TSTP Solution File: LCL804-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL804-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Sun Jul 17 13:50:21 EDT 2022
% Result : Timeout 300.05s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL804-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 20:54:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.11/1.51 ============================== Prover9 ===============================
% 1.11/1.51 Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.51 Process 2429 was started by sandbox on n017.cluster.edu,
% 1.11/1.51 Sun Jul 3 20:54:12 2022
% 1.11/1.51 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2276_n017.cluster.edu".
% 1.11/1.51 ============================== end of head ===========================
% 1.11/1.51
% 1.11/1.51 ============================== INPUT =================================
% 1.11/1.51
% 1.11/1.51 % Reading from file /tmp/Prover9_2276_n017.cluster.edu
% 1.11/1.51
% 1.11/1.51 set(prolog_style_variables).
% 1.11/1.51 set(auto2).
% 1.11/1.51 % set(auto2) -> set(auto).
% 1.11/1.51 % set(auto) -> set(auto_inference).
% 1.11/1.51 % set(auto) -> set(auto_setup).
% 1.11/1.51 % set(auto_setup) -> set(predicate_elim).
% 1.11/1.51 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.51 % set(auto) -> set(auto_limits).
% 1.11/1.51 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.51 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.51 % set(auto) -> set(auto_denials).
% 1.11/1.51 % set(auto) -> set(auto_process).
% 1.11/1.51 % set(auto2) -> assign(new_constants, 1).
% 1.11/1.51 % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.51 % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.51 % set(auto2) -> assign(max_hours, 1).
% 1.11/1.51 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.51 % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.51 % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.51 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.51 % set(auto2) -> set(sort_initial_sos).
% 1.11/1.51 % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.51 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.51 % set(auto2) -> assign(max_megs, 400).
% 1.11/1.51 % set(auto2) -> assign(stats, some).
% 1.11/1.51 % set(auto2) -> clear(echo_input).
% 1.11/1.51 % set(auto2) -> set(quiet).
% 1.11/1.51 % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.51 % set(auto2) -> clear(print_given).
% 1.11/1.51 assign(lrs_ticks,-1).
% 1.11/1.51 assign(sos_limit,10000).
% 1.11/1.51 assign(order,kbo).
% 1.11/1.51 set(lex_order_vars).
% 1.11/1.51 clear(print_given).
% 1.11/1.51
% 1.11/1.51 % formulas(sos). % not echoed (1156 formulas)
% 1.11/1.51
% 1.11/1.51 ============================== end of input ==========================
% 1.11/1.51
% 1.11/1.51 % From the command line: assign(max_seconds, 300).
% 1.11/1.51
% 1.11/1.51 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.51
% 1.11/1.51 % Formulas that are not ordinary clauses:
% 1.11/1.51
% 1.11/1.51 ============================== end of process non-clausal formulas ===
% 1.11/1.51
% 1.11/1.51 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.51
% 1.11/1.51 ============================== PREDICATE ELIMINATION =================
% 1.11/1.51 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.11/1.51 2 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 1.11/1.51 3 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 1.11/1.51 4 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 1.11/1.51 5 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 1.11/1.51 6 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 1.11/1.51 7 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 1.11/1.51 8 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 1.11/1.51 9 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 1.11/1.51 10 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.11/1.51 11 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 1.11/1.51 12 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 1.11/1.51 13 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(B,C,A),A) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 1.11/1.51 14 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,B,A),A) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 1.11/1.51 15 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Orderings_Oord__class_Omax(B,C,A)),D) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 1.11/1.51 16 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),c_Orderings_Oord__class_Omax(C,D,A)) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D),A) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 1.11/1.51 17 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 1.11/1.51 18 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 1.11/1.51 19 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 1.11/1.51 20 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 1.11/1.51 21 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 1.11/1.51 22 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 1.11/1.51 23 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 1.11/1.51 24 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 1.11/1.51 25 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 1.11/1.51 26 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 1.11/1.51 27 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 1.11/1.51 28 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) != C | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 1.11/1.51 29 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 1.11/1.51 30 -class_Orderings_Olinorder(A) | -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(A) = c_Orderings_Oord__class_Omin(A) # label(cls_inf__min_0) # label(axiom). [assumption].
