TSTP Solution File: SWV875-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 21:15:07 EDT 2022
% Result : Unsatisfiable 2.65s 2.96s
% Output : Refutation 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n011.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 : Thu Jun 16 04:03:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.28/1.64 ============================== Prover9 ===============================
% 1.28/1.64 Prover9 (32) version 2009-11A, November 2009.
% 1.28/1.64 Process 27454 was started by sandbox on n011.cluster.edu,
% 1.28/1.64 Thu Jun 16 04:03:52 2022
% 1.28/1.64 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27300_n011.cluster.edu".
% 1.28/1.64 ============================== end of head ===========================
% 1.28/1.64
% 1.28/1.64 ============================== INPUT =================================
% 1.28/1.64
% 1.28/1.64 % Reading from file /tmp/Prover9_27300_n011.cluster.edu
% 1.28/1.64
% 1.28/1.64 set(prolog_style_variables).
% 1.28/1.64 set(auto2).
% 1.28/1.64 % set(auto2) -> set(auto).
% 1.28/1.64 % set(auto) -> set(auto_inference).
% 1.28/1.64 % set(auto) -> set(auto_setup).
% 1.28/1.64 % set(auto_setup) -> set(predicate_elim).
% 1.28/1.64 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.28/1.64 % set(auto) -> set(auto_limits).
% 1.28/1.64 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.28/1.64 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.28/1.64 % set(auto) -> set(auto_denials).
% 1.28/1.64 % set(auto) -> set(auto_process).
% 1.28/1.64 % set(auto2) -> assign(new_constants, 1).
% 1.28/1.64 % set(auto2) -> assign(fold_denial_max, 3).
% 1.28/1.64 % set(auto2) -> assign(max_weight, "200.000").
% 1.28/1.64 % set(auto2) -> assign(max_hours, 1).
% 1.28/1.64 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.28/1.64 % set(auto2) -> assign(max_seconds, 0).
% 1.28/1.64 % set(auto2) -> assign(max_minutes, 5).
% 1.28/1.64 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.28/1.64 % set(auto2) -> set(sort_initial_sos).
% 1.28/1.64 % set(auto2) -> assign(sos_limit, -1).
% 1.28/1.64 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.28/1.64 % set(auto2) -> assign(max_megs, 400).
% 1.28/1.64 % set(auto2) -> assign(stats, some).
% 1.28/1.64 % set(auto2) -> clear(echo_input).
% 1.28/1.64 % set(auto2) -> set(quiet).
% 1.28/1.64 % set(auto2) -> clear(print_initial_clauses).
% 1.28/1.64 % set(auto2) -> clear(print_given).
% 1.28/1.64 assign(lrs_ticks,-1).
% 1.28/1.64 assign(sos_limit,10000).
% 1.28/1.64 assign(order,kbo).
% 1.28/1.64 set(lex_order_vars).
% 1.28/1.64 clear(print_given).
% 1.28/1.64
% 1.28/1.64 % formulas(sos). % not echoed (1108 formulas)
% 1.28/1.64
% 1.28/1.64 ============================== end of input ==========================
% 1.28/1.64
% 1.28/1.64 % From the command line: assign(max_seconds, 300).
% 1.28/1.64
% 1.28/1.64 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.28/1.64
% 1.28/1.64 % Formulas that are not ordinary clauses:
% 1.28/1.64
% 1.28/1.64 ============================== end of process non-clausal formulas ===
% 1.28/1.64
% 1.28/1.64 ============================== PROCESS INITIAL CLAUSES ===============
% 1.28/1.64
% 1.28/1.64 ============================== PREDICATE ELIMINATION =================
% 1.28/1.64 1 -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].
% 1.28/1.64 2 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].
% 1.28/1.64 3 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].
% 1.28/1.64 4 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].
% 1.28/1.64 5 hAPP(hAPP(A,B),B) = B | -c_Lattices_Olower__semilattice(C,D,A,E) # label(cls_lower__semilattice_Oinf__idem_0) # label(axiom). [assumption].
% 1.28/1.64 6 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].
% 1.28/1.64 7 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].
% 1.28/1.64 8 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].
% 1.28/1.64 9 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].
% 1.28/1.64 10 c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,C) = hAPP(hAPP(A,D),c_Finite__Set_Ofold(A,B,E,C,C)) | -c_Finite__Set_Ofinite(E,C) | -c_Lattices_Olower__semilattice(F,V6,A,C) # label(cls_lower__semilattice_Ofold__inf__insert_0) # label(axiom). [assumption].
% 1.28/1.65 11 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].
% 1.28/1.65 12 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].
% 1.28/1.65 13 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].
% 1.28/1.65 14 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].
% 1.28/1.65 15 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].
% 1.28/1.65 16 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].
% 1.28/1.65 17 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].
% 1.28/1.65 18 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].
% 1.28/1.65 19 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].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) != B | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(1,b,2,b)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),B)). [resolve(1,b,3,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = B | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(1,b,4,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B. [resolve(1,b,5,b)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,D,A,A)) | -c_Finite__Set_Ofinite(D,A). [resolve(1,b,10,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(A),A). [resolve(1,b,11,b)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),C),D)). [resolve(1,b,12,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),B),D)). [resolve(1,b,13,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(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_Orderings_Oord__class_Omax(A),D),C))). [resolve(1,b,14,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(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_Orderings_Oord__class_Omax(A),C),D))). [resolve(1,b,15,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),D)). [resolve(1,b,18,c)].
% 1.28/1.65 Derived: -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),D)). [resolve(1,b,19,c)].
% 1.28/1.65 20 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].
% 1.28/1.65 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(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)) | -class_Orderings_Olinorder(A). [resolve(20,d,1,b)].
% 1.28/1.65 21 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].
% 1.28/1.65 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),C)) | -class_Orderings_Olinorder(A). [resolve(21,b,1,b)].
% 1.28/1.65 22 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].
% 1.28/1.65 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),B)) | -class_Orderings_Olinorder(A). [resolve(22,b,1,b)].
% 1.28/1.65 23 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].
% 1.28/1.65 24 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].
% 1.28/1.65 25 -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].
% 1.28/1.65 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(25,b,2,b)].
% 1.28/1.65 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(25,b,3,c)].
% 1.28/1.65 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(25,b,4,c)].
% 1.28/1.65 Derived: -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(25,b,11,b)].
% 1.28/1.65 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(25,b,12,c)].
% 1.28/1.65 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(25,b,13,c)].
% 1.28/1.65 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(25,b,14,c)].
% 1.28/1.65 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(25,b,15,c)].
