maximum clause weight is 22.000.
% 4.46/4.77 % Given clauses 1458.
% 4.46/4.77
% 4.46/4.77 451 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.46/4.77 468 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 4.46/4.77 636 hAPP(c_Fun_Ofcomp(A,B,C,D,E),F) = hAPP(B,hAPP(A,F)) # label(cls_fcomp__apply_0) # label(axiom). [assumption].
% 4.46/4.77 638 A != hAPP(c_Suc,A) # label(cls_n__not__Suc__n_0) # label(axiom). [assumption].
% 4.46/4.77 639 hAPP(c_Suc,A) != A. [copy(638),flip(a)].
% 4.46/4.77 741 hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 4.46/4.77 763 hAPP(A,hAPP(B,C)) = hAPP(c_Fun_Ocomp(A,B,D,E,F),C) # label(cls_o__eq__dest__lhs_0) # label(axiom). [assumption].
% 4.46/4.77 764 hAPP(c_Fun_Ocomp(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)). [copy(763),flip(a)].
% 4.46/4.77 1469 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(451,a,468,a)].
% 4.46/4.77 1743 hAPP(A,hAPP(c_COMBS(B,C,D,E,F),V6)) = hAPP(A,hAPP(hAPP(B,V6),hAPP(C,V6))). [para(741(a,1),636(a,2,2)),rewrite([636(3)])].
% 4.46/4.77 8141 hAPP(hAPP(A,B),hAPP(C,B)) != hAPP(c_Suc,hAPP(c_COMBS(A,C,D,E,F),B)). [para(1743(a,2),639(a,1)),flip(a)].
% 4.46/4.77 9860 hAPP(c_Suc,hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C,D),E)) != hAPP(E,hAPP(A,E)). [para(1469(a,1),8141(a,1,1)),flip(a)].
% 4.46/4.77 16556 hAPP(c_Suc,hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D)) != hAPP(D,D). [para(1469(a,1),9860(a,2,2))].
% 4.46/4.77 16557 $F. [resolve(16556,a,764,a(flip))].
% 4.46/4.77
% 4.46/4.77 % SZS output end Refutation
% 4.46/4.77 ============================== end of proof ==========================
% 4.46/4.77
% 4.46/4.77 ============================== STATISTICS ============================
% 4.46/4.77
% 4.46/4.77 Given=1458. Generated=40914. Kept=15661. proofs=1.
% 4.46/4.77 Usable=1449. Sos=9999. Demods=565. Limbo=69, Disabled=5810. Hints=0.
% 4.46/4.77 Megabytes=23.46.
% 4.46/4.77 User_CPU=3.37, System_CPU=0.03, Wall_clock=4.
% 4.46/4.77
% 4.46/4.77 ============================== end of statistics =====================
% 4.46/4.77
% 4.46/4.77 ============================== end of search =========================
% 4.46/4.77
% 4.46/4.77 THEOREM PROVED
% 4.46/4.77 % SZS status Unsatisfiable
% 4.46/4.77
% 4.46/4.77 Exiting with 1 proof.
% 4.46/4.77
% 4.46/4.77 Process 30448 exit (max_proofs) Tue Jun 14 23:50:14 2022
% 4.46/4.77 Prover9 interrupted
%------------------------------------------------------------------------------