% 1.11/1.51 31 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 1.11/1.51 32 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 1.11/1.51 33 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 1.11/1.51 34 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.11/1.51 35 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.11/1.51 36 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.11/1.51 37 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.11/1.51 38 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.11/1.51 39 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.11/1.51 40 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.11/1.51 41 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 1.11/1.51 42 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 1.11/1.51 43 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),c_Orderings_Oord__class_Omax(B,C,A)) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 1.11/1.51 44 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 1.11/1.51 45 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 1.11/1.51 46 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 1.11/1.51 47 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 1.11/1.51 48 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 1.11/1.51 49 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 1.11/1.51 50 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 1.11/1.51 51 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 1.11/1.51 52 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 1.11/1.51 53 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 1.11/1.51 54 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.11/1.51 55 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),B) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 1.11/1.51 56 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 1.11/1.51 57 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 1.11/1.51 58 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 1.11/1.51 59 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 1.11/1.51 60 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 1.11/1.51 61 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 1.11/1.51 62 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 1.11/1.51 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 1.11/1.51 64 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 1.11/1.51 65 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 1.11/1.51 66 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 1.11/1.51 67 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 1.11/1.51 68 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 1.11/1.51 69 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.11/1.51 70 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.11/1.51 71 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.11/1.51 72 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.11/1.51 73 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,B,A) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 1.11/1.51 74 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = c_Orderings_Oord__class_Omax(C,B,A) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 1.11/1.51 75 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),c_Orderings_Oord__class_Omax(C,D,A)),A) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 1.11/1.51 76 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),A) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 1.11/1.51 77 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 1.11/1.51 78 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 1.11/1.51 79 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A) = c_Orderings_Oord__class_Omax(B,C,A) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 1.11/1.51 80 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Orderings_Oord__class_Omax(B,C,A)),c_Orderings_Oord__class_Omax(B,D,A)),A) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 1.11/1.51 81 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Orderings_Oord__class_Omax(B,D,A)),c_Orderings_Oord__class_Omax(C,D,A)) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 1.11/1.51 82 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Orderings_Oord__class_Omax(B,C,A)),c_Orderings_Oord__class_Omax(B,D,A)) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 1.11/1.51 83 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.11/1.51 84 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.11/1.51 85 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.11/1.51 86 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.11/1.51 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,2,a)].
% 1.11/1.51 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),A,tc_nat). [resolve(1,a,3,a)].
% 1.11/1.51 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),B,tc_nat). [resolve(1,a,4,a)].
% 1.11/1.51 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,5,a)].
% 1.11/1.51 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,8,a)].
% 1.11/1.51 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,9,a)].
% 1.11/1.51 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B). [resolve(1,a,10,a)].
% 1.11/1.51 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat). [resolve(1,a,13,a)].
% 1.11/1.51 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_nat),tc_nat). [resolve(1,a,14,a)].
% 1.11/1.51 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),C) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat). [resolve(1,a,15,a)].
% 1.11/1.51 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),c_Orderings_Oord__class_Omax(B,C,tc_nat)) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C),tc_nat). [resolve(1,a,16,a)].
% 1.11/1.51 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(1,a,17,a)].
% 1.11/1.51 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B),tc_nat). [resolve(1,a,18,a)].
% 1.11/1.51 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat). [resolve(1,a,19,a)].
% 1.11/1.51 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(1,a,20,a)].
% 1.11/1.51 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,21,a)].
% 1.11/1.51 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A),B,tc_nat). [resolve(1,a,26,a)].
% 1.11/1.51 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(1,a,27,a)].
% 1.11/1.51 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(1,a,28,a)].