% 1.28/1.65 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(25,b,18,c)].
% 1.28/1.74 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(25,b,19,c)].
% 1.28/1.74 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(25,b,20,d)].
% 1.28/1.74 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(25,b,21,b)].
% 1.28/1.74 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(25,b,22,b)].
% 1.28/1.74 26 hBOOL(hAPP(hAPP(A,c_Finite__Set_Ofold(B,C,D,E,E)),hAPP(hAPP(B,F),C))) | -hBOOL(hAPP(hAPP(c_in(E),F),D)) | -c_Finite__Set_Ofinite(D,E) | -c_Lattices_Olower__semilattice(A,V6,B,E) # label(cls_lower__semilattice_Ofold__inf__le__inf_0) # label(axiom). [assumption].
% 1.28/1.74 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,C,A,A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B))) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -c_Finite__Set_Ofinite(C,A) | -class_Orderings_Olinorder(A). [resolve(26,d,1,b)].
% 1.28/1.74 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,C,A,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B))) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(26,d,25,b)].
% 1.28/1.74 27 hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -hBOOL(hAPP(hAPP(A,B),hAPP(c_Finite__Set_Ofold1(F,D),E))) | E = c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)) | -c_Finite__Set_Ofinite(E,D) | -c_Lattices_Olower__semilattice(A,V6,F,D) # label(cls_lower__semilattice_Obelow__fold1__iff_0) # label(axiom). [assumption].
% 1.28/1.74 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) | -class_Orderings_Olinorder(A). [resolve(27,f,1,b)].
% 1.28/1.74 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),D)) | -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(27,f,25,b)].
% 1.28/1.74 28 hBOOL(hAPP(hAPP(A,hAPP(c_Finite__Set_Ofold1(B,C),D)),E)) | -hBOOL(hAPP(hAPP(c_in(C),E),D)) | -c_Finite__Set_Ofinite(D,C) | -c_Lattices_Olower__semilattice(A,F,B,C) # label(cls_lower__semilattice_Ofold1__belowI_0) # label(axiom). [assumption].
% 1.28/1.74 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A),B)),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) | -class_Orderings_Olinorder(A). [resolve(28,d,1,b)].
% 1.28/1.74 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(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) | -class_Lattices_Oupper__semilattice(A). [resolve(28,d,25,b)].
% 1.28/1.74 29 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.28/1.74 30 -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].
% 1.28/1.74 31 -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].
% 1.28/1.74 32 -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].
% 1.28/1.74 33 -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].
% 1.28/1.74 34 -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].
% 1.28/1.74 35 -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].
% 1.28/1.74 36 -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].
% 1.28/1.74 37 -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].
% 1.28/1.74 38 -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].
% 1.28/1.74 39 -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].
% 1.28/1.74 40 -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].
% 1.28/1.74 41 -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].
% 1.28/1.74 42 -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].
% 1.28/1.74 43 -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].
% 1.28/1.74 44 -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].
% 1.28/1.74 45 -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].
% 1.28/1.74 46 -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].
% 1.28/1.74 47 -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].
% 1.28/1.74 48 -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].
% 1.28/1.74 49 -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].
% 1.28/1.74 50 -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].
% 1.28/1.74 51 -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].
% 1.28/1.74 52 -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].
% 1.28/1.74 53 -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].
% 1.28/1.74 54 -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].
% 1.28/1.74 55 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.28/1.74 56 -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].
% 1.28/1.74 57 -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].
% 1.28/1.74 58 -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].
% 1.28/1.74 59 -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].
% 1.28/1.74 60 -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].
% 1.28/1.74 61 -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].
% 1.28/1.74 62 -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].
% 1.28/1.74 63 -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].
% 1.28/1.74 64 -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].
% 1.28/1.74 65 -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].
% 1.28/1.74 66 -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].
% 1.28/1.74 67 -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].
% 1.28/1.74 68 -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].
% 1.28/1.74 69 -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].
% 1.28/1.74 70 -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].
% 1.28/1.74 71 -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].
% 1.28/1.74 72 -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].
% 1.28/1.74 73 -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].
% 1.28/1.74 74 -class_Orderings_Olinorder(A) | c_Orderings_Olinorder(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),A) # label(cls_dual__linorder_0) # label(axiom). [assumption].
% 1.28/1.74 75 -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].
% 1.28/1.74 76 -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].
% 1.28/1.74 77 -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].
% 1.28/1.74 78 -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].
% 1.28/1.74 79 -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].
% 1.28/1.74 80 -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].
% 1.28/1.74 81 -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].
% 1.28/1.74 82 -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].
% 1.28/1.74 83 -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].
% 1.28/1.74 84 -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].
% 1.28/1.74 85 -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].
% 1.28/1.74 86 -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].
% 1.28/1.74 87 -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].
% 1.28/1.74 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)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.28/1.74 89 -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].
% 1.28/1.74 90 -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].
% 1.28/1.74 91 -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].
% 1.28/1.74 92 -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].
% 1.28/1.74 93 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_lessThan__subset__iff_1) # label(axiom). [assumption].
% 1.28/1.74 94 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) # label(cls_lessThan__subset__iff_0) # label(axiom). [assumption].
% 1.28/1.74 95 -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].
% 1.28/1.74 96 -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].
% 1.28/1.74 97 -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].
% 1.28/1.74 98 -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].
% 1.28/1.74 99 -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].
% 1.28/1.74 100 -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].
% 1.28/1.74 101 -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].
% 1.28/1.74 102 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 1.28/1.74 103 -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].
% 1.28/1.74 104 -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].
% 1.28/1.74 105 -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].
% 1.28/1.74 106 -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].
% 1.28/1.74 107 -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].
% 1.28/1.74 108 -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].
% 1.28/1.74 109 -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].
% 1.28/1.74 110 -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].
% 1.28/1.74 111 -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].
% 1.28/1.74 112 -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].
% 1.28/1.74 113 -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].
% 1.28/1.74 114 -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].
% 1.28/1.74 115 -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].
% 1.28/1.75 116 -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].
% 1.28/1.75 117 -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].
% 1.28/1.75 118 -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].
% 1.28/1.75 119 -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].
% 1.28/1.75 120 -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].
% 1.28/1.75 121 -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].
% 1.28/1.75 122 -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].
% 1.28/1.75 123 -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].
% 1.28/1.75 124 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -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].
% 1.28/1.75 125 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -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].
% 1.28/1.75 126 -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].
% 1.28/1.75 127 -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].
% 1.28/1.75 128 -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(hAPP(hAPP(c_in(A),D),B)) | 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].
