TSTP Solution File: SWV844-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV844-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:15:00 EDT 2022
% Result : Unsatisfiable 2.52s 2.87s
% Output : Refutation 2.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV844-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 10:05:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.20/1.61 ============================== Prover9 ===============================
% 1.20/1.61 Prover9 (32) version 2009-11A, November 2009.
% 1.20/1.61 Process 4457 was started by sandbox2 on n015.cluster.edu,
% 1.20/1.61 Wed Jun 15 10:05:26 2022
% 1.20/1.61 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4304_n015.cluster.edu".
% 1.20/1.61 ============================== end of head ===========================
% 1.20/1.61
% 1.20/1.61 ============================== INPUT =================================
% 1.20/1.61
% 1.20/1.61 % Reading from file /tmp/Prover9_4304_n015.cluster.edu
% 1.20/1.61
% 1.20/1.61 set(prolog_style_variables).
% 1.20/1.61 set(auto2).
% 1.20/1.61 % set(auto2) -> set(auto).
% 1.20/1.61 % set(auto) -> set(auto_inference).
% 1.20/1.61 % set(auto) -> set(auto_setup).
% 1.20/1.61 % set(auto_setup) -> set(predicate_elim).
% 1.20/1.61 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.20/1.61 % set(auto) -> set(auto_limits).
% 1.20/1.61 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.20/1.61 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.20/1.61 % set(auto) -> set(auto_denials).
% 1.20/1.61 % set(auto) -> set(auto_process).
% 1.20/1.61 % set(auto2) -> assign(new_constants, 1).
% 1.20/1.61 % set(auto2) -> assign(fold_denial_max, 3).
% 1.20/1.61 % set(auto2) -> assign(max_weight, "200.000").
% 1.20/1.61 % set(auto2) -> assign(max_hours, 1).
% 1.20/1.61 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.20/1.61 % set(auto2) -> assign(max_seconds, 0).
% 1.20/1.61 % set(auto2) -> assign(max_minutes, 5).
% 1.20/1.61 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.20/1.61 % set(auto2) -> set(sort_initial_sos).
% 1.20/1.61 % set(auto2) -> assign(sos_limit, -1).
% 1.20/1.61 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.20/1.61 % set(auto2) -> assign(max_megs, 400).
% 1.20/1.61 % set(auto2) -> assign(stats, some).
% 1.20/1.61 % set(auto2) -> clear(echo_input).
% 1.20/1.61 % set(auto2) -> set(quiet).
% 1.20/1.61 % set(auto2) -> clear(print_initial_clauses).
% 1.20/1.61 % set(auto2) -> clear(print_given).
% 1.20/1.61 assign(lrs_ticks,-1).
% 1.20/1.61 assign(sos_limit,10000).
% 1.20/1.61 assign(order,kbo).
% 1.20/1.61 set(lex_order_vars).
% 1.20/1.61 clear(print_given).
% 1.20/1.61
% 1.20/1.61 % formulas(sos). % not echoed (1042 formulas)
% 1.20/1.61
% 1.20/1.61 ============================== end of input ==========================
% 1.20/1.61
% 1.20/1.61 % From the command line: assign(max_seconds, 300).
% 1.20/1.61
% 1.20/1.61 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.20/1.61
% 1.20/1.61 % Formulas that are not ordinary clauses:
% 1.20/1.61
% 1.20/1.61 ============================== end of process non-clausal formulas ===
% 1.20/1.61
% 1.20/1.61 ============================== PROCESS INITIAL CLAUSES ===============
% 1.20/1.61
% 1.20/1.61 ============================== PREDICATE ELIMINATION =================
% 1.20/1.61 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.20/1.61 2 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 1.20/1.61 3 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C))) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 1.20/1.61 4 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 1.20/1.61 5 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),D),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B)),C)) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 1.20/1.61 6 -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(A),A) # label(cls_ab__semigroup__idem__mult__max_0) # label(axiom). [assumption].
% 1.20/1.61 7 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B)),C)) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 1.20/1.61 8 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C)) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 1.20/1.61 9 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 1.20/1.61 10 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 1.20/1.61 11 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 1.20/1.61 12 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 1.20/1.61 13 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B)),C)) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 1.20/1.61 14 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C)) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 1.20/1.61 15 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 1.20/1.61 16 -class_Orderings_Olinorder(A) | -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(A) = c_Orderings_Oord__class_Omax(A) # label(cls_sup__max_0) # label(axiom). [assumption].
% 1.20/1.61 17 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B)),C)) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 1.20/1.61 18 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.20/1.61 19 -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].
% 1.20/1.61 20 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.20/1.61 21 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.20/1.61 22 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.20/1.61 23 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.20/1.61 24 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 1.20/1.61 25 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 1.20/1.61 26 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 1.20/1.61 27 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 1.20/1.61 28 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 1.20/1.61 29 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C))) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 1.20/1.61 30 -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(A),A) # label(cls_ab__semigroup__idem__mult__min_0) # label(axiom). [assumption].
% 1.20/1.61 31 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 1.20/1.61 32 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 1.20/1.61 33 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 1.20/1.61 34 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B))) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 1.20/1.61 35 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C))) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 1.20/1.61 36 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 1.20/1.61 37 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 1.20/1.61 38 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 1.20/1.61 39 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),B)) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 1.20/1.61 40 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),C)) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 1.20/1.61 41 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 1.20/1.61 42 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 1.20/1.61 43 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 1.20/1.61 44 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 1.20/1.61 45 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 1.20/1.61 46 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__atLeastLessThan_0) # label(axiom). [assumption].
