TSTP Solution File: SWV820-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV820-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:56 EDT 2022
% Result : Unsatisfiable 187.43s 187.76s
% Output : Refutation 187.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV820-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 06:49:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.41/1.68 ============================== Prover9 ===============================
% 1.41/1.68 Prover9 (32) version 2009-11A, November 2009.
% 1.41/1.68 Process 27401 was started by sandbox2 on n011.cluster.edu,
% 1.41/1.68 Thu Jun 16 06:49:52 2022
% 1.41/1.68 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27247_n011.cluster.edu".
% 1.41/1.68 ============================== end of head ===========================
% 1.41/1.68
% 1.41/1.68 ============================== INPUT =================================
% 1.41/1.68
% 1.41/1.68 % Reading from file /tmp/Prover9_27247_n011.cluster.edu
% 1.41/1.68
% 1.41/1.68 set(prolog_style_variables).
% 1.41/1.68 set(auto2).
% 1.41/1.68 % set(auto2) -> set(auto).
% 1.41/1.68 % set(auto) -> set(auto_inference).
% 1.41/1.68 % set(auto) -> set(auto_setup).
% 1.41/1.68 % set(auto_setup) -> set(predicate_elim).
% 1.41/1.68 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.41/1.68 % set(auto) -> set(auto_limits).
% 1.41/1.68 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.41/1.68 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.41/1.68 % set(auto) -> set(auto_denials).
% 1.41/1.68 % set(auto) -> set(auto_process).
% 1.41/1.68 % set(auto2) -> assign(new_constants, 1).
% 1.41/1.68 % set(auto2) -> assign(fold_denial_max, 3).
% 1.41/1.68 % set(auto2) -> assign(max_weight, "200.000").
% 1.41/1.68 % set(auto2) -> assign(max_hours, 1).
% 1.41/1.68 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.41/1.68 % set(auto2) -> assign(max_seconds, 0).
% 1.41/1.68 % set(auto2) -> assign(max_minutes, 5).
% 1.41/1.68 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.41/1.68 % set(auto2) -> set(sort_initial_sos).
% 1.41/1.68 % set(auto2) -> assign(sos_limit, -1).
% 1.41/1.68 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.41/1.68 % set(auto2) -> assign(max_megs, 400).
% 1.41/1.68 % set(auto2) -> assign(stats, some).
% 1.41/1.68 % set(auto2) -> clear(echo_input).
% 1.41/1.68 % set(auto2) -> set(quiet).
% 1.41/1.68 % set(auto2) -> clear(print_initial_clauses).
% 1.41/1.68 % set(auto2) -> clear(print_given).
% 1.41/1.68 assign(lrs_ticks,-1).
% 1.41/1.68 assign(sos_limit,10000).
% 1.41/1.68 assign(order,kbo).
% 1.41/1.68 set(lex_order_vars).
% 1.41/1.68 clear(print_given).
% 1.41/1.68
% 1.41/1.68 % formulas(sos). % not echoed (708 formulas)
% 1.41/1.68
% 1.41/1.68 ============================== end of input ==========================
% 1.41/1.68
% 1.41/1.68 % From the command line: assign(max_seconds, 300).
% 1.41/1.68
% 1.41/1.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.41/1.68
% 1.41/1.68 % Formulas that are not ordinary clauses:
% 1.41/1.68
% 1.41/1.68 ============================== end of process non-clausal formulas ===
% 1.41/1.68
% 1.41/1.68 ============================== PROCESS INITIAL CLAUSES ===============
% 1.41/1.68
% 1.41/1.68 ============================== PREDICATE ELIMINATION =================
% 1.41/1.68 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.41/1.68 2 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMax(B,A)),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 1.41/1.68 3 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Finite__Set_Olinorder__class_OMax(C,A))) | -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 1.41/1.68 4 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_lessequals(B),hAPP(C,D)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),D),E)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) # label(cls_strict__mono__less__eq_1) # label(axiom). [assumption].
% 1.41/1.68 5 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(B),hAPP(E,C)),hAPP(E,D))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(E,A,B)) # label(cls_strict__mono__less__eq_0) # label(axiom). [assumption].
% 1.41/1.68 6 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(B),hAPP(C,D)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),E)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) # label(cls_strict__mono__less_1) # label(axiom). [assumption].
% 1.41/1.68 7 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(B),hAPP(