% 1.28/1.75 129 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),D)) | -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].
% 1.28/1.75 130 -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(hAPP(hAPP(c_in(A),D),B)) | 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].
% 1.28/1.75 131 -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].
% 1.28/1.75 132 -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].
% 1.28/1.75 133 -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].
% 1.28/1.75 134 -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].
% 1.28/1.75 135 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = 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].
% 1.28/1.75 136 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = 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].
% 1.28/1.75 137 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C))) | -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 1.28/1.75 138 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 1.28/1.75 139 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | hBOOL(hAPP(hAPP(c_in(A),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(B,C,A)),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__eqI_0) # label(axiom). [assumption].
% 1.28/1.75 140 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | hBOOL(hAPP(hAPP(c_in(A),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(B,C,A)),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__eqI_0) # label(axiom). [assumption].
% 1.28/1.75 141 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),hAPP(c_Finite__Set_Olinorder__class_OMax(A),B)),B)) | 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].
% 1.28/1.75 142 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),B)) | 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].
% 1.28/1.75 143 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 1.28/1.75 144 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 1.28/1.75 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(29,a,30,a)].
% 1.28/1.75 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(29,a,31,a)].
% 1.28/1.75 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(29,a,32,a)].
% 1.28/1.75 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(29,a,33,a)].
% 1.28/1.75 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(29,a,38,a)].
% 1.28/1.75 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(29,a,39,a)].
% 1.28/1.75 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(29,a,40,a)].
% 1.28/1.75 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(29,a,41,a)].
% 1.28/1.75 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(29,a,42,a)].
% 1.28/1.75 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(29,a,43,a)].
% 1.28/1.75 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(29,a,44,a)].
% 1.28/1.75 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(29,a,45,a)].
% 1.28/1.75 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(29,a,46,a)].
% 1.28/1.75 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(29,a,47,a)].
% 1.28/1.75 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(29,a,52,a)].
% 1.28/1.75 Derived: -class_Lattices_Oupper__semilattice(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat). [resolve(29,a,53,a)].
% 1.28/1.75 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(29,a,54,a)].
% 1.28/1.75 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(29,a,55,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(29,a,56,a)].
% 1.28/1.75 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(29,a,57,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A))). [resolve(29,a,58,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B))). [resolve(29,a,59,a)].
% 1.28/1.75 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(29,a,60,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),A)). [resolve(29,a,63,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),B)). [resolve(29,a,64,a)].
% 1.28/1.75 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(29,a,65,a)].
% 1.28/1.75 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(29,a,68,a)].
% 1.28/1.75 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(29,a,69,a)].
% 1.28/1.75 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(29,a,70,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(29,a,71,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(29,a,72,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,73,a)].
% 1.28/1.75 Derived: c_Orderings_Olinorder(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),tc_nat). [resolve(29,a,74,a)].
% 1.28/1.75 Derived: -class_Lattices_Olower__semilattice(tc_nat) | c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat). [resolve(29,a,75,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(29,a,76,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(29,a,77,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,78,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,79,a)].
% 1.28/1.75 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,82,a)].
% 1.28/1.75 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(29,a,86,a)].
% 1.28/1.75 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(29,a,87,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(29,a,91,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = A. [resolve(29,a,92,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(29,a,93,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))). [resolve(29,a,94,a)].
% 1.28/1.75 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(29,a,95,a)].
% 1.28/1.75 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(29,a,96,a)].
% 1.28/1.75 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(29,a,99,a)].
% 1.28/1.75 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(29,a,100,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),A). [resolve(29,a,101,a)].
% 1.28/1.75 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(29,a,102,a)].
% 1.28/1.75 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(29,a,103,a)].
% 1.28/1.75 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(29,a,104,a)].
% 1.28/1.75 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(29,a,105,a)].
% 1.28/1.75 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(29,a,106,a)].
% 1.28/1.75 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(29,a,109,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A). [resolve(29,a,110,a)].
% 1.28/1.75 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(29,a,111,a)].
% 1.28/1.75 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = A. [resolve(29,a,112,a)].
% 1.28/1.75 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(29,a,113,a)].
% 1.28/1.75 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(29,a,114,a)].
% 1.28/1.75 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(29,a,115,a)].
% 1.28/1.75 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(29,a,116,a)].
% 1.28/1.75 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(29,a,117,a)].
% 1.28/1.75 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(29,a,119,a)].
% 1.28/1.75 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(29,a,120,a)].
% 1.28/1.75 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(29,a,121,a)].
% 1.28/1.75 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(29,a,122,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,123,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -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(29,a,124,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -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(29,a,125,a)].
% 1.28/1.75 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(29,a,126,a)].
% 1.28/1.75 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(29,a,127,a)].
% 1.28/1.75 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(hAPP(hAPP(c_in(tc_nat),C),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,128,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -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(29,a,129,a)].
% 1.28/1.75 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(hAPP(hAPP(c_in(tc_nat),C),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,130,a)].
% 1.28/1.75 Derived: c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(29,a,131,a)].
% 1.28/1.75 Derived: c_Finite__Set_Olinorder__class_OMin(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(29,a,132,a)].
% 1.28/1.75 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(29,a,133,a)].
% 1.28/1.75 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(29,a,134,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(29,a,135,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(29,a,136,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B))) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(29,a,137,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,138,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_in(tc_nat),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(A,B,tc_nat)),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,139,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_in(tc_nat),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(A,B,tc_nat)),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,140,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,141,a)].
% 1.28/1.75 Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,142,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))) = A. [resolve(29,a,143,a)].
% 1.28/1.75 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))) = A. [resolve(29,a,144,a)].
% 1.28/1.75 145 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) != B | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(1,b,2,b)].
% 1.28/1.75 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(145,a,29,a)].
% 1.28/1.75 146 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),B)). [resolve(1,b,3,c)].
% 1.28/1.75 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(146,a,29,a)].
% 1.28/1.75 147 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = B | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)). [resolve(1,b,4,c)].
% 1.28/1.75 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(147,a,29,a)].
% 1.28/1.75 148 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B. [resolve(1,b,5,b)].
% 1.28/1.75 149 -class_Orderings_Olinorder(A) | c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,D,A,A)) | -c_Finite__Set_Ofinite(D,A). [resolve(1,b,10,c)].
% 1.28/1.75 Derived: c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),A,C,tc_nat,tc_nat)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(149,a,29,a)].
% 1.28/1.75 150 -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(A),A). [resolve(1,b,11,b)].
% 1.28/1.75 151 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),C),D)). [resolve(1,b,12,c)].
% 1.28/1.75 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(151,a,29,a)].