% 1.20/1.61 47 -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].
% 1.20/1.61 48 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 1.20/1.61 49 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) != C | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 1.20/1.61 50 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 1.20/1.61 51 -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].
% 1.20/1.61 52 -class_Orderings_Olinorder(A) | c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),c_Orderings_Oord__class_Omax(A),A) # label(cls_max__lattice_0) # label(axiom). [assumption].
% 1.20/1.61 53 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)))) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 1.20/1.61 54 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 1.20/1.61 55 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 1.20/1.61 56 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 1.20/1.61 57 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 1.20/1.61 58 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 1.20/1.61 59 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.20/1.61 60 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.20/1.61 61 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.20/1.61 62 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.20/1.61 63 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.20/1.61 64 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.20/1.61 65 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.20/1.61 66 -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].
% 1.20/1.61 67 -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].
% 1.20/1.61 68 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 1.20/1.61 69 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 1.20/1.61 70 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 1.20/1.61 71 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 1.20/1.61 72 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 1.20/1.61 73 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C)) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 1.20/1.61 74 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B)),C)) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 1.20/1.61 75 -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].
% 1.20/1.61 76 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 1.20/1.61 77 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 1.20/1.61 78 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 1.20/1.61 79 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C))) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 1.20/1.61 80 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 1.20/1.61 81 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 1.20/1.61 82 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(D,E,A)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__atLeastAtMost_0) # label(axiom). [assumption].
% 1.20/1.61 83 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 1.20/1.61 84 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D))),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)))) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 1.20/1.61 85 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.20/1.61 86 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.20/1.61 87 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(D,E,A)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__greaterThanAtMost_0) # label(axiom). [assumption].
% 1.20/1.61 88 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.20/1.61 89 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(D,B,A)),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A))) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom). [assumption].
% 1.20/1.61 90 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),D),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A))) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom). [assumption].
% 1.20/1.61 91 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OgreaterThanAtMost(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I20_J_0) # label(axiom). [assumption].
% 1.20/1.61 92 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 1.20/1.61 93 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(B,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(D,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 1.20/1.61 94 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_strict__below__fold1__iff_0) # label(axiom). [assumption].
% 1.20/1.61 95 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C)) | -hBOOL(c_in(D,B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__strict__below__iff_2) # label(axiom). [assumption].
% 1.20/1.61 96 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(A) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A) # label(cls_Max__def__raw_0) # label(axiom). [assumption].
% 1.20/1.61 97 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(A) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A) # label(cls_linorder__class_OMin__def__raw_0) # label(axiom). [assumption].
% 1.20/1.61 98 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 1.20/1.61 99 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 1.20/1.61 100 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 1.20/1.61 101 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 1.20/1.61 102 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 1.20/1.61 103 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I22_J_0) # label(axiom). [assumption].
% 1.20/1.61 104 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -hBOOL(c_in(C,B,A)) | hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(B,C,A),B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__eqI_0) # label(axiom). [assumption].
% 1.20/1.61 105 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -hBOOL(c_in(C,B,A)) | hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(B,C,A),B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__eqI_0) # label(axiom). [assumption].
% 1.20/1.61 106 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),C))) | -c_Finite__Set_Ofinite(B,A) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),C),B)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_fold1__antimono_0) # label(axiom). [assumption].
% 1.20/1.61 107 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I5_J_0) # label(axiom). [assumption].
% 1.20/1.61 108 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I6_J_0) # label(axiom). [assumption].
% 1.20/1.61 109 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),D),C)) | -hBOOL(c_in(D,B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__below__iff_2) # label(axiom). [assumption].
% 1.20/1.61 110 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__Un_0) # label(axiom). [assumption].
% 1.20/1.61 111 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(c_Finite__Set_Olinorder__class_OMax(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__Un_0) # label(axiom). [assumption].
% 1.20/1.61 112 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__insert_0) # label(axiom). [assumption].
% 1.20/1.61 113 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Min__insert_0) # label(axiom). [assumption].
% 1.20/1.61 114 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -hBOOL(c_in(C,B,A)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(B,C,A)),C)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__eqI_1) # label(axiom). [assumption].
% 1.20/1.61 115 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -hBOOL(c_in(C,B,A)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(B,C,A))) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__eqI_1) # label(axiom). [assumption].
% 1.20/1.61 116 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C))) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 1.20/1.61 117 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),C)) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 1.20/1.61 118 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 1.20/1.61 119 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Olinorder__class_OMax(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C))) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),B),C)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 1.20/1.61 120 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C))) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),C),B)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 1.20/1.61 121 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.20/1.61 122 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 1.20/1.61 123 -class_Orderings_Olinorder(A) | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(A),B),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 1.20/1.61 124 -class_Orderings_Olinorder(A) | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(A),B),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,2,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B))). [resolve(1,a,3,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C))). [resolve(1,a,4,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A)),B)). [resolve(1,a,5,a)].
% 1.20/1.61 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(1,a,6,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A)),B)). [resolve(1,a,7,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)),B)). [resolve(1,a,8,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,9,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,10,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),B))). [resolve(1,a,15,a)].
% 1.20/1.61 Derived: -class_Lattices_Oupper__semilattice(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat). [resolve(1,a,16,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A)),B)). [resolve(1,a,17,a)].
