TSTP Solution File: SWV871-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV871-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 21:15:06 EDT 2022
% Result : Timeout 300.02s 300.27s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV871-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 17:37:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.11/1.46 ============================== Prover9 ===============================
% 1.11/1.46 Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.46 Process 26847 was started by sandbox on n013.cluster.edu,
% 1.11/1.46 Tue Jun 14 17:37:29 2022
% 1.11/1.46 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26694_n013.cluster.edu".
% 1.11/1.46 ============================== end of head ===========================
% 1.11/1.46
% 1.11/1.46 ============================== INPUT =================================
% 1.11/1.46
% 1.11/1.46 % Reading from file /tmp/Prover9_26694_n013.cluster.edu
% 1.11/1.46
% 1.11/1.46 set(prolog_style_variables).
% 1.11/1.46 set(auto2).
% 1.11/1.46 % set(auto2) -> set(auto).
% 1.11/1.46 % set(auto) -> set(auto_inference).
% 1.11/1.46 % set(auto) -> set(auto_setup).
% 1.11/1.46 % set(auto_setup) -> set(predicate_elim).
% 1.11/1.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.46 % set(auto) -> set(auto_limits).
% 1.11/1.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.46 % set(auto) -> set(auto_denials).
% 1.11/1.46 % set(auto) -> set(auto_process).
% 1.11/1.46 % set(auto2) -> assign(new_constants, 1).
% 1.11/1.46 % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.46 % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.46 % set(auto2) -> assign(max_hours, 1).
% 1.11/1.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.46 % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.46 % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.46 % set(auto2) -> set(sort_initial_sos).
% 1.11/1.46 % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.46 % set(auto2) -> assign(max_megs, 400).
% 1.11/1.46 % set(auto2) -> assign(stats, some).
% 1.11/1.46 % set(auto2) -> clear(echo_input).
% 1.11/1.46 % set(auto2) -> set(quiet).
% 1.11/1.46 % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.46 % set(auto2) -> clear(print_given).
% 1.11/1.46 assign(lrs_ticks,-1).
% 1.11/1.46 assign(sos_limit,10000).
% 1.11/1.46 assign(order,kbo).
% 1.11/1.46 set(lex_order_vars).
% 1.11/1.46 clear(print_given).
% 1.11/1.46
% 1.11/1.46 % formulas(sos). % not echoed (908 formulas)
% 1.11/1.46
% 1.11/1.46 ============================== end of input ==========================
% 1.11/1.46
% 1.11/1.46 % From the command line: assign(max_seconds, 300).
% 1.11/1.46
% 1.11/1.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.46
% 1.11/1.46 % Formulas that are not ordinary clauses:
% 1.11/1.46
% 1.11/1.46 ============================== end of process non-clausal formulas ===
% 1.11/1.46
% 1.11/1.46 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.46
% 1.11/1.46 ============================== PREDICATE ELIMINATION =================
% 1.11/1.46 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].
% 1.11/1.46 2 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].
% 1.11/1.46 3 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].
% 1.11/1.46 4 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].
% 1.11/1.46 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].
% 1.11/1.46 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].
% 1.11/1.46 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].
% 1.11/1.46 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].
% 1.11/1.46 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].
% 1.11/1.46 10 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].
% 1.11/1.46 11 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].
% 1.11/1.46 12 hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),hAPP(hAPP(c_Set_Oinsert(B),D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),E)) | -c_Finite__Set_Ofinite(E,B) | -c_Lattices_Olower__semilattice(F,V6,A,B) # label(cls_lower__semilattice_Ofold__inf__insert_0) # label(axiom). [assumption].
% 1.11/1.46 13 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].
% 1.11/1.46 14 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].
% 1.11/1.46 15 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].
% 1.11/1.46 16 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].
% 1.11/1.46 17 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].
% 1.11/1.46 18 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].
% 1.11/1.46 19 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].
% 1.11/1.46 20 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].
% 1.11/1.46 21 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].
% 1.11/1.46 22 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].
% 1.11/1.46 23 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].
% 1.11/1.46 24 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].
% 1.11/1.46 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,c)].
% 1.11/1.46 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,3,b)].
% 1.11/1.46 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,4,c)].
% 1.11/1.46 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B. [resolve(1,b,5,b)].