% 1.11/1.51 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(1,a,29,a)].
% 1.11/1.51 Derived: -class_Lattices_Olower__semilattice(tc_nat) | c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat). [resolve(1,a,30,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = A | -c_lessequals(A,B,tc_nat). [resolve(1,a,31,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) != A | c_lessequals(A,B,tc_nat). [resolve(1,a,32,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = B | -c_lessequals(B,A,tc_nat). [resolve(1,a,33,a)].
% 1.11/1.52 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,34,a)].
% 1.11/1.52 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,35,a)].
% 1.11/1.52 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(1,a,37,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)). [resolve(1,a,41,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)). [resolve(1,a,42,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),c_Orderings_Oord__class_Omax(A,B,tc_nat)) = A. [resolve(1,a,43,a)].
% 1.11/1.52 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(1,a,44,a)].
% 1.11/1.52 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(1,a,45,a)].
% 1.11/1.52 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,46,a)].
% 1.11/1.52 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,47,a)].
% 1.11/1.52 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(1,a,52,a)].
% 1.11/1.60 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A),B,tc_nat). [resolve(1,a,53,a)].
% 1.11/1.60 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,54,a)].
% 1.11/1.60 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(1,a,55,a)].
% 1.11/1.60 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,56,a)].
% 1.11/1.60 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,57,a)].
% 1.11/1.60 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(1,a,60,a)].
% 1.11/1.60 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(1,a,61,a)].
% 1.11/1.60 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),A). [resolve(1,a,62,a)].
% 1.11/1.61 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,63,a)].
% 1.11/1.61 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,64,a)].
% 1.11/1.61 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat). [resolve(1,a,65,a)].
% 1.11/1.61 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B),tc_nat). [resolve(1,a,66,a)].
% 1.11/1.61 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,69,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,A,tc_nat) = A. [resolve(1,a,73,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = c_Orderings_Oord__class_Omax(B,A,tc_nat). [resolve(1,a,74,a)].
% 1.11/1.61 Derived: c_lessequals(c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C),tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),c_Orderings_Oord__class_Omax(B,C,tc_nat)),tc_nat). [resolve(1,a,75,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),tc_nat) = A. [resolve(1,a,76,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(1,a,77,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(1,a,78,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(A,B,tc_nat). [resolve(1,a,79,a)].
% 1.11/1.61 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),c_Orderings_Oord__class_Omax(A,C,tc_nat)),tc_nat). [resolve(1,a,80,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),c_Orderings_Oord__class_Omax(A,C,tc_nat)),c_Orderings_Oord__class_Omax(B,C,tc_nat)). [resolve(1,a,81,a)].
% 1.11/1.61 Derived: c_Orderings_Oord__class_Omax(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),c_Orderings_Oord__class_Omax(A,C,tc_nat)). [resolve(1,a,82,a)].
% 1.11/1.61 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,83,a)].
% 1.11/1.61 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,85,a)].
% 1.11/1.61 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,86,a)].
% 1.11/1.61 87 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.11/1.65 88 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Suc(B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.11/1.65 89 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.11/1.65 90 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.11/1.65 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(87,a,88,a)].
% 1.11/1.65 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(87,a,89,a)].
% 1.11/1.65 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(87,a,90,a)].
% 1.11/1.65 91 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.11/1.65 92 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.11/1.65 93 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.11/1.65 94 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.11/1.65 95 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.11/1.65 96 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.11/1.65 97 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,tc_nat) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.11/1.65 98 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.11/1.65 99 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | -c_lessequals(C,D,tc_nat) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.11/1.65 100 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.11/1.65 101 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.11/1.65 102 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.11/1.65 103 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.11/1.65 104 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.11/1.65 105 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.11/1.65 106 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.11/1.65 107 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.11/1.65 108 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.11/1.65 109 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.11/1.65 110 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.11/1.65 111 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.11/1.65 112 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.11/1.65 113 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.11/1.65 114 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Suc(D)),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.11/1.65 115 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.11/1.65 116 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.11/1.65 117 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.11/1.65 118 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.11/1.65 119 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | B = D | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.11/1.65 120 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.11/1.65 121 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.11/1.65 122 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.11/1.65 123 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.11/1.65 124 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.11/1.65 125 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.11/1.65 126 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.11/1.65 127 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Suc(C)) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.11/1.65 128 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.11/1.65 129 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.11/1.65 130 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.11/1.65 131 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.11/1.65 132 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.11/1.65 133 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.11/1.65 134 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.11/1.65 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,92,a)].