% 1.28/1.75 152 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),B),D)). [resolve(1,b,13,c)].
% 1.28/1.75 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,29,a)].
% 1.28/1.75 153 -class_Orderings_Olinorder(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_Orderings_Oord__class_Omax(A),D),C))). [resolve(1,b,14,c)].
% 1.28/1.75 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(153,a,29,a)].
% 1.28/1.75 154 -class_Orderings_Olinorder(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_Orderings_Oord__class_Omax(A),C),D))). [resolve(1,b,15,c)].
% 1.28/1.75 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(154,a,29,a)].
% 1.28/1.75 155 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),D)). [resolve(1,b,18,c)].
% 1.28/1.75 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(155,a,29,a)].
% 1.28/1.75 156 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),C),D)). [resolve(1,b,19,c)].
% 1.28/1.75 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(156,a,29,a)].
% 1.55/1.80 157 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(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)) | -class_Orderings_Olinorder(A). [resolve(20,d,1,b)].
% 1.55/1.80 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(157,d,29,a)].
% 1.55/1.80 158 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),C)) | -class_Orderings_Olinorder(A). [resolve(21,b,1,b)].
% 1.55/1.80 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(158,b,29,a)].
% 1.55/1.80 159 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),B)) | -class_Orderings_Olinorder(A). [resolve(22,b,1,b)].
% 1.55/1.80 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(159,b,29,a)].
% 1.55/1.80 160 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),B,C,A,A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B))) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -c_Finite__Set_Ofinite(C,A) | -class_Orderings_Olinorder(A). [resolve(26,d,1,b)].
% 1.55/1.80 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),A,B,tc_nat,tc_nat)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A))) | -hBOOL(hAPP(hAPP(c_in(tc_nat),C),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(160,d,29,a)].
% 1.55/1.80 161 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) | -class_Orderings_Olinorder(A). [resolve(27,f,1,b)].
% 1.55/1.80 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -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(161,f,29,a)].
% 1.55/1.80 162 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A),B)),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) | -class_Orderings_Olinorder(A). [resolve(28,d,1,b)].
% 1.55/1.80 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(hAPP(hAPP(c_in(tc_nat),B),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(162,d,29,a)].
% 1.55/1.80 163 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.55/1.80 164 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),C,A,D)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),E,A,D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,tc_bool)),C),E),A,D)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,tc_bool)),C),E),A,D)) | -c_Finite__Set_Ofinite(E,D) | -c_Finite__Set_Ofinite(C,D) # label(cls_comm__monoid__add_Ofold__image__Un__Int_0) # label(axiom). [assumption].
% 1.55/1.80 165 -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].
% 1.55/1.80 166 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.55/1.80 167 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.55/1.80 168 -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].
% 1.55/1.80 169 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 1.55/1.80 170 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 1.55/1.80 171 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 1.55/1.80 172 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),C,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__0_0) # label(axiom). [assumption].
% 1.55/1.80 173 -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].
% 1.55/1.80 174 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.55/1.80 175 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),C,A,D) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__def_0) # label(axiom). [assumption].
% 1.55/1.80 176 -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].
% 1.55/1.80 177 -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].
% 1.55/1.80 178 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(A),A,A) # label(cls_comm__monoid__add_Ofun__left__comm_0) # label(axiom). [assumption].
% 1.55/1.80 179 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.55/1.80 180 -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_Ofold__image(c_HOL_Oplus__class_Oplus(A),E,c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),A,B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),E,c_HOL_Ozero__class_Ozero(A),C,A,B)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),E,c_HOL_Ozero__class_Ozero(A),D,A,B)) # label(cls_comm__monoid__add_Ofold__Un__disjoint_0) # label(axiom). [assumption].
% 1.55/1.80 181 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 1.55/1.80 182 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 1.55/1.80 183 -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),E))) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,A,A),E)) # label(cls_comm__monoid__add_Ofold__graph__insert__swap_0) # label(axiom). [assumption].
% 1.55/1.80 184 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,C,hAPP(hAPP(c_Set_Oinsert(D),E),F),A,D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,C,F,A,D)) | hBOOL(hAPP(hAPP(c_in(D),E),F)) | -c_Finite__Set_Ofinite(F,D) # label(cls_comm__monoid__add_Ofold__image__insert_0) # label(axiom). [assumption].
% 1.55/1.80 185 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,D)),c_Finite__Set_Osetsum(B,E,C,A)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.55/1.80 186 -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),c_HOL_Ominus__class_Ominus(D,hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool))),A,A),E)) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,A,A),E)) # label(cls_comm__monoid__add_Ofold__graph__permute__diff_0) # label(axiom). [assumption].
% 1.55/1.80 187 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(A),B,C,A,A) | hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_comm__monoid__add_Ofold1__eq__fold_0) # label(axiom). [assumption].
% 1.55/1.80 188 -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].
% 1.55/1.80 189 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),C)) | hBOOL(hAPP(hAPP(c_in(A),B),C)) | -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].
% 1.55/1.80 190 -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,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(D),E),c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))),tc_fun(D,tc_bool)),D,A)) | -hBOOL(hAPP(hAPP(c_in(D),E),C)) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 1.55/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,C)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),B),D),tc_nat,C)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,tc_bool)),B),D),tc_nat,C)) | -c_Finite__Set_Ofinite(D,C) | -c_Finite__Set_Ofinite(B,C). [resolve(163,a,164,a)].
% 1.55/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(163,a,165,a)].
% 1.55/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)). [resolve(163,a,166,b)].
% 1.55/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(163,a,167,b)].
% 1.55/1.80 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(163,a,168,a)].
% 1.55/1.80 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(163,a,169,a)].
% 1.55/1.80 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(163,a,171,a)].
% 1.55/1.80 Derived: c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),B,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(163,a,172,a)].
% 1.55/1.80 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(163,a,173,a)].
% 1.55/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(163,a,174,b)].
% 1.55/1.80 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,C) | -c_Finite__Set_Ofinite(B,C). [resolve(163,a,175,a)].
% 1.55/1.80 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(163,a,176,a)].
% 1.55/1.80 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(163,a,177,a)].
% 1.55/1.80 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat). [resolve(163,a,178,a)].
% 1.55/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(163,a,179,b)].
% 1.55/1.80 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_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),D,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),D,c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,A)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),D,c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat,A)). [resolve(163,a,180,a)].
% 1.55/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(163,a,181,a)].
% 1.55/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(163,a,182,a)].
% 1.55/1.80 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),D))) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(163,a,183,a)].