% 1.11/1.46 Derived: -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(A),A). [resolve(1,b,10,b)].
% 1.11/1.46 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,11,c)].
% 1.11/1.46 Derived: -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),hAPP(hAPP(c_Set_Oinsert(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(1,b,12,c)].
% 1.11/1.47 Derived: -class_Orderings_Olinorder(A) | 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)). [resolve(1,b,13,d)].
% 1.11/1.47 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)),C)). [resolve(1,b,14,b)].
% 1.11/1.47 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)),B)). [resolve(1,b,15,b)].
% 1.11/1.47 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,18,c)].
% 1.11/1.47 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,19,c)].
% 1.11/1.47 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,20,c)].
% 1.11/1.47 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,23,c)].
% 1.11/1.47 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,24,c)].
% 1.11/1.47 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].
% 1.11/1.47 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,c)].
% 1.11/1.47 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,3,b)].
% 1.11/1.47 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,4,c)].
% 1.11/1.47 Derived: -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(25,b,10,b)].
% 1.11/1.47 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,11,c)].
% 1.11/1.47 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,13,d)].
% 1.11/1.47 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,14,b)].
% 1.11/1.47 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,15,b)].
% 1.11/1.47 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,18,c)].
% 1.11/1.52 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,19,c)].
% 1.11/1.52 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,20,c)].
% 1.11/1.52 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,23,c)].
% 1.11/1.52 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,24,c)].
% 1.11/1.52 26 hBOOL(hAPP(hAPP(A,hAPP(hAPP(c_Finite__Set_Ofold(B,C,C),D),E)),hAPP(hAPP(B,F),D))) | -c_in(F,E,C) | -c_Finite__Set_Ofinite(E,C) | -c_Lattices_Olower__semilattice(A,V6,B,C) # label(cls_lower__semilattice_Ofold__inf__le__inf_0) # label(axiom). [assumption].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B))) | -c_in(D,C,A) | -c_Finite__Set_Ofinite(C,A) | -class_Orderings_Olinorder(A). [resolve(26,d,1,b)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),C)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B))) | -c_in(D,C,A) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(26,d,25,b)].
% 1.11/1.52 27 hBOOL(hAPP(hAPP(A,hAPP(c_Finite__Set_Ofold1(B,C),D)),E)) | -c_in(E,D,C) | -c_Finite__Set_Ofinite(D,C) | -c_Lattices_Olower__semilattice(A,F,B,C) # label(cls_lower__semilattice_Ofold1__belowI_0) # label(axiom). [assumption].
% 1.11/1.52 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)) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) | -class_Orderings_Olinorder(A). [resolve(27,d,1,b)].
% 1.11/1.52 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)) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) | -class_Lattices_Oupper__semilattice(A). [resolve(27,d,25,b)].
% 1.11/1.52 28 hBOOL(hAPP(hAPP(A,B),C)) | -c_in(C,D,E) | -hBOOL(hAPP(hAPP(A,B),hAPP(c_Finite__Set_Ofold1(F,E),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(E,tc_bool)) | -c_Finite__Set_Ofinite(D,E) | -c_Lattices_Olower__semilattice(A,V6,F,E) # label(cls_lower__semilattice_Obelow__fold1__iff_0) # label(axiom). [assumption].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -c_in(C,D,A) | -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(28,f,1,b)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -c_in(C,D,A) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),hAPP(c_Finite__Set_Ofold1(c_Lattices_Oupper__semilattice__class_Osup(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) | -class_Lattices_Oupper__semilattice(A). [resolve(28,f,25,b)].
% 1.11/1.52 29 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 42 -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].
% 1.11/1.52 43 -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].
% 1.11/1.52 44 -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].
% 1.11/1.52 45 -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].
% 1.11/1.52 46 -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].
% 1.11/1.52 47 -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].
% 1.11/1.52 48 -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].
% 1.11/1.52 49 -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].
% 1.11/1.52 50 -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].
% 1.11/1.52 51 -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].
% 1.11/1.52 52 -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].
% 1.11/1.52 53 -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].
% 1.11/1.52 54 -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].
% 1.11/1.52 55 -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].
% 1.11/1.52 56 -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].
% 1.11/1.52 57 -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].
% 1.11/1.52 58 -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].
% 1.11/1.52 59 -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].
% 1.11/1.52 60 -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].