% 1.11/1.65 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,93,a)].
% 1.11/1.65 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(91,a,94,a)].
% 1.11/1.65 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(91,a,95,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(91,a,96,a)].
% 1.11/1.65 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(91,a,97,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,98,a)].
% 1.11/1.65 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(91,a,99,a)].
% 1.11/1.65 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(91,a,100,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C),tc_nat). [resolve(91,a,101,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,102,a)].
% 1.11/1.65 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(91,a,103,a)].
% 1.11/1.65 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(91,a,104,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,105,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(91,a,106,a)].
% 1.11/1.65 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(91,a,107,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,108,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,109,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(91,a,110,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(91,a,111,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(91,a,112,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(91,a,113,a)].
% 1.11/1.65 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Suc(C)),tc_nat). [resolve(91,a,114,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,115,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(91,a,116,a)].
% 1.11/1.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(91,a,117,a)].
% 1.11/1.65 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(91,a,118,a)].
% 1.11/1.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,119,a)].
% 1.11/1.65 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,120,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(91,a,121,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,122,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(91,a,123,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,126,a)].
% 1.45/1.70 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),c_Suc(B)) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(91,a,127,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(91,a,128,a)].
% 1.45/1.70 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(91,a,129,a)].
% 1.45/1.70 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(91,a,131,a)].
% 1.45/1.70 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,133,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(91,a,134,a)].
% 1.45/1.70 135 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.45/1.70 136 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.45/1.70 137 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.45/1.70 138 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.45/1.70 139 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.45/1.70 140 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.45/1.70 141 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.45/1.70 142 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.45/1.70 143 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.45/1.70 144 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.45/1.70 145 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.45/1.70 146 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.45/1.70 147 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.45/1.70 148 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.45/1.70 149 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.45/1.70 150 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.45/1.70 151 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(135,a,136,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(135,a,137,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(135,a,138,a)].
% 1.45/1.70 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(135,a,139,a)].
% 1.45/1.70 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(135,a,140,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(135,a,141,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(135,a,142,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(135,a,143,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(135,a,144,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(135,a,145,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(135,a,146,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(135,a,147,a)].
% 1.45/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(135,a,148,a)].
% 1.54/1.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(135,a,149,a)].
% 1.54/1.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(135,a,151,a)].
% 1.54/1.78 152 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.54/1.78 153 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.54/1.78 154 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.54/1.78 155 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.54/1.78 156 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.54/1.78 157 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.54/1.78 158 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.54/1.78 159 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.54/1.78 160 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.54/1.78 161 -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].
% 1.54/1.78 162 -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].
% 1.54/1.78 163 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.54/1.78 164 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.54/1.78 165 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 1.54/1.78 166 -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].
% 1.54/1.78 167 -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].
% 1.54/1.78 168 -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].
% 1.54/1.78 169 -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].
% 1.54/1.78 170 -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].
% 1.54/1.78 171 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.54/1.78 172 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.54/1.78 173 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.54/1.78 174 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.54/1.78 175 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.54/1.78 176 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.54/1.78 177 -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].
% 1.54/1.78 178 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__semiring_Ogb__semiring__axioms_H_0) # label(axiom). [assumption].