% 1.20/1.61 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(1,a,18,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(1,a,19,a)].
% 1.20/1.61 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,20,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(1,a,24,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(1,a,25,a)].
% 1.20/1.61 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(1,a,30,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),B))). [resolve(1,a,31,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)). [resolve(1,a,32,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)). [resolve(1,a,33,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A))). [resolve(1,a,34,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B))). [resolve(1,a,35,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,36,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),A)). [resolve(1,a,39,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),B)). [resolve(1,a,40,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,41,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(1,a,44,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,45,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(1,a,46,a)].
% 1.20/1.61 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,47,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,48,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,49,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,50,a)].
% 1.20/1.61 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,51,a)].
% 1.20/1.61 Derived: c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(1,a,52,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)))). [resolve(1,a,53,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(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_Orderings_Oord__class_Omax(tc_nat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)). [resolve(1,a,54,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)). [resolve(1,a,55,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,56,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,57,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,58,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,59,a)].
% 1.20/1.61 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,62,a)].
% 1.20/1.61 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,66,a)].
% 1.20/1.61 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,67,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = A. [resolve(1,a,68,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,69,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(1,a,70,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)),B)). [resolve(1,a,73,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A)),B)). [resolve(1,a,74,a)].
% 1.20/1.61 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,75,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(1,a,76,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(1,a,77,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C))). [resolve(1,a,78,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B))). [resolve(1,a,79,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(1,a,82,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A). [resolve(1,a,83,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)))). [resolve(1,a,84,a)].
% 1.20/1.61 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,85,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,tc_nat)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(1,a,87,a)].
% 1.20/1.61 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(1,a,88,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat))). [resolve(1,a,89,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat))). [resolve(1,a,90,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,91,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,92,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,93,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(c_in(B,C,tc_nat)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),C))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(1,a,94,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)) | -hBOOL(c_in(C,A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,95,a)].
% 1.20/1.61 Derived: c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(1,a,96,a)].
% 1.20/1.61 Derived: c_Finite__Set_Olinorder__class_OMin(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(1,a,97,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = A. [resolve(1,a,98,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)). [resolve(1,a,99,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)). [resolve(1,a,100,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B). [resolve(1,a,101,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,102,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,103,a)].
% 1.20/1.61 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -hBOOL(c_in(B,A,tc_nat)) | hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(A,B,tc_nat),A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,104,a)].
% 1.20/1.61 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -hBOOL(c_in(B,A,tc_nat)) | hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(A,B,tc_nat),A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,105,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),B))) | -c_Finite__Set_Ofinite(A,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),B),A)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(1,a,106,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,107,a)].
% 1.20/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,108,a)].
% 1.20/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)) | -hBOOL(c_in(C,A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,109,a)].
% 1.20/1.61 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,110,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,111,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,112,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,113,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -hBOOL(c_in(B,A,tc_nat)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(A,B,tc_nat)),B)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,114,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -hBOOL(c_in(B,A,tc_nat)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(A,B,tc_nat))) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,115,a)].
% 1.20/1.63 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B))) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,116,a)].
% 1.20/1.63 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),B)) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,117,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = A. [resolve(1,a,118,a)].
% 1.20/1.63 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B))) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),A),B)). [resolve(1,a,119,a)].
% 1.20/1.63 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B))) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),B),A)). [resolve(1,a,120,a)].
% 1.20/1.63 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,121,a)].
% 1.20/1.63 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = A. [resolve(1,a,122,a)].
% 1.20/1.63 Derived: hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,123,a)].
% 1.20/1.63 Derived: hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,124,a)].
% 1.20/1.63 125 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A),A) # label(cls_dual__semilattice_0) # label(axiom). [assumption].
% 1.20/1.63 126 hAPP(hAPP(A,B),C) = C | -hBOOL(hAPP(hAPP(D,C),B)) | -c_Lattices_Olower__semilattice(D,E,A,F) # label(cls_lower__semilattice_Oinf__absorb2_0) # label(axiom). [assumption].
% 1.20/1.63 127 hAPP(hAPP(A,B),C) != B | -c_Lattices_Olower__semilattice(D,E,A,F) | hBOOL(hAPP(hAPP(D,B),C)) # label(cls_lower__semilattice_Ole__iff__inf_1) # label(axiom). [assumption].
% 1.20/1.63 128 hAPP(hAPP(A,B),C) = B | -hBOOL(hAPP(hAPP(D,B),C)) | -c_Lattices_Olower__semilattice(D,E,A,F) # label(cls_lower__semilattice_Ole__iff__inf_0) # label(axiom). [assumption].
% 1.20/1.63 129 hAPP(hAPP(A,B),B) = B | -c_Lattices_Olower__semilattice(C,D,A,E) # label(cls_lower__semilattice_Oinf__idem_0) # label(axiom). [assumption].
% 1.20/1.63 130 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Lattices_Olower__semilattice(E,F,A,V6) # label(cls_lower__semilattice_Oinf__assoc_0) # label(axiom). [assumption].
% 1.20/1.63 131 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Lattices_Olower__semilattice(D,E,A,F) # label(cls_lower__semilattice_Oinf__commute_0) # label(axiom). [assumption].