% 1.11/1.52 61 -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].
% 1.11/1.52 62 -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].
% 1.11/1.52 63 -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].
% 1.11/1.52 64 -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].
% 1.11/1.52 65 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.11/1.52 66 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),B) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 1.11/1.52 67 -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].
% 1.11/1.52 68 -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].
% 1.11/1.52 69 -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].
% 1.11/1.52 70 -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].
% 1.11/1.52 71 -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].
% 1.11/1.52 72 -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].
% 1.11/1.52 73 -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].
% 1.11/1.52 74 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.11/1.52 75 -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].
% 1.11/1.52 76 -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].
% 1.11/1.52 77 -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].
% 1.11/1.52 78 -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].
% 1.11/1.52 79 -class_Orderings_Olinorder(A) | -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(A) = c_Orderings_Oord__class_Omin(A) # label(cls_inf__min_0) # label(axiom). [assumption].
% 1.11/1.52 80 -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].
% 1.11/1.52 81 -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].
% 1.11/1.52 82 -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].
% 1.11/1.52 83 -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].
% 1.11/1.52 84 -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].
% 1.11/1.52 85 -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].
% 1.11/1.52 86 -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].
% 1.11/1.52 87 -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].
% 1.11/1.52 88 -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].
% 1.11/1.52 89 -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].
% 1.11/1.52 90 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 1.11/1.52 91 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 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].
% 1.11/1.52 100 -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].
% 1.11/1.52 101 -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].
% 1.11/1.52 102 -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].
% 1.11/1.52 103 -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].
% 1.11/1.52 104 -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].
% 1.11/1.52 105 -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].
% 1.11/1.52 106 -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].
% 1.11/1.52 107 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 1.11/1.52 108 -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].
% 1.11/1.52 109 -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].
% 1.11/1.52 110 -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].
% 1.11/1.52 111 -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].
% 1.11/1.52 112 -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].
% 1.11/1.52 113 -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].
% 1.11/1.52 114 -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].
% 1.11/1.52 115 -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].
% 1.11/1.52 116 -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].
% 1.11/1.52 117 -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].
% 1.11/1.52 118 -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].
% 1.11/1.52 119 -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].
% 1.11/1.52 120 -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].
% 1.11/1.52 121 -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].
% 1.11/1.52 122 -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].
% 1.11/1.52 123 -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].
% 1.11/1.52 124 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -c_in(C,B,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(B,C,A)),C)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__eqI_1) # label(axiom). [assumption].
% 1.11/1.52 125 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -c_in(C,B,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(B,C,A))) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__eqI_1) # label(axiom). [assumption].
% 1.11/1.52 126 -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].
% 1.11/1.52 127 -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].
% 1.11/1.52 128 -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)) | -c_in(D,B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__below__iff_2) # label(axiom). [assumption].
% 1.11/1.52 129 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_in(C,D,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),D))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_strict__below__fold1__iff_0) # label(axiom). [assumption].
% 1.11/1.52 130 -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)) | -c_in(D,B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__strict__below__iff_2) # label(axiom). [assumption].
% 1.11/1.52 131 -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].
% 1.11/1.52 132 -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].
% 1.11/1.52 133 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C))) | -c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 1.11/1.52 134 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),C)) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 1.11/1.52 135 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),B) = C | -c_in(C,B,A) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(B,C,A),B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__eqI_0) # label(axiom). [assumption].
% 1.11/1.52 136 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),B) = C | -c_in(C,B,A) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(B,C,A),B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__eqI_0) # label(axiom). [assumption].
% 1.11/1.52 137 -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].
% 1.11/1.52 138 -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].
% 1.11/1.52 139 -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].
% 1.11/1.52 140 -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].
% 1.11/1.52 141 -class_Orderings_Olinorder(A) | c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(A),B),B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 1.11/1.52 142 -class_Orderings_Olinorder(A) | c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(A),B),B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 1.11/1.52 143 -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].
% 1.11/1.52 144 -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].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(29,a,38,a)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A))). [resolve(29,a,42,a)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B))). [resolve(29,a,43,a)].
% 1.11/1.52 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,44,a)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),A)). [resolve(29,a,47,a)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),B)). [resolve(29,a,48,a)].
% 1.11/1.52 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,49,a)].
% 1.11/1.52 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,52,a)].