% 1.55/1.80 Derived: c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),tc_nat,C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,B,E,tc_nat,C)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C). [resolve(163,a,184,a)].
% 1.55/1.80 Derived: c_Finite__Set_Osetsum(A,hAPP(hAPP(c_Set_Oinsert(B),C),D),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,C)),c_Finite__Set_Osetsum(A,D,B,tc_nat)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [resolve(163,a,185,a)].
% 1.55/1.80 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool))),tc_nat,tc_nat),D)) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),C)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(163,a,186,a)].
% 1.55/1.80 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(163,a,187,a)].
% 1.55/1.80 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(163,a,188,a)].
% 1.73/2.01 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(163,a,189,a)].
% 1.73/2.01 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,c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_Set_Oinsert(C),D),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C,tc_nat)) | -hBOOL(hAPP(hAPP(c_in(C),D),B)) | -c_Finite__Set_Ofinite(B,C). [resolve(163,a,190,a)].
% 1.73/2.01 191 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.73/2.01 192 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.73/2.01 193 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.73/2.01 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(191,a,192,a)].
% 1.73/2.01 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(191,a,193,a)].
% 1.73/2.01 194 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.73/2.01 195 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.73/2.01 196 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.73/2.01 197 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.73/2.01 198 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.73/2.01 199 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.73/2.01 200 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.73/2.01 201 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.73/2.01 202 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.73/2.01 203 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.73/2.01 204 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.73/2.01 205 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.73/2.01 206 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.73/2.02 207 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.73/2.02 208 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.73/2.02 209 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.73/2.02 210 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(194,a,197,a)].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(194,a,198,a)].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(194,a,199,a)].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -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(194,a,200,a)].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(194,a,201,a)].
% 1.73/2.02 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(194,a,202,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(194,a,203,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(194,a,204,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(194,a,206,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(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(194,a,207,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -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(194,a,208,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(194,a,209,a)].
% 1.81/2.05 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(194,a,210,a)].
% 1.81/2.05 211 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.81/2.05 212 -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].
% 1.81/2.05 213 -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].
% 1.81/2.05 214 -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].
% 1.81/2.05 215 -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].
% 1.81/2.05 216 -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].
% 1.81/2.05 217 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.81/2.05 218 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.81/2.05 219 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.81/2.05 220 -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].
% 1.81/2.05 221 -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].
% 1.81/2.05 222 -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].
% 1.81/2.05 223 -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].
% 1.81/2.05 224 -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].
% 1.81/2.05 225 -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].
% 1.81/2.05 226 -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].
% 1.81/2.05 227 -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].
% 1.81/2.05 228 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_2) # label(axiom). [assumption].
% 1.81/2.05 229 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero_0) # label(axiom). [assumption].
% 1.81/2.05 230 -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].
% 1.81/2.05 231 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.81/2.05 232 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.81/2.05 233 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.81/2.05 234 -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].
% 1.81/2.05 235 -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].
% 1.81/2.05 236 -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].
% 1.81/2.05 237 -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].
% 1.81/2.05 238 -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].
% 1.81/2.05 239 -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].
% 1.81/2.05 240 -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].
% 1.81/2.05 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(211,a,214,a)].
% 1.81/2.05 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(211,a,215,a)].
% 1.81/2.05 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(211,a,216,a)].
% 1.81/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(211,a,217,a)].
% 1.91/2.17 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(211,a,218,a)].
% 1.91/2.17 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(211,a,220,a)].
% 1.91/2.17 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(211,a,222,a)].
% 1.91/2.17 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(211,a,224,a)].
% 1.91/2.17 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(211,a,227,a)].
% 1.91/2.17 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_in(C),B),D)) | -c_Finite__Set_Ofinite(D,C) | c_Finite__Set_Osetprod(A,D,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(211,a,228,b)].
% 1.91/2.17 Derived: hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_in(C),B),D)) | -c_Finite__Set_Ofinite(D,C) | c_Finite__Set_Osetprod(A,D,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(211,a,229,a)].
% 1.91/2.17 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(211,a,230,a)].
% 1.91/2.17 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(211,a,234,a)].
% 1.91/2.17 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(211,a,235,a)].
% 1.91/2.17 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(211,a,236,a)].
% 1.91/2.17 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(211,a,237,a)].
% 1.91/2.17 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(211,a,239,a)].
% 1.91/2.17 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(211,a,240,a)].
% 1.91/2.17 241 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.91/2.17 242 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.91/2.17 243 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.91/2.17 244 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.91/2.17 245 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.91/2.17 246 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.91/2.17 247 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.91/2.17 248 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.91/2.17 249 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.91/2.17 250 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.91/2.17 251 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.91/2.17 252 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.91/2.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(241,a,242,a)].
% 1.98/2.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(241,a,243,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(241,a,244,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(241,a,245,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(241,a,246,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(241,a,248,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(241,a,249,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(241,a,250,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(241,a,251,a)].
% 1.98/2.27 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(241,a,252,a)].
% 1.98/2.27 253 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.98/2.27 254 -class_Ring__and__Field_Omult__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 1.98/2.27 255 -class_Ring__and__Field_Omult__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 1.98/2.27 256 -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].
% 1.98/2.27 257 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].
% 1.98/2.27 258 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].
% 1.98/2.28 259 -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].
% 1.98/2.28 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(259,b,257,b)].
% 1.98/2.28 Derived: -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B. [resolve(259,b,258,b)].
% 1.98/2.28 260 hAPP(c_Finite__Set_Ofold1(A,B),hAPP(hAPP(c_Set_Oinsert(B),C),D)) = c_Finite__Set_Ofold(A,C,D,B,B) | -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].
% 1.98/2.28 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,C,A,A) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(260,c,256,b)].
% 1.98/2.28 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),B,C,A,A) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Olower__semilattice(A). [resolve(260,c,259,b)].
% 1.98/2.28 261 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].
% 1.98/2.28 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(261,f,256,b)].
% 1.98/2.28 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(261,f,259,b)].
% 1.98/2.28 262 hAPP(c_Finite__Set_Ofold1(A,B),hAPP(hAPP(c_Set_Oinsert(B),C),D)) = 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].
% 1.98/2.28 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = 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(262,d,256,b)].
% 1.98/2.28 Derived: hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = 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(262,d,259,b)].
% 2.05/2.35 263 -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(25,b,11,b)].
% 2.05/2.35 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(263,b,257,b)].
% 2.05/2.35 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B. [resolve(263,b,258,b)].
% 2.05/2.35 264 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(29,a,38,a)].
% 2.05/2.35 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = c_Finite__Set_Ofold(c_Orderings_Oord__class_Omin(tc_nat),A,B,tc_nat,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(264,a,260,c)].