% 1.20/1.63 132 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_Lattices_Olower__semilattice(D,E,A,F) # label(cls_lower__semilattice_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.20/1.63 133 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Lattices_Olower__semilattice(E,F,A,V6) # label(cls_lower__semilattice_Oinf__left__commute_0) # label(axiom). [assumption].
% 1.20/1.63 134 c_OrderedGroup_Oab__semigroup__idem__mult(A,B) | -c_Lattices_Olower__semilattice(C,D,A,B) # label(cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) # label(axiom). [assumption].
% 1.20/1.63 135 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)) | -hBOOL(hAPP(hAPP(A,D),E)) | -c_Lattices_Olower__semilattice(F,A,B,V6) # label(cls_lower__semilattice_Oless__infI2_0) # label(axiom). [assumption].
% 1.20/1.63 136 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)) | -hBOOL(hAPP(hAPP(A,C),E)) | -c_Lattices_Olower__semilattice(F,A,B,V6) # label(cls_lower__semilattice_Oless__infI1_0) # label(axiom). [assumption].
% 1.20/1.63 137 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(D,E),C))) | -c_Lattices_Olower__semilattice(A,F,D,V6) # label(cls_lower__semilattice_Ole__inf__iff_1) # label(axiom). [assumption].
% 1.20/1.63 138 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(D,C),E))) | -c_Lattices_Olower__semilattice(A,F,D,V6) # label(cls_lower__semilattice_Ole__inf__iff_0) # label(axiom). [assumption].
% 1.20/1.63 139 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(D,C),E))) | -c_Lattices_Olower__semilattice(A,F,D,V6) # label(cls_lower__semilattice_Ole__infE_0) # label(axiom). [assumption].
% 1.20/1.63 140 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(D,E),C))) | -c_Lattices_Olower__semilattice(A,F,D,V6) # label(cls_lower__semilattice_Ole__infE_1) # label(axiom). [assumption].
% 1.20/1.63 141 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)) | -hBOOL(hAPP(hAPP(A,C),E)) | -c_Lattices_Olower__semilattice(A,F,B,V6) # label(cls_lower__semilattice_Ole__infI1_0) # label(axiom). [assumption].
% 1.20/1.63 142 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)) | -hBOOL(hAPP(hAPP(A,D),E)) | -c_Lattices_Olower__semilattice(A,F,B,V6) # label(cls_lower__semilattice_Ole__infI2_0) # label(axiom). [assumption].
% 1.20/1.63 143 hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(C,D),E))) | -hBOOL(hAPP(hAPP(A,B),E)) | -hBOOL(hAPP(hAPP(A,B),D)) | -c_Lattices_Olower__semilattice(A,F,C,V6) # label(cls_lower__semilattice_Ole__infI_0) # label(axiom). [assumption].
% 1.20/1.63 144 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D)) | -c_Lattices_Olower__semilattice(A,E,B,F) # label(cls_lower__semilattice_Oinf__le2_0) # label(axiom). [assumption].
% 1.20/1.63 145 hBOOL(hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C)) | -c_Lattices_Olower__semilattice(A,E,B,F) # label(cls_lower__semilattice_Oinf__le1_0) # label(axiom). [assumption].
% 1.20/1.63 146 hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(C,D),E))) | -hBOOL(hAPP(hAPP(A,B),E)) | -hBOOL(hAPP(hAPP(A,B),D)) | -c_Lattices_Olower__semilattice(A,F,C,V6) # label(cls_lower__semilattice_Ole__inf__iff_2) # label(axiom). [assumption].
% 1.20/1.64 147 hBOOL(hAPP(hAPP(A,B),hAPP(hAPP(C,D),E))) | -hBOOL(hAPP(hAPP(A,B),E)) | -hBOOL(hAPP(hAPP(A,B),D)) | -c_Lattices_Olower__semilattice(A,F,C,V6) # label(cls_lower__semilattice_Oinf__greatest_0) # label(axiom). [assumption].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),B)). [resolve(125,b,126,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != B | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(125,b,127,b)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(125,b,128,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(125,b,134,b)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),C),D)). [resolve(125,b,135,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),B),D)). [resolve(125,b,136,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),C))). [resolve(125,b,137,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))). [resolve(125,b,138,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),D)). [resolve(125,b,141,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),D)). [resolve(125,b,142,c)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(125,b,143,d)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),C)). [resolve(125,b,144,b)].
% 1.20/1.64 Derived: -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),B)). [resolve(125,b,145,b)].
% 1.20/1.64 148 hBOOL(hAPP(hAPP(A,hAPP(hAPP(c_Finite__Set_Ofold(B,C,C),D),E)),hAPP(hAPP(B,F),D))) | -hBOOL(c_in(F,E,C)) | -c_Finite__Set_Ofinite(E,C) | -c_Lattices_Olower__semilattice(A,V6,B,C) # label(cls_lower__semilattice_Ofold__inf__le__inf_0) # label(axiom). [assumption].
% 1.20/1.64 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),C)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B))) | -hBOOL(c_in(D,C,A)) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(148,d,125,b)].
% 1.20/1.64 149 hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),c_Set_Oinsert(D,E,B)) = hAPP(hAPP(A,D),hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),E)) | -c_Finite__Set_Ofinite(E,B) | -c_Lattices_Olower__semilattice(F,V6,A,B) # label(cls_lower__semilattice_Ofold__inf__insert_0) # label(axiom). [assumption].