% 1.54/1.78 179 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.54/1.78 180 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.54/1.78 181 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.54/1.78 182 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.54/1.78 183 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.54/1.78 184 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.54/1.78 185 -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].
% 1.54/1.78 186 -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].
% 1.54/1.78 187 -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].
% 1.54/1.78 188 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.54/1.78 189 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.54/1.78 190 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.54/1.78 191 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.54/1.78 192 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.54/1.78 193 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.54/1.78 194 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.54/1.78 195 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(152,a,153,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(152,a,154,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(152,a,156,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(152,a,157,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(152,a,159,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(152,a,161,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(152,a,163,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(152,a,164,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(152,a,165,a)].
% 1.54/1.78 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(152,a,166,a)].
% 1.54/1.78 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(152,a,168,a)].
% 1.54/1.78 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(152,a,169,a)].
% 1.54/1.78 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(152,a,170,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(152,a,171,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(152,a,172,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(152,a,173,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(152,a,174,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(152,a,175,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(152,a,176,a)].
% 1.54/1.78 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(152,a,177,a)].
% 1.54/1.78 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(152,a,178,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(152,a,179,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(152,a,180,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(152,a,181,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(152,a,182,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(152,a,183,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(152,a,185,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(152,a,186,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(152,a,188,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(152,a,189,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(152,a,190,a)].
% 1.54/1.78 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(152,a,191,a)].
% 1.59/1.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(152,a,192,a)].
% 1.59/1.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(152,a,194,a)].
% 1.59/1.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(152,a,195,a)].
% 1.59/1.85 196 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.59/1.85 197 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 1.59/1.85 198 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 1.59/1.85 199 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.59/1.85 200 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.59/1.85 201 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.59/1.85 202 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 1.59/1.85 203 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.59/1.85 204 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 1.59/1.85 205 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 1.59/1.85 206 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.59/1.85 207 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 1.59/1.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(199,a,202,a)].
% 1.59/1.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(199,a,205,a)].
% 1.59/1.87 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(199,a,206,a)].
% 1.59/1.87 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C). [resolve(199,a,207,a)].
% 1.59/1.87 208 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.59/1.87 209 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.59/1.87 210 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.59/1.87 211 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.59/1.87 212 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.59/1.87 213 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 1.59/1.87 214 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.59/1.87 215 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.59/1.87 216 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.59/1.87 217 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.59/1.87 218 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.59/1.87 219 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.59/1.87 220 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.68/1.97 221 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.68/1.97 222 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(208,a,209,a)].
% 1.68/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(208,a,210,a)].
% 1.68/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(208,a,211,a)].
% 1.68/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(208,a,212,a)].
% 1.68/1.97 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(208,a,213,a)].
% 1.68/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(208,a,214,a)].
% 1.68/1.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(208,a,215,a)].
% 1.68/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(208,a,216,a)].
% 1.68/1.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(208,a,217,a)].
% 1.68/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(208,a,218,a)].
% 1.68/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(208,a,219,a)].
% 1.68/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(208,a,220,a)].
% 1.68/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(208,a,221,a)].
% 1.68/1.97 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),C) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(208,a,222,a)].
% 1.68/1.97 223 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.68/1.97 224 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.75/2.02 225 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.75/2.02 226 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.75/2.02 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(223,a,224,a)].
% 1.75/2.02 227 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.75/2.02 228 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) # label(cls_listsum_0) # label(axiom). [assumption].
% 1.75/2.02 229 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 1.75/2.02 230 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_ONil(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum_Osimps_I1_J_0) # label(axiom). [assumption].
% 1.75/2.02 231 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_OCons(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A)) # label(cls_listsum_Osimps_I2_J_0) # label(axiom). [assumption].
% 1.75/2.02 232 -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].
% 1.75/2.02 233 -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].
% 1.75/2.02 234 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Oappend(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A)) # label(cls_listsum__append_0) # label(axiom). [assumption].
% 1.75/2.02 235 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),C,B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum__0_0) # label(axiom). [assumption].