% 1.11/1.52 Derived: c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(29,a,53,a)].
% 1.11/1.52 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,54,a)].
% 1.11/1.52 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,55,a)].
% 1.11/1.52 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,56,a)].
% 1.11/1.52 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,57,a)].
% 1.11/1.52 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,62,a)].
% 1.11/1.52 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,63,a)].
% 1.11/1.52 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,64,a)].
% 1.11/1.52 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(29,a,65,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(29,a,66,a)].
% 1.11/1.52 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,67,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(29,a,71,a)].
% 1.11/1.52 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,72,a)].
% 1.11/1.52 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,73,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B). [resolve(29,a,74,a)].
% 1.11/1.52 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,75,a)].
% 1.11/1.52 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,76,a)].
% 1.11/1.52 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,77,a)].
% 1.11/1.52 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,78,a)].
% 1.11/1.52 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,79,a)].
% 1.11/1.52 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,80,a)].
% 1.11/1.52 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,81,a)].
% 1.11/1.52 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,82,a)].
% 1.11/1.52 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,83,a)].
% 1.11/1.52 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,86,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)). [resolve(29,a,90,a)].
% 1.11/1.52 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)). [resolve(29,a,91,a)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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,101,a)].
% 1.11/1.52 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,102,a)].
% 1.11/1.52 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,103,a)].
% 1.11/1.52 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,104,a)].
% 1.11/1.52 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,105,a)].
% 1.11/1.52 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,107,a)].
% 1.11/1.52 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(29,a,108,a)].
% 1.11/1.52 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,109,a)].
% 1.11/1.52 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,110,a)].
% 1.11/1.52 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,111,a)].
% 1.11/1.52 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,112,a)].
% 1.11/1.52 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,115,a)].
% 1.11/1.52 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,116,a)].
% 1.11/1.52 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,117,a)].
% 1.11/1.52 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,118,a)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(29,a,123,a)].
% 1.11/1.52 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -c_in(B,A,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(A,B,tc_nat)),B)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,124,a)].
% 1.11/1.52 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -c_in(B,A,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(A,B,tc_nat))) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,125,a)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 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)) | -c_in(C,A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,128,a)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_in(B,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),C))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(29,a,129,a)].
% 1.11/1.52 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)) | -c_in(C,A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,130,a)].
% 1.11/1.52 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)].
% 1.11/1.52 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)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B))) | -c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(29,a,133,a)].
% 1.11/1.52 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),B)) | -c_in(B,A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,134,a)].
% 1.11/1.52 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A) = B | -c_in(B,A,tc_nat) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(A,B,tc_nat),A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,135,a)].
% 1.11/1.53 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A) = B | -c_in(B,A,tc_nat) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(A,B,tc_nat),A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,136,a)].
% 1.11/1.53 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,137,a)].
% 1.11/1.53 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,138,a)].
% 1.11/1.53 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,139,a)].
% 1.11/1.53 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,140,a)].
% 1.11/1.53 Derived: c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,141,a)].
% 1.11/1.53 Derived: c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(29,a,142,a)].
% 1.11/1.53 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)].
% 1.11/1.53 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)].
% 1.11/1.53 145 -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,c)].
% 1.11/1.53 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)].
% 1.11/1.53 146 -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,3,b)].
% 1.11/1.53 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(146,a,29,a)].
% 1.11/1.53 147 -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,4,c)].
% 1.11/1.53 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(147,a,29,a)].
% 1.11/1.53 148 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B. [resolve(1,b,5,b)].
% 1.11/1.53 149 -class_Orderings_Olinorder(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(A),A). [resolve(1,b,10,b)].
% 1.11/1.53 150 -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,11,c)].
% 1.11/1.53 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(150,a,29,a)].
% 1.11/1.53 151 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),hAPP(hAPP(c_Set_Oinsert(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(1,b,12,c)].
% 1.11/1.53 Derived: hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),hAPP(hAPP(c_Set_Oinsert(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(151,a,29,a)].
% 1.11/1.53 152 -class_Orderings_Olinorder(A) | 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)). [resolve(1,b,13,d)].
% 1.11/1.53 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)). [resolve(152,a,29,a)].
% 1.11/1.53 153 -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)),C)). [resolve(1,b,14,b)].
% 1.11/1.53 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(153,a,29,a)].