% 2.05/2.35 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(264,a,261,f)].
% 2.05/2.35 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(264,a,262,d)].
% 2.05/2.35 265 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(29,a,43,a)].
% 2.05/2.35 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),A,B,tc_nat,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(265,a,260,c)].
% 2.05/2.35 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(265,a,261,f)].
% 2.05/2.35 Derived: hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(265,a,262,d)].
% 2.05/2.35 266 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(A),A,A) # label(cls_fun__left__comm_0) # label(axiom). [assumption].
% 2.05/2.35 267 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Finite__Set_Ofun__left__comm(A,E,F) # label(cls_fun__left__comm_Ofun__left__comm_0) # label(axiom). [assumption].
% 2.05/2.35 268 A = B | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(C,D,E,F,V6),A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(C,D,E,F,V6),B)) | -c_Finite__Set_Ofun__left__comm(C,F,V6) # label(cls_fun__left__comm_Ofold__graph__determ_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: -class_OrderedGroup_Oab__semigroup__mult(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)). [resolve(266,b,267,b)].
% 2.05/2.36 Derived: -class_OrderedGroup_Oab__semigroup__mult(A) | B = C | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),D,E,A,A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),D,E,A,A),C)). [resolve(266,b,268,d)].
% 2.05/2.36 269 c_Finite__Set_Ofold(A,B,C,D,E) = F | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,B,C,D,E),F)) | -c_Finite__Set_Ofun__left__comm(A,D,E) # label(cls_fun__left__comm_Ofold__equality_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) = D | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,C,A,A),D)) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(269,c,266,b)].
% 2.05/2.36 270 c_Finite__Set_Ofun__left__comm(A,B,B) | -c_OrderedGroup_Oab__semigroup__mult(A,B) # label(cls_ab__semigroup__mult_Ofun__left__comm_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: -c_OrderedGroup_Oab__semigroup__mult(A,B) | C = D | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,E,F,B,B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,E,F,B,B),D)). [resolve(270,a,268,d)].
% 2.05/2.36 Derived: -c_OrderedGroup_Oab__semigroup__mult(A,B) | c_Finite__Set_Ofold(A,C,D,B,B) = E | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,C,D,B,B),E)). [resolve(270,a,269,c)].
% 2.05/2.36 271 hAPP(hAPP(A,B),c_Finite__Set_Ofold(A,C,D,E,F)) = c_Finite__Set_Ofold(A,hAPP(hAPP(A,B),C),D,E,F) | -c_Finite__Set_Ofinite(D,E) | -c_Finite__Set_Ofun__left__comm(A,E,F) # label(cls_fun__left__comm_Ofold__fun__comm_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),C,D,A,A)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A,A) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(271,c,266,b)].
% 2.05/2.36 Derived: hAPP(hAPP(A,B),c_Finite__Set_Ofold(A,C,D,E,E)) = c_Finite__Set_Ofold(A,hAPP(hAPP(A,B),C),D,E,E) | -c_Finite__Set_Ofinite(D,E) | -c_OrderedGroup_Oab__semigroup__mult(A,E). [resolve(271,c,270,a)].
% 2.05/2.36 272 -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,B,C,D,E),F)) | hBOOL(hAPP(hAPP(c_in(D),V6),C)) | -c_Finite__Set_Ofun__left__comm(A,D,E) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,B,hAPP(hAPP(c_Set_Oinsert(D),V6),C),D,E),hAPP(hAPP(A,V6),F))) # label(cls_fun__left__comm_Ofold__insert__aux_2) # label(axiom). [assumption].
% 2.05/2.36 273 c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,F) = c_Finite__Set_Ofold(A,hAPP(hAPP(A,D),B),E,C,F) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofun__left__comm(A,C,F) # label(cls_fun__left__comm_Ofold__insert2_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),D,A,A) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(273,d,266,b)].
% 2.05/2.36 Derived: c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,C) = c_Finite__Set_Ofold(A,hAPP(hAPP(A,D),B),E,C,C) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) | -c_OrderedGroup_Oab__semigroup__mult(A,C). [resolve(273,d,270,a)].
% 2.05/2.36 274 c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,F) = hAPP(hAPP(A,D),c_Finite__Set_Ofold(A,B,E,C,F)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofun__left__comm(A,C,F) # label(cls_fun__left__comm_Ofold__insert_0) # label(axiom). [assumption].
% 2.05/2.36 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,D,A,A)) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(274,d,266,b)].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,C) = hAPP(hAPP(A,D),c_Finite__Set_Ofold(A,B,E,C,C)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) | -c_OrderedGroup_Oab__semigroup__mult(A,C). [resolve(274,d,270,a)].
% 2.13/2.37 275 c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,F) = hAPP(hAPP(A,D),c_Finite__Set_Ofold(A,B,c_HOL_Ominus__class_Ominus(E,hAPP(hAPP(c_Set_Oinsert(C),D),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C,F)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofun__left__comm(A,C,F) # label(cls_fun__left__comm_Ofold__insert__remove_0) # label(axiom). [assumption].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,c_HOL_Ominus__class_Ominus(D,hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool)),A,A)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(275,c,266,b)].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,C) = hAPP(hAPP(A,D),c_Finite__Set_Ofold(A,B,c_HOL_Ominus__class_Ominus(E,hAPP(hAPP(c_Set_Oinsert(C),D),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C,C)) | -c_Finite__Set_Ofinite(E,C) | -c_OrderedGroup_Oab__semigroup__mult(A,C). [resolve(275,c,270,a)].
% 2.13/2.37 276 c_Finite__Set_Ofold(A,B,C,D,E) = hAPP(hAPP(A,F),c_Finite__Set_Ofold(A,B,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(D),F),c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))),tc_fun(D,tc_bool)),D,E)) | -hBOOL(hAPP(hAPP(c_in(D),F),C)) | -c_Finite__Set_Ofinite(C,D) | -c_Finite__Set_Ofun__left__comm(A,D,E) # label(cls_fun__left__comm_Ofold__rec_0) # label(axiom). [assumption].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(A),D),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool)),A,A)) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -c_Finite__Set_Ofinite(C,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(276,d,266,b)].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(A,B,C,D,D) = hAPP(hAPP(A,E),c_Finite__Set_Ofold(A,B,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(D),E),c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))),tc_fun(D,tc_bool)),D,D)) | -hBOOL(hAPP(hAPP(c_in(D),E),C)) | -c_Finite__Set_Ofinite(C,D) | -c_OrderedGroup_Oab__semigroup__mult(A,D). [resolve(276,d,270,a)].