% 1.75/2.02 Derived: c_List_Olistsum(A,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat). [resolve(227,a,228,a)].
% 1.75/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(227,a,229,a)].
% 1.75/2.02 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(227,a,230,a)].
% 1.75/2.02 Derived: c_List_Olistsum(c_List_Olist_OCons(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Olistsum(B,tc_nat)). [resolve(227,a,231,a)].
% 1.75/2.02 Derived: c_List_Olistsum(c_List_Oappend(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olistsum(A,tc_nat)),c_List_Olistsum(B,tc_nat)). [resolve(227,a,234,a)].
% 1.75/2.02 Derived: c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),B,A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(227,a,235,a)].
% 1.75/2.02 236 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.75/2.02 237 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),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].
% 1.75/2.02 238 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.75/2.02 239 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.75/2.02 240 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.75/2.02 241 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.75/2.02 242 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.75/2.02 243 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.75/2.02 244 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.75/2.02 245 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.75/2.02 246 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.75/2.02 247 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.75/2.02 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(236,a,238,a)].
% 1.75/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(236,a,239,a)].
% 1.75/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(236,a,240,a)].
% 1.75/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(236,a,241,a)].
% 1.75/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(236,a,242,a)].
% 1.75/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(236,a,243,a)].
% 1.75/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(236,a,244,a)].
% 1.75/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(236,a,245,a)].
% 1.75/2.05 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(236,a,247,a)].
% 1.75/2.05 248 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(152,a,178,a)].
% 1.75/2.05 249 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) | -c_Groebner__Basis_Ogb__semiring(E,F,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.75/2.05 250 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,B,V6,V7,V8) # label(cls_gb__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.75/2.05 251 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(F,B,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.75/2.05 252 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) = hAPP(hAPP(C,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,B),E)) | -c_Groebner__Basis_Ogb__semiring(C,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.75/2.05 253 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.75/2.05 254 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.75/2.05 255 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.75/2.05 256 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.75/2.05 257 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.75/2.05 258 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.75/2.05 259 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.75/2.05 260 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.75/2.05 261 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.75/2.05 262 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.75/2.05 263 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.75/2.05 264 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.75/2.05 265 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(A,F,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.75/2.05 266 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.75/2.05 267 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.75/2.05 268 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.75/2.05 269 hAPP(hAPP(A,B),c_HOL_Oone__class_Oone(tc_nat)) = B | -c_Groebner__Basis_Ogb__semiring(C,D,A,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 1.75/2.05 270 hAPP(hAPP(A,B),hAPP(hAPP(C,B),D)) = hAPP(hAPP(C,B),c_Suc(D)) | -c_Groebner__Basis_Ogb__semiring(E,A,C,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.75/2.05 271 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C) = hAPP(hAPP(B,C),c_Suc(D)) | -c_Groebner__Basis_Ogb__semiring(E,A,B,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.75/2.05 272 hAPP(hAPP(A,B),c_Suc(C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.75/2.05 273 hAPP(hAPP(A,B),c_Suc(C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.75/2.05 274 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.75/2.05 275 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.75/2.05 276 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E))) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.75/2.05 277 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.75/2.05 278 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,V6) # label(cls_gb__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.75/2.05 279 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.75/2.05 280 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.75/2.05 281 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.75/2.05 282 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(B,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.75/2.05 283 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.75/2.05 284 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.75/2.05 285 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.75/2.05 286 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,V6) # label(cls_gb__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.75/2.05 287 hAPP(hAPP(A,B),hAPP(hAPP(C,D),B)) = hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.75/2.05 288 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.75/2.05 289 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D)) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.75/2.05 290 hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat)) = C | -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,V6) # label(cls_gb__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.75/2.05 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(248,a,249,b)].
% 1.75/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(248,a,250,b)].
% 1.75/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(248,a,253,b)].
% 1.75/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(248,a,255,b)].