% 1.20/1.66 150 hBOOL(hAPP(hAPP(A,hAPP(c_Finite__Set_Ofold1(B,C),D)),E)) | -hBOOL(c_in(E,D,C)) | -c_Finite__Set_Ofinite(D,C) | -c_Lattices_Olower__semilattice(A,F,B,C) # label(cls_lower__semilattice_Ofold1__belowI_0) # label(axiom). [assumption].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),B)),C)) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) | -class_Lattices_Oupper__semilattice(A). [resolve(150,d,125,b)].
% 1.20/1.66 151 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(c_in(C,D,E)) | -hBOOL(hAPP(hAPP(A,B),hAPP(c_Finite__Set_Ofold1(F,E),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(E,tc_bool)) | -c_Finite__Set_Ofinite(D,E) | -c_Lattices_Olower__semilattice(A,V6,F,E) # label(cls_lower__semilattice_Obelow__fold1__iff_0) # label(axiom). [assumption].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) | -class_Lattices_Oupper__semilattice(A). [resolve(151,f,125,b)].
% 1.20/1.66 152 c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(1,a,52,a)].
% 1.20/1.66 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),B),A)). [resolve(152,a,126,c)].
% 1.20/1.66 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)). [resolve(152,a,127,b)].
% 1.20/1.66 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)). [resolve(152,a,128,c)].
% 1.20/1.66 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(152,a,129,b)].
% 1.20/1.66 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(152,a,134,b)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),B),C)). [resolve(152,a,135,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),A),C)). [resolve(152,a,136,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),B))). [resolve(152,a,137,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))). [resolve(152,a,138,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),C)). [resolve(152,a,141,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),B),C)). [resolve(152,a,142,c)].
% 1.20/1.66 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)). [resolve(152,a,143,d)].
% 1.48/1.73 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),B)). [resolve(152,a,144,b)].
% 1.48/1.73 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),A)). [resolve(152,a,145,b)].
% 1.48/1.73 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A))) | -hBOOL(c_in(C,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(152,a,148,d)].
% 1.48/1.73 Derived: hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),c_Set_Oinsert(B,C,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(152,a,149,c)].
% 1.48/1.73 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),A)),B)) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(152,a,150,d)].
% 1.48/1.73 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)) | -hBOOL(c_in(B,C,tc_nat)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),C))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(152,a,151,f)].
% 1.48/1.73 153 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.48/1.73 154 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,tc_bool)),C),D) != c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B) | c_Finite__Set_Osetsum(E,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(E,C,B,A)),c_Finite__Set_Osetsum(E,D,B,A)) # label(cls_setsum__Un__disjoint_0) # label(axiom). [assumption].
% 1.48/1.73 155 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.48/1.73 156 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),D),E),C,A)),c_Finite__Set_Osetsum(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,tc_bool)),D),E),C,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,D,C,A)),c_Finite__Set_Osetsum(B,E,C,A)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__Un__Int_0) # label(axiom). [assumption].
% 1.48/1.73 157 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.48/1.73 158 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.48/1.73 159 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,A,C),D),c_Set_Oinsert(E,F,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,A,C),D),F)) | hBOOL(c_in(E,F,C)) | -c_Finite__Set_Ofinite(F,C) # label(cls_comm__monoid__add_Ofold__image__insert_0) # label(axiom). [assumption].
% 1.48/1.73 160 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oinsert(C,D,E),E,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,D,E,A)) | hBOOL(c_in(C,D,E)) | -c_Finite__Set_Ofinite(D,E) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.48/1.73 161 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,c_Set_Oinsert(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(A,tc_bool)),D),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)),A),E,A,A) | hBOOL(c_in(C,D,A)) | -hBOOL(c_in(B,D,A)) | -c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,E,A,A) # label(cls_comm__monoid__add_Ofold__graph__permute__diff_0) # label(axiom). [assumption].
% 1.48/1.73 162 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(A),A,A),B),C) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_comm__monoid__add_Ofold1__eq__fold_0) # label(axiom). [assumption].
% 1.48/1.73 163 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),C)) # label(cls_comm__monoid__add_Ofold1__Un_0) # label(axiom). [assumption].
% 1.48/1.73 164 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,c_Set_Oinsert(C,D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),E),A,A) | hBOOL(c_in(C,D,A)) | -c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,E,A,A) # label(cls_comm__monoid__add_Ofold__graph__insert__swap_0) # label(axiom). [assumption].
% 1.48/1.73 165 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),C),D,C,A,A),E,C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,E,C,A)),c_Finite__Set_Osetsum(D,E,C,A)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.48/1.73 166 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),c_Finite__Set_Osetsum(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(D,tc_bool)),C),c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)),D)),D,A)) | -hBOOL(c_in(E,C,D)) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 1.48/1.73 167 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),C)) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_comm__monoid__add_Ofold1__insert_0) # label(axiom). [assumption].
% 1.48/1.73 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | -c_Finite__Set_Ofinite(B,A) | c_Finite__Set_Osetsum(D,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(D,B,A,tc_nat)),c_Finite__Set_Osetsum(D,C,A,tc_nat)). [resolve(153,a,154,a)].
% 1.48/1.73 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(153,a,155,a)].
% 1.48/1.73 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,tc_nat)),c_Finite__Set_Osetsum(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,tc_bool)),C),D),B,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,C,B,tc_nat)),c_Finite__Set_Osetsum(A,D,B,tc_nat)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(153,a,156,a)].