% 1.11/1.53 154 -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)),B)). [resolve(1,b,15,b)].
% 1.11/1.53 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(154,a,29,a)].
% 1.11/1.53 155 -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,18,c)].
% 1.11/1.53 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(155,a,29,a)].
% 1.11/1.53 156 -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,19,c)].
% 1.11/1.53 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(156,a,29,a)].
% 1.11/1.53 157 -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,20,c)].
% 1.11/1.53 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(157,a,29,a)].
% 1.11/1.53 158 -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,23,c)].
% 1.11/1.56 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(158,a,29,a)].
% 1.11/1.56 159 -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,24,c)].
% 1.11/1.56 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(159,a,29,a)].
% 1.11/1.56 160 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(A),A,A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B))) | -c_in(D,C,A) | -c_Finite__Set_Ofinite(C,A) | -class_Orderings_Olinorder(A). [resolve(26,d,1,b)].
% 1.11/1.56 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),hAPP(hAPP(c_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A))) | -c_in(C,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(160,d,29,a)].
% 1.11/1.56 161 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)) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) | -class_Orderings_Olinorder(A). [resolve(27,d,1,b)].
% 1.11/1.56 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)) | -c_in(B,A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(161,d,29,a)].
% 1.11/1.56 162 hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(A),A,A,tc_bool),B),C)) | -c_in(C,D,A) | -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(28,f,1,b)].
% 1.11/1.56 Derived: hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),B)) | -c_in(B,C,tc_nat) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat),C))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(162,f,29,a)].
% 1.11/1.56 163 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.11/1.56 164 -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].
% 1.11/1.56 165 -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].
% 1.11/1.56 166 -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].
% 1.11/1.56 167 -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].
% 1.11/1.56 168 -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].
% 1.11/1.56 169 -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].
% 1.11/1.56 170 -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].
% 1.11/1.56 171 -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].
% 1.11/1.56 172 -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].
% 1.11/1.56 173 -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].
% 1.11/1.56 174 -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].
% 1.11/1.56 175 -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].
% 1.11/1.56 176 -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].
% 1.11/1.56 177 -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].
% 1.11/1.56 178 -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].
% 1.11/1.56 179 -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].
% 1.11/1.56 180 -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].
% 1.11/1.56 181 -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].
% 1.11/1.56 182 -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].
% 1.11/1.56 183 -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].
% 1.11/1.56 184 -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].
% 1.11/1.56 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,164,a)].
% 1.11/1.56 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(163,a,166,a)].
% 1.11/1.56 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(163,a,167,a)].
% 1.11/1.56 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(163,a,168,a)].
% 1.11/1.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(163,a,169,a)].
% 1.11/1.56 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(163,a,171,a)].
% 1.11/1.56 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(163,a,173,a)].
% 1.11/1.56 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,174,a)].
% 1.11/1.56 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,175,a)].
% 1.11/1.56 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(163,a,176,a)].
% 1.11/1.56 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(163,a,177,a)].
% 1.11/1.56 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(163,a,178,a)].
% 1.11/1.59 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(163,a,179,a)].
% 1.11/1.59 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(163,a,180,a)].
% 1.11/1.59 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(163,a,181,a)].
% 1.11/1.59 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(163,a,183,a)].
% 1.11/1.59 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(163,a,184,a)].
% 1.11/1.59 185 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.11/1.59 186 -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].
% 1.11/1.59 187 -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].
% 1.11/1.59 188 -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].
% 1.11/1.59 189 -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].
% 1.11/1.59 190 -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].
% 1.11/1.59 191 -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))) | c_in(C,D,A) | -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].
% 1.11/1.59 192 -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)) | -c_in(E,C,D) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 1.11/1.59 193 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,A,C),D),hAPP(hAPP(c_Set_Oinsert(C),E),F)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(A),B,A,C),D),F)) | c_in(E,F,C) | -c_Finite__Set_Ofinite(F,C) # label(cls_comm__monoid__add_Ofold__image__insert_0) # label(axiom). [assumption].
% 1.11/1.59 194 -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)) | c_in(D,E,C) | -c_Finite__Set_Ofinite(E,C) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.11/1.59 195 -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)) | c_in(C,D,A) | -c_in(B,D,A) | -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].