% 2.13/2.37 277 c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat). [resolve(163,a,178,a)].
% 2.13/2.37 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(277,a,267,b)].
% 2.13/2.37 Derived: A = B | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),C,D,tc_nat,tc_nat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),C,D,tc_nat,tc_nat),B)). [resolve(277,a,268,d)].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = C | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat),C)). [resolve(277,a,269,c)].
% 2.13/2.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(277,a,271,c)].
% 2.13/2.37 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat),C)) | hBOOL(hAPP(hAPP(c_in(tc_nat),D),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),D),B),tc_nat,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C))). [resolve(277,a,272,c)].
% 2.13/2.37 Derived: c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),C,tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(277,a,273,d)].
% 2.27/2.50 Derived: c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,C,tc_nat,tc_nat)) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(277,a,274,d)].
% 2.27/2.50 Derived: c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(277,a,275,c)].
% 2.27/2.50 Derived: c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_Set_Oinsert(tc_nat),C),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),C),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(277,a,276,d)].
% 2.27/2.50 278 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.50 279 -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].
% 2.27/2.50 280 -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].
% 2.27/2.50 281 -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].
% 2.27/2.50 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(278,a,279,a)].
% 2.27/2.50 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(278,a,280,a)].
% 2.27/2.50 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(278,a,281,a)].
% 2.27/2.50 282 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.50 283 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.27/2.50 284 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.27/2.50 285 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetprod(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),D),E),C,A)),c_Finite__Set_Osetprod(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,tc_bool)),D),E),C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetprod(B,D,C,A)),c_Finite__Set_Osetprod(B,E,C,A)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(D,C) # label(cls_setprod__Un__Int_0) # label(axiom). [assumption].
% 2.27/2.53 286 -class_OrderedGroup_Ocomm__monoid__mult(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_Osetprod(E,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetprod(E,C,B,A)),c_Finite__Set_Osetprod(E,D,B,A)) # label(cls_setprod__Un__disjoint_0) # label(axiom). [assumption].
% 2.27/2.53 287 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,hAPP(hAPP(c_Set_Oinsert(C),D),E),C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),c_Finite__Set_Osetprod(B,E,C,A)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) # label(cls_setprod__insert_0) # label(axiom). [assumption].
% 2.27/2.53 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetprod(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,tc_nat)),c_Finite__Set_Osetprod(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,tc_bool)),C),D),B,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetprod(A,C,B,tc_nat)),c_Finite__Set_Osetprod(A,D,B,tc_nat)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(284,a,285,a)].
% 2.27/2.53 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_Osetprod(D,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),A,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetprod(D,B,A,tc_nat)),c_Finite__Set_Osetprod(D,C,A,tc_nat)). [resolve(284,a,286,a)].
% 2.27/2.53 Derived: c_Finite__Set_Osetprod(A,hAPP(hAPP(c_Set_Oinsert(B),C),D),B,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(A,C)),c_Finite__Set_Osetprod(A,D,B,tc_nat)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [resolve(284,a,287,a)].
% 2.27/2.53 288 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.53 289 -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].
% 2.27/2.53 290 -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].
% 2.27/2.53 291 -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].
% 2.27/2.53 292 -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].
% 2.27/2.53 293 -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].
% 2.33/2.63 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(288,a,289,a)].
% 2.33/2.63 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(288,a,290,a)].
% 2.33/2.63 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(288,a,291,a)].
% 2.33/2.63 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(288,a,292,a)].
% 2.33/2.63 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(288,a,293,a)].
% 2.33/2.63 294 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.33/2.63 295 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 2.33/2.63 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(294,a,295,a)].
% 2.33/2.63 296 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.33/2.63 297 -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].
% 2.33/2.63 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(296,a,297,a)].
% 2.33/2.63 298 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.33/2.63 299 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.33/2.63 300 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.46/2.71 301 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.46/2.71 302 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.46/2.71 303 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.46/2.71 304 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.46/2.71 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(298,a,299,a)].
% 2.46/2.71 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(298,a,300,a)].
% 2.46/2.71 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(298,a,304,a)].
% 2.46/2.71 305 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.46/2.71 306 -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].
% 2.46/2.71 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(305,a,306,a)].
% 2.46/2.71 307 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.46/2.71 308 -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].
% 2.46/2.71 309 -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].
% 2.46/2.71 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(307,a,309,a)].
% 2.46/2.71 310 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.46/2.71 311 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.50/2.81 312 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.50/2.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(310,a,311,a)].
% 2.50/2.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(310,a,312,a)].
% 2.50/2.81 313 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.50/2.81 314 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.50/2.81 315 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.50/2.81 316 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.50/2.81 317 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.50/2.81 318 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.50/2.81 319 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.50/2.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(317,a,318,a)].
% 2.50/2.81 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(317,a,319,a)].
% 2.50/2.81 320 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.58/2.84 321 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.58/2.84 322 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.58/2.84 323 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.58/2.84 324 -class_OrderedGroup_Oab__semigroup__mult(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E))) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,A,A),E)) # label(cls_fold__graph__insert__swap_0) # label(axiom). [assumption].
% 2.58/2.84 325 -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].
% 2.58/2.84 326 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,C,hAPP(hAPP(c_Set_Oinsert(D),E),F),A,D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,E)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,C,F,A,D)) | hBOOL(hAPP(hAPP(c_in(D),E),F)) | -c_Finite__Set_Ofinite(F,D) # label(cls_fold__image__insert_0) # label(axiom). [assumption].
% 2.58/2.84 327 -class_OrderedGroup_Oab__semigroup__mult(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),c_HOL_Ominus__class_Ominus(D,hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool))),A,A),E)) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,A,A),E)) # label(cls_fold__graph__permute__diff_0) # label(axiom). [assumption].
% 2.58/2.84 328 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) | hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_fold1__eq__fold_0) # label(axiom). [assumption].
% 2.58/2.84 329 -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].
% 2.58/2.84 330 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),hAPP(hAPP(c_Set_Oinsert(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),C)) | hBOOL(hAPP(hAPP(c_in(A),B),C)) | -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].
% 2.58/2.84 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D))) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(323,a,324,a)].
% 2.58/2.84 Derived: c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,B,hAPP(hAPP(c_Set_Oinsert(C),D),E),tc_nat,C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(A,D)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,B,E,tc_nat,C)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C). [resolve(323,a,326,a)].
% 2.58/2.85 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool))),tc_nat,tc_nat),D)) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),C)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(323,a,327,a)].
% 2.58/2.85 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,B,tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(323,a,328,a)].