% 1.56/1.85 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(153,a,157,a)].
% 1.56/1.85 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(153,a,158,a)].
% 1.56/1.85 Derived: hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,B),C),c_Set_Oinsert(D,E,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,B),C),E)) | hBOOL(c_in(D,E,B)) | -c_Finite__Set_Ofinite(E,B). [resolve(153,a,159,a)].
% 1.56/1.85 Derived: c_Finite__Set_Osetsum(A,c_Set_Oinsert(B,C,D),D,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,C,D,tc_nat)) | hBOOL(c_in(B,C,D)) | -c_Finite__Set_Ofinite(C,D). [resolve(153,a,160,a)].
% 1.56/1.85 Derived: c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,c_Set_Oinsert(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_nat,tc_bool)),C),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)),tc_nat),D,tc_nat,tc_nat) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(c_in(A,C,tc_nat)) | -c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(153,a,161,a)].
% 1.56/1.85 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat),A),B) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(153,a,162,a)].
% 1.56/1.85 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),A),B) != c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B)). [resolve(153,a,163,a)].
% 1.56/1.85 Derived: c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,c_Set_Oinsert(B,C,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),D),tc_nat,tc_nat) | hBOOL(c_in(B,C,tc_nat)) | -c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(153,a,164,a)].
% 1.56/1.85 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),B),C,B,tc_nat,tc_nat),D,B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,D,B,tc_nat)),c_Finite__Set_Osetsum(C,D,B,tc_nat)). [resolve(153,a,165,a)].
% 1.56/1.85 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),c_Finite__Set_Osetsum(A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(C,tc_bool)),B),c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C)),C,tc_nat)) | -hBOOL(c_in(D,B,C)) | -c_Finite__Set_Ofinite(B,C). [resolve(153,a,166,a)].
% 1.56/1.85 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B)) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(153,a,167,a)].
% 1.56/1.85 168 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.56/1.85 169 -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].
% 1.56/1.85 170 -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].
% 1.56/1.85 171 -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),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].
% 1.56/1.85 172 -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].
% 1.56/1.85 173 -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].
% 1.56/1.85 174 -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].
% 1.56/1.85 175 -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].
% 1.56/1.85 176 -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].
% 1.56/1.85 177 -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].
% 1.56/1.85 178 -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].
% 1.56/1.85 179 -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].
% 1.56/1.85 180 -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].
% 1.56/1.85 181 -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].
% 1.56/1.85 182 -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].
% 1.56/1.85 183 -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].
% 1.56/1.85 184 -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].
% 1.56/1.85 185 -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].
% 1.56/1.85 186 -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].
% 1.56/1.85 187 -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].
% 1.56/1.85 188 -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].
% 1.56/1.85 189 -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].
% 1.56/1.85 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(168,a,169,a)].
% 1.56/1.85 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(168,a,170,a)].
% 1.56/1.85 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(168,a,171,a)].
% 1.56/1.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(168,a,174,a)].
% 1.56/1.85 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(168,a,176,a)].
% 1.56/1.85 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(168,a,178,a)].
% 1.61/1.90 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(168,a,181,a)].
% 1.61/1.90 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(168,a,182,a)].
% 1.61/1.90 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(168,a,183,a)].
% 1.61/1.90 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(168,a,184,a)].
% 1.61/1.90 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(168,a,185,a)].
% 1.61/1.90 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(168,a,187,a)].
% 1.61/1.90 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(168,a,188,a)].
% 1.61/1.90 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(168,a,189,a)].
% 1.61/1.90 190 -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A) # label(cls_ab__semigroup__idem__mult__sup_0) # label(axiom). [assumption].
% 1.61/1.90 191 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_OrderedGroup_Oab__semigroup__idem__mult(A,D) # label(cls_ab__semigroup__idem__mult_Omult__left__idem_0) # label(axiom). [assumption].
% 1.61/1.90 192 hAPP(hAPP(A,B),B) = B | -c_OrderedGroup_Oab__semigroup__idem__mult(A,C) # label(cls_ab__semigroup__idem__mult_Omult__idem_0) # label(axiom). [assumption].
% 1.61/1.90 193 -class_Lattices_Olower__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(A),A) # label(cls_ab__semigroup__idem__mult__inf_0) # label(axiom). [assumption].
% 1.61/1.90 Derived: -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C). [resolve(193,b,191,b)].
% 1.61/1.90 Derived: -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B. [resolve(193,b,192,b)].
% 1.61/1.90 194 hAPP(c_Finite__Set_Ofold1(A,B),c_Set_Oinsert(C,D,B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),D) | -c_Finite__Set_Ofinite(D,B) | -c_OrderedGroup_Oab__semigroup__idem__mult(A,B) # label(cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) # label(axiom). [assumption].
% 1.61/1.90 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),C) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(194,c,190,b)].
% 1.61/1.90 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),A,A),B),C) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Olower__semilattice(A). [resolve(194,c,193,b)].
% 1.61/1.92 195 hAPP(c_Finite__Set_Ofold1(A,B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D)) = hAPP(hAPP(A,hAPP(c_Finite__Set_Ofold1(A,B),C)),hAPP(c_Finite__Set_Ofold1(A,B),D)) | D = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_Finite__Set_Ofinite(D,B) | C = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_Finite__Set_Ofinite(C,B) | -c_OrderedGroup_Oab__semigroup__idem__mult(A,B) # label(cls_ab__semigroup__idem__mult_Ofold1__Un2_0) # label(axiom). [assumption].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | -class_Lattices_Oupper__semilattice(A). [resolve(195,f,190,b)].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | -class_Lattices_Olower__semilattice(A). [resolve(195,f,193,b)].