% 1.75/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(248,a,257,b)].
% 1.75/2.05 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(248,a,258,b)].
% 1.75/2.05 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(248,a,262,b)].
% 1.75/2.05 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(248,a,263,b)].
% 1.75/2.05 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(248,a,264,b)].
% 1.75/2.05 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(248,a,265,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(248,a,269,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(248,a,272,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(248,a,277,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(248,a,278,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(248,a,286,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(248,a,287,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(248,a,288,b)].
% 1.98/2.23 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(248,a,290,b)].
% 1.98/2.23 291 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.98/2.23 292 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 1.98/2.23 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(291,a,292,a)].
% 1.98/2.23 293 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.98/2.23 294 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 1.98/2.23 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(293,a,294,a)].
% 1.98/2.23 295 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.98/2.23 296 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.98/2.23 297 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.98/2.23 298 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.98/2.23 299 -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].
% 1.98/2.23 300 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.98/2.28 301 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.98/2.28 302 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.98/2.28 303 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 1.98/2.28 304 -class_Ring__and__Field_Osemiring__1(A) | c_List_Olistsum(c_List_Omap(c_COMBK(B,A,C),D,C,A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(c_Nat_Osize__class_Osize(D,tc_List_Olist(C)),A)),B) # label(cls_listsum__triv_0) # label(axiom). [assumption].
% 1.98/2.28 305 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.98/2.28 306 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 1.98/2.28 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(300,a,301,a)].
% 1.98/2.28 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(300,a,302,a)].
% 1.98/2.28 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(300,a,303,a)].
% 1.98/2.28 Derived: c_List_Olistsum(c_List_Omap(c_COMBK(A,tc_nat,B),C,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_Nat_Osize__class_Osize(C,tc_List_Olist(B)),tc_nat)),A). [resolve(300,a,304,a)].
% 1.98/2.28 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(300,a,305,a)].
% 1.98/2.28 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(300,a,306,a)].
% 1.98/2.28 307 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.98/2.28 308 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.98/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(307,a,308,a)].
% 1.98/2.28 309 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.98/2.28 310 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.06/2.34 311 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.06/2.34 312 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.06/2.34 313 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.06/2.34 314 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.06/2.34 315 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.06/2.34 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(309,a,310,a)].
% 2.06/2.34 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(309,a,311,a)].
% 2.06/2.34 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(309,a,315,a)].
% 2.06/2.34 316 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.06/2.34 317 -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].
% 2.06/2.34 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(316,a,317,a)].
% 2.06/2.34 318 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.06/2.34 319 -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].
% 2.06/2.34 320 -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].
% 2.06/2.34 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(318,a,320,a)].
% 2.06/2.34 321 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.06/2.34 322 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.17/2.42 323 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.17/2.42 324 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.17/2.42 325 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.17/2.42 326 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.17/2.42 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(321,a,322,a)].
% 2.17/2.42 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(321,a,325,a)].
% 2.17/2.42 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(321,a,326,a)].
% 2.17/2.42 327 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.17/2.42 328 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.17/2.42 329 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.17/2.42 330 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.17/2.42 331 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.17/2.42 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(329,a,330,a)].
% 2.17/2.42 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(329,a,331,a)].
% 2.17/2.42 332 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.17/2.42 333 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.27/2.51 334 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.27/2.51 335 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.27/2.51 336 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.27/2.51 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(334,a,335,a)].
% 2.27/2.51 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(334,a,336,a)].
% 2.27/2.51 337 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.27/2.51 338 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.27/2.51 339 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 2.27/2.51 340 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 2.27/2.51 341 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 2.27/2.51 342 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.27/2.51 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,338,a)].
% 2.27/2.51 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,339,a)].
% 2.27/2.51 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(337,a,340,a)].
% 2.27/2.51 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,342,a)].
% 2.27/2.51 343 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.97/3.22 344 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 2.97/3.22 345 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.97/3.22 346 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.97/3.22 347 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.97/3.22 348 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.97/3.22 Derived: A = A. [resolve(347,b,348,a)].