% 2.58/2.85 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_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(323,a,329,a)].
% 2.58/2.85 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),B)) = 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(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(323,a,330,a)].
% 2.58/2.85 331 -class_OrderedGroup_Oab__semigroup__mult(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)). [resolve(266,b,267,b)].
% 2.58/2.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(331,a,323,a)].
% 2.58/2.85 332 -class_OrderedGroup_Oab__semigroup__mult(A) | B = C | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),D,E,A,A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),D,E,A,A),C)). [resolve(266,b,268,d)].
% 2.58/2.85 Derived: A = B | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),C,D,tc_nat,tc_nat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),C,D,tc_nat,tc_nat),B)). [resolve(332,a,323,a)].
% 2.58/2.85 333 c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) = D | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,C,A,A),D)) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(269,c,266,b)].
% 2.58/2.85 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,B,tc_nat,tc_nat) = C | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,B,tc_nat,tc_nat),C)). [resolve(333,c,323,a)].
% 2.58/2.85 334 hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),C,D,A,A)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A,A) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(271,c,266,b)].
% 2.58/2.85 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat,tc_nat) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(334,c,323,a)].
% 2.65/2.96 335 c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),D,A,A) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(273,d,266,b)].
% 2.65/2.96 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),C,tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(335,d,323,a)].
% 2.65/2.96 336 c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,D,A,A)) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(274,d,266,b)].
% 2.65/2.96 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,C,tc_nat,tc_nat)) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(336,d,323,a)].
% 2.65/2.96 337 c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,hAPP(hAPP(c_Set_Oinsert(A),C),D),A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,c_HOL_Ominus__class_Ominus(D,hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool)),A,A)) | -c_Finite__Set_Ofinite(D,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(275,c,266,b)].
% 2.65/2.96 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(tc_nat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(337,c,323,a)].
% 2.65/2.96 338 c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_Set_Oinsert(A),D),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),tc_fun(A,tc_bool)),A,A)) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -c_Finite__Set_Ofinite(C,A) | -class_OrderedGroup_Oab__semigroup__mult(A). [resolve(276,d,266,b)].
% 2.65/2.96 Derived: c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,B,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_Set_Oinsert(tc_nat),C),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_bool)),tc_nat,tc_nat)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),C),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(338,d,323,a)].
% 2.65/2.96 339 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.65/2.96 340 -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].
% 2.65/2.96
% 2.65/2.96 ============================== end predicate elimination =============
% 2.65/2.96
% 2.65/2.96 Auto_denials: (non-Horn, no changes).
% 2.65/2.96
% 2.65/2.96 Term ordering decisions:
% 2.65/2.96 Function symbol KB weights: tc_nat=1. tc_bool=1. t_a=1. tc_Com_Ostate=1. v_x=1. c_Com_Obody=1. t_b=1. tc_Com_Ocom=1. tc_Com_Opname=1. c_Com_Ocom_OSKIP=1. v_c=1. v_G=1. hAPP=1. tc_fun=1. c_Finite__Set_Ofold1=1. c_Finite__Set_Ocard=1. c_SetInterval_Oord__class_OlessThan=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Com_Ocom_OSemi=1. c_Option_Oset=1. c_Option_Othe=1. c_The=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_Set_Ocontents=1. c_lessequals=1. c_Set_Oinsert=1. c_HOL_Oord__class_Oless=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_in=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ozero__class_Ozero=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Oord__class_Omax=1. c_Orderings_Oord__class_Omin=1. c_Option_Ooption_OSome=1. tc_Option_Ooption=1. c_Option_Ooption_ONone=1. c_Suc=1. c_Natural_Oevalc=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Com_Ocom_OBODY=1. c_fequal=1. c_Finite__Set_Olattice__class_OInf__fin=1. c_Hoare__Mirabelle_OMGT=1. c_HOL_Ominus__class_Ominus=1. c_Map_Odom=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_COMBK=1. c_Finite__Set_Ofold1Set=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_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1=1. c_Finite__Set_Olattice_OInf__fin=1. c_Finite__Set_Olattice_OSup__fin=1. c_COMBC=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Map_Omap__add=1. c_Set_Ovimage=1. c_Map_Orestrict__map=1. c_Finite__Set_Osetsum=1. c_Finite__Set_Osetprod=1. c_Map_Osko__Map__Xmap__le__def__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_Map_Osko__Map__XdomD__1__1=1. c_Finite__Set_Ofold=1. c_Fun_Ofun__upd=1. c_Finite__Set_Ofold__graph=1. c_Option_Ooption_Ooption__case=1. c_Finite__Set_Ofold__image=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 2.65/2.96
% 2.65/2.96 ============================== PROOF =================================
% 2.65/2.96 % SZS status Unsatisfiable
% 2.65/2.96 % SZS output start Refutation
% 2.65/2.96
% 2.65/2.96 % Proof 1 at 1.45 (+ 0.01) seconds.
% 2.65/2.96 % Length of proof is 3.
% 2.65/2.96 % Level of proof is 1.
% 2.65/2.96 % Maximum clause weight is 7.000.
% 2.65/2.96 % Given clauses 0.
% 2.65/2.96
% 2.65/2.96 1007 hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),A),A)) # label(cls_evalc_OSkip_0) # label(axiom). [assumption].
% 2.65/2.96 1031 -hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 2.65/2.96 1032 $F. [copy(1031),unit_del(a,1007)].
% 2.65/2.96
% 2.65/2.96 % SZS output end Refutation
% 2.65/2.96 ============================== end of proof ==========================
% 2.65/2.96
% 2.65/2.96 ============================== STATISTICS ============================
% 2.65/2.96
% 2.65/2.96 Given=0. Generated=614. Kept=527. proofs=1.
% 2.65/2.96 Usable=0. Sos=0. Demods=78. Limbo=527, Disabled=1106. Hints=0.
% 2.65/2.96 Megabytes=2.80.
% 2.65/2.96 User_CPU=1.45, System_CPU=0.01, Wall_clock=1.
% 2.65/2.96
% 2.65/2.96 ============================== end of statistics =====================
% 2.65/2.96
% 2.65/2.96 ============================== end of search =========================
% 2.65/2.96
% 2.65/2.96 THEOREM PROVED
% 2.65/2.96 % SZS status Unsatisfiable
% 2.65/2.96
% 2.65/2.96 Exiting with 1 proof.
% 2.65/2.96
% 2.65/2.96 Process 27454 exit (max_proofs) Thu Jun 16 04:03:53 2022
% 2.65/2.96 Prover9 interrupted
%------------------------------------------------------------------------------