% 1.61/1.92 196 hAPP(c_Finite__Set_Ofold1(A,B),c_Set_Oinsert(C,D,B)) = hAPP(hAPP(A,C),hAPP(c_Finite__Set_Ofold1(A,B),D)) | -c_Finite__Set_Ofinite(D,B) | D = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_OrderedGroup_Oab__semigroup__idem__mult(A,B) # label(cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) # label(axiom). [assumption].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),C)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -class_Lattices_Oupper__semilattice(A). [resolve(196,d,190,b)].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),C)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -class_Lattices_Olower__semilattice(A). [resolve(196,d,193,b)].
% 1.61/1.92 197 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(1,a,6,a)].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),B) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(197,a,194,c)].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(197,a,195,f)].
% 1.61/1.92 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),B)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(197,a,196,d)].
% 1.70/1.97 198 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(1,a,30,a)].
% 1.70/1.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(198,a,192,b)].
% 1.70/1.97 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omin(tc_nat),tc_nat,tc_nat),A),B) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(198,a,194,c)].
% 1.70/1.97 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(198,a,195,f)].
% 1.70/1.97 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),B)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(198,a,196,d)].
% 1.70/1.97 199 -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(125,b,134,b)].
% 1.70/1.97 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C). [resolve(199,b,191,b)].
% 1.70/1.97 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B. [resolve(199,b,192,b)].
% 1.70/1.97 200 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(152,a,134,b)].
% 1.70/1.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B). [resolve(200,a,191,b)].
% 1.70/1.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(200,a,192,b)].
% 1.70/1.97 201 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.70/1.97 202 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.70/1.97 203 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.70/1.97 204 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.70/1.97 205 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.86/2.14 206 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(201,a,202,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(201,a,203,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(201,a,204,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(201,a,205,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(201,a,206,a)].
% 1.86/2.14 207 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.86/2.14 208 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.86/2.14 209 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.86/2.14 210 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(207,a,208,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(207,a,209,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(207,a,210,a)].
% 1.86/2.14 211 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.86/2.14 212 -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].
% 1.86/2.14 213 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.86/2.14 214 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.86/2.14 215 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.86/2.14 216 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.86/2.14 217 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.86/2.14 218 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.86/2.14 219 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.86/2.14 220 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.86/2.14 221 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.86/2.14 222 -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].
% 1.86/2.14 223 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(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(213,a,215,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(213,a,217,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(213,a,219,a)].
% 1.86/2.14 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(213,a,221,a)].
% 2.04/2.33 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(213,a,222,a)].
% 2.04/2.33 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(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(213,a,223,a)].
% 2.04/2.33 224 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.04/2.33 225 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),D,A,A),E),C,D,A) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 2.04/2.33 226 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 2.04/2.33 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetsum(A,B,C,tc_nat)),D) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),C),C,tc_nat,tc_nat),D),B,C,tc_nat). [resolve(224,a,225,a)].
% 2.04/2.33 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(224,a,226,a)].
% 2.04/2.33 227 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.04/2.33 228 -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].
% 2.04/2.33 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(227,a,228,a)].
% 2.04/2.33 229 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.04/2.33 230 -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].
% 2.04/2.33 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(229,a,230,a)].
% 2.04/2.33 231 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.04/2.33 232 -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].
% 2.04/2.33 233 -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].
% 2.04/2.33 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(231,a,233,a)].
% 2.04/2.33 234 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.08/2.33 235 -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].
% 2.08/2.33 236 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,A,C),D),c_Set_Oinsert(E,F,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,E)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,A,C),D),F)) | hBOOL(c_in(E,F,C)) | -c_Finite__Set_Ofinite(F,C) # label(cls_fold__image__insert_0) # label(axiom). [assumption].
% 2.08/2.33 237 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(A,tc_bool)),D),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)),A),E,A,A) | hBOOL(c_in(C,D,A)) | -hBOOL(c_in(B,D,A)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,E,A,A) # label(cls_fold__graph__permute__diff_0) # label(axiom). [assumption].
% 2.08/2.33 238 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),A,A),B),C) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_fold1__eq__fold_0) # label(axiom). [assumption].
% 2.08/2.33 239 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),C)) # label(cls_fold1__Un_0) # label(axiom). [assumption].
% 2.08/2.33 240 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,D,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),A,A) | hBOOL(c_in(C,D,A)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,E,A,A) # label(cls_fold__graph__insert__swap_0) # label(axiom). [assumption].
% 2.08/2.33 241 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),C)) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_fold1__insert_0) # label(axiom). [assumption].
% 2.08/2.33 Derived: hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,B),C),c_Set_Oinsert(D,E,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(A,D)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,B),C),E)) | hBOOL(c_in(D,E,B)) | -c_Finite__Set_Ofinite(E,B). [resolve(234,a,236,a)].
% 2.08/2.33 Derived: c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_nat,tc_bool)),C),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)),tc_nat),D,tc_nat,tc_nat) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(c_in(A,C,tc_nat)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(234,a,237,a)].
% 2.08/2.33 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat),A),B) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(234,a,238,a)].