% 1.11/1.59 196 -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_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(A),A,A),B),C) | c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) # label(cls_comm__monoid__add_Ofold1__eq__fold_0) # label(axiom). [assumption].
% 1.11/1.59 197 -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].
% 1.11/1.59 198 -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)) | c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_comm__monoid__add_Ofold1__insert_0) # label(axiom). [assumption].
% 1.11/1.59 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(185,a,187,a)].
% 1.11/1.59 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(185,a,188,a)].
% 1.11/1.59 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))) | c_in(B,C,tc_nat) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(185,a,191,a)].
% 1.11/1.59 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)) | -c_in(D,B,C) | -c_Finite__Set_Ofinite(B,C). [resolve(185,a,192,a)].
% 1.11/1.74 Derived: hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,B),C),hAPP(hAPP(c_Set_Oinsert(B),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,B),C),E)) | c_in(D,E,B) | -c_Finite__Set_Ofinite(E,B). [resolve(185,a,193,a)].
% 1.11/1.74 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)) | c_in(C,D,B) | -c_Finite__Set_Ofinite(D,B). [resolve(185,a,194,a)].
% 1.11/1.74 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)) | c_in(B,C,tc_nat) | -c_in(A,C,tc_nat) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(185,a,195,a)].
% 1.11/1.74 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_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat),A),B) | c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(185,a,196,a)].
% 1.11/1.74 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(185,a,197,a)].
% 1.11/1.74 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)) | c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(185,a,198,a)].
% 1.11/1.74 199 -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].
% 1.11/1.74 200 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].
% 1.11/1.74 201 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].
% 1.11/1.74 202 -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].
% 1.11/1.74 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(202,b,200,b)].
% 1.11/1.74 Derived: -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B. [resolve(202,b,201,b)].
% 1.11/1.74 203 hAPP(c_Finite__Set_Ofold1(A,B),hAPP(hAPP(c_Set_Oinsert(B),C),D)) = hAPP(hAPP(c_Finite__Set_Ofold(A,B,B),C),D) | -c_Finite__Set_Ofinite(D,B) | -c_OrderedGroup_Oab__semigroup__idem__mult(A,B) # label(cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) # label(axiom). [assumption].
% 1.11/1.74 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_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),C) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Oupper__semilattice(A). [resolve(203,c,199,b)].
% 1.11/1.75 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_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),A,A),B),C) | -c_Finite__Set_Ofinite(C,A) | -class_Lattices_Olower__semilattice(A). [resolve(203,c,202,b)].
% 1.11/1.75 204 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].
% 1.11/1.75 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(204,d,199,b)].
% 1.11/1.75 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(204,d,202,b)].
% 1.11/1.75 205 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].
% 1.11/1.75 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(205,f,199,b)].
% 1.11/1.75 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(205,f,202,b)].
% 1.11/1.75 206 -class_Lattices_Oupper__semilattice(A) | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(A),A). [resolve(25,b,10,b)].
% 1.11/1.75 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(206,b,200,b)].
% 1.11/1.75 Derived: -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B. [resolve(206,b,201,b)].
% 1.11/1.75 207 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(29,a,38,a)].
% 1.11/1.80 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_Finite__Set_Ofold(c_Orderings_Oord__class_Omin(tc_nat),tc_nat,tc_nat),A),B) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(207,a,203,c)].
% 1.11/1.80 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(207,a,204,d)].
% 1.11/1.80 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(207,a,205,f)].
% 1.11/1.80 208 c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(29,a,53,a)].
% 1.11/1.80 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_Finite__Set_Ofold(c_Orderings_Oord__class_Omax(tc_nat),tc_nat,tc_nat),A),B) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(208,a,203,c)].
% 1.11/1.80 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(208,a,204,d)].
% 1.11/1.80 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(208,a,205,f)].
% 1.11/1.80 209 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.11/1.80 210 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.11/1.80 211 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.11/1.80 212 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.11/1.80 213 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.57/1.83 214 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.57/1.83 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(209,a,210,a)].
% 1.57/1.83 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(209,a,211,a)].
% 1.57/1.83 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(209,a,212,a)].
% 1.57/1.83 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(209,a,213,a)].
% 1.57/1.83 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(209,a,214,a)].