% 2.97/3.22
% 2.97/3.22 ============================== end predicate elimination =============
% 2.97/3.22
% 2.97/3.22 Auto_denials: (non-Horn, no changes).
% 2.97/3.22
% 2.97/3.22 Term ordering decisions:
% 2.97/3.22 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. tc_bool=1. tc_Type_Otype=1. c_Lambda_OdB_OApp=1. c_Lambda_Osubst=1. c_Lambda_Olift=1. c_InductTermi_OIT=1. c_Type_Otyping=1. c_implies=1. t_a=1. v_T____=1. v_i____=1. c_and=1. tc_String_Ochar=1. v_as____=1. v_e____=1. v_n____=1. v_u____=1. v_ua______=1. hAPP=1. tc_fun=1. c_Nat_Osize__class_Osize=1. c_List_Orev=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_List_Olistsum=1. c_Nitpick_Onat__gcd=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Otimes__class_Otimes=1. c_Suc=1. c_HOL_Oone__class_Oone=1. c_List_Olist_ONil=1. c_Power_Opower__class_Opower=1. tc_List_Olist=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Orderings_Oord__class_Omin=1. c_Lambda_OdB_OVar=1. c_Lambda_OdB_OAbs=1. c_Type_Oshift=1. c_Orderings_Obot__class_Obot=1. c_All=1. c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1=1. c_nat_Onat__size=1. c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1=1. v_sko__List__Xreplicate__Xinduct__1=1. v_sko__List__Xupt__Xinduct__1=1. v_sko__Nat__Xnat__Xinduct__1=1. v_sko__Nat__Xnat__Xinducts__1=1. c_Ex=1. c_String_Ochar_Ochar__size=1. c_HOL_Ominus__class_Ominus=1. c_List_Oappend=1. c_List_Olist_OCons=1. c_Orderings_Oord__class_Omax=1. c_COMBB=1. c_List_Otake=1. c_List_Odrop=1. c_List_Oreplicate=1. c_COMBC=1. c_Lambda_Oliftn=1. c_List_Orotate=1. c_Lambda_Osubstn=1. c_COMBS=1. c_COMBK=1. c_List_Osko__List__Xmap__idI__1__1=1. c_List_Osko__List__Xin__listsp__conv__set__1__1=1. c_List_Omap=1. c_List_Olist__update=1. c_Nat_Onat_Onat__case=1. c_List_Ofoldl=1. c_Fun_Ocomp=1. c_List_Osko__List__Xmap__cong__1__1=1. c_List_Osko__List__Xmap__eq__conv__1__1=1. c_List_Osko__List__Xmap__ext__1__1=1.
% 2.97/3.22
% 2.97/3.22 ============================== end of process initial clauses ========
% 2.97/3.22
% 2.97/3.22 ============================== CLAUSES FOR SEARCH ====================
% 2.97/3.22
% 2.97/3.22 ============================== end of clauses for search =============
% 2.97/3.22
% 2.97/3.22 ============================== SEARCH ================================
% 2.97/3.22
% 2.97/3.22 % Starting search at 1.28 seconds.
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=66.000, iters=3625
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=49.000, iters=3338
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=48.000, iters=3339
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=45.000, iters=3341
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=44.000, iters=3340
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=43.000, iters=3384
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=41.000, iters=3336
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=40.000, iters=3339
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=39.000, iters=3370
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=38.000, iters=3350
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=37.000, iters=3389
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=36.000, iters=3336
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=35.000, iters=3407
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=34.000, iters=3405
% 2.97/3.22
% 2.97/3.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 86 (0.00 of 1.82 sec).
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=32.000, iters=3335
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=31.000, iters=3428
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=30.000, iters=3381
% 2.97/3.22
% 2.97/3.22 Low Water (keep): wt=29.000, itCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------