% 2.08/2.33 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),A),B) != c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),B)). [resolve(234,a,239,a)].
% 2.21/2.48 Derived: c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,C,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D),tc_nat,tc_nat) | hBOOL(c_in(B,C,tc_nat)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(234,a,240,a)].
% 2.21/2.48 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),B)) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(234,a,241,a)].
% 2.21/2.48 242 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.21/2.48 243 -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].
% 2.21/2.48
% 2.21/2.48 ============================== end predicate elimination =============
% 2.21/2.48
% 2.21/2.48 Auto_denials: (non-Horn, no changes).
% 2.21/2.48
% 2.21/2.48 Term ordering decisions:
% 2.21/2.48 Function symbol KB weights: tc_nat=1. tc_bool=1. t_a=1. t_b=1. v_x=1. tc_Com_Ostate=1. v_P=1. v_Q=1. v_R=1. tc_Com_Ocom=1. v_G=1. v_c0=1. v_F=1. v_P_H=1. v_Q_H=1. t_c=1. c_Com_Ocom_OSKIP=1. hAPP=1. tc_fun=1. c_Finite__Set_Ofold1=1. c_Finite__Set_Ocard=1. c_Complete__Lattice_OInf__class_OInf=1. c_Com_Ocom_OSemi=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. v_sko__Hoare__Mirabelle__Xconseq1__1=1. v_sko__Hoare__Mirabelle__Xconseq1__2=1. v_sko__Hoare__Mirabelle__Xconseq2__1=1. v_sko__Hoare__Mirabelle__Xconseq2__2=1. c_lessequals=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Oord__class_Oless=1. c_HOL_Ominus__class_Ominus=1. c_HOL_Oplus__class_Oplus=1. c_Orderings_Oord__class_Omax=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Otop__class_Otop=1. c_Orderings_Oord__class_Omin=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ouminus__class_Ouminus=1. c_Suc=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_fequal=1. c_Set_Oinsert=1. c_in=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_Finite__Set_Ofold=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_COMBK=1. c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1=1. c_Set_Oimage=1. c_COMBC=1. c_Set_Ovimage=1. c_Finite__Set_Osetsum=1. c_Fun_Othe__inv__into=1. c_Finite__Set_Ofold__image=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1. v_sko__Hoare__Mirabelle__Xconseq12__2=1. v_sko__Hoare__Mirabelle__Xconseq12__3=1. v_sko__Hoare__Mirabelle__Xescape__1=1. v_sko__Hoare__Mirabelle__Xescape__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_Fun_Ofun__upd=1. c_COMBB=1. c_COMBS=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 2.52/2.87
% 2.52/2.87 ============================== end of process initial clauses ========
% 2.52/2.87
% 2.52/2.87 ============================== CLAUSES FOR SEARCH ====================
% 2.52/2.87
% 2.52/2.87 ============================== end of clauses for search =============
% 2.52/2.87
% 2.52/2.87 ============================== SEARCH ================================
% 2.52/2.87
% 2.52/2.87 % Starting search at 1.03 seconds.
% 2.52/2.87
% 2.52/2.87 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 63 (0.00 of 1.36 sec).
% 2.52/2.87
% 2.52/2.87 Low Water (keep): wt=54.000, iters=3510
% 2.52/2.87
% 2.52/2.87 ============================== PROOF =================================
% 2.52/2.87 % SZS status Unsatisfiable
% 2.52/2.87 % SZS output start Refutation
% 2.52/2.87
% 2.52/2.87 % Proof 1 at 1.42 (+ 0.01) seconds.
% 2.52/2.87 % Length of proof is 4.
% 2.52/2.87 % Level of proof is 1.
% 2.52/2.87 % Maximum clause weight is 50.000.
% 2.52/2.87 % Given clauses 532.
% 2.52/2.87
% 2.52/2.87 896 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 2.52/2.87 898 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 2.52/2.87 899 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,A)),hAPP(v_c0,A)),hAPP(v_Q,A)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,A)),hAPP(v_c0,A)),hAPP(v_Q_H,A)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 2.52/2.87 4551 $F. [resolve(899,b,896,a),unit_del(a,898)].
% 2.52/2.87
% 2.52/2.87 % SZS output end Refutation
% 2.52/2.87 ============================== end of proof ==========================
% 2.52/2.87
% 2.52/2.87 ============================== STATISTICS ============================
% 2.52/2.87
% 2.52/2.87 Given=532. Generated=6657. Kept=4089. proofs=1.
% 2.52/2.87 Usable=522. Sos=3345. Demods=477. Limbo=0, Disabled=1468. Hints=0.
% 2.52/2.87 Megabytes=14.86.
% 2.52/2.87 User_CPU=1.42, System_CPU=0.01, Wall_clock=1.
% 2.52/2.87
% 2.52/2.87 ============================== end of statistics =====================
% 2.52/2.87
% 2.52/2.87 ============================== end of search =========================
% 2.52/2.87
% 2.52/2.87 THEOREM PROVED
% 2.52/2.87 % SZS status Unsatisfiable
% 2.52/2.87
% 2.52/2.87 Exiting with 1 proof.
% 2.52/2.87
% 2.52/2.87 Process 4457 exit (max_proofs) Wed Jun 15 10:05:27 2022
% 2.52/2.87 Prover9 interrupted
%------------------------------------------------------------------------------