% 1.57/1.83 215 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.57/1.83 216 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.57/1.83 217 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.57/1.83 218 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.57/1.83 219 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.57/1.83 220 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.57/1.83 221 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.57/1.83 222 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.57/1.85 223 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.57/1.85 224 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 1.57/1.85 225 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 1.57/1.85 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(215,a,216,a)].
% 1.57/1.85 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(215,a,217,a)].
% 1.57/1.85 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(215,a,218,a)].
% 1.57/1.85 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(215,a,219,a)].
% 1.57/1.85 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(215,a,221,a)].
% 1.57/1.85 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(215,a,223,a)].
% 1.57/1.85 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(215,a,224,a)].
% 1.57/1.85 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(215,a,225,a)].
% 1.57/1.85 226 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.57/1.85 227 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.57/1.85 228 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.57/1.85 229 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.57/1.85 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(226,a,229,a)].
% 1.78/2.05 230 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.78/2.05 231 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.78/2.05 232 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.78/2.05 233 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.78/2.05 234 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),D,A,A),E),C,D,A) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.78/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(232,a,233,a)].
% 1.78/2.05 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetsum(A,B,C,tc_nat)),D) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),C),C,tc_nat,tc_nat),D),B,C,tc_nat). [resolve(232,a,234,a)].
% 1.78/2.05 235 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.78/2.05 236 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.78/2.05 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(235,a,236,a)].
% 1.78/2.05 237 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.78/2.05 238 -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].
% 1.78/2.05 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(237,a,238,a)].
% 1.78/2.05 239 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.78/2.05 240 -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].
% 1.78/2.05 241 -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].
% 1.78/2.05 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(239,a,241,a)].
% 1.78/2.05 242 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.78/2.05 243 -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))) | c_in(C,D,A) | -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].
% 1.78/2.05 244 -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].
% 1.78/2.05 245 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,A,C),D),hAPP(hAPP(c_Set_Oinsert(C),E),F)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,E)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(A),B,A,C),D),F)) | c_in(E,F,C) | -c_Finite__Set_Ofinite(F,C) # label(cls_fold__image__insert_0) # label(axiom). [assumption].
% 1.78/2.05 246 -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)) | c_in(C,D,A) | -c_in(B,D,A) | -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].
% 1.78/2.05 247 -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_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),A,A),B),C) | c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) # label(cls_fold1__eq__fold_0) # label(axiom). [assumption].
% 1.78/2.05 248 -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].
% 1.78/2.05 249 -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)) | c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_fold1__insert_0) # label(axiom). [assumption].
% 1.78/2.05 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))) | c_in(B,C,tc_nat) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(242,a,243,a)].
% 1.78/2.05 Derived: hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,B),C),hAPP(hAPP(c_Set_Oinsert(B),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(A,D)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,B),C),E)) | c_in(D,E,B) | -c_Finite__Set_Ofinite(E,B). [resolve(242,a,245,a)].
% 1.78/2.05 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)) | c_in(B,C,tc_nat) | -c_in(A,C,tc_nat) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(242,a,246,a)].
% 1.86/2.16 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_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat),A),B) | c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(242,a,247,a)].
% 1.86/2.16 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(242,a,248,a)].
% 1.86/2.16 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)) | c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(242,a,249,a)].
% 1.86/2.16 250 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.86/2.16 251 -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].
% 1.86/2.16
% 1.86/2.16 ============================== end predicate elimination =============
% 1.86/2.16
% 1.86/2.16 Auto_denials: (non-Horn, no changes).
% 1.86/2.16
% 1.86/2.16 Term ordering decisions:
% 1.86/2.16 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. tc_Com_Ostate=1. c_Com_Obody=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_Option_Ooption_OSome=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_Finite__Set_Ocard=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_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Oord__class_Oless=1. c_HOL_Oplus__class_Oplus=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Oord__class_Omax=1. c_HOL_Otimes__class_Otimes=1. c_Orderings_Oord__class_Omin=1. tc_Option_Ooption=1. c_Option_Ooption_ONone=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_SetInterval_Oord__class_OatLeastAtMost=1. c_Finite__Set_Ofold=1. c_Map_Odom=1. c_Set_Ovimage=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_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Map_Omap__add=1. c_Finite__Set_Osetsum=1. c_Finite__Set_Ofold__image=1. c_Map_Osko__Map__Xmap__le__def__1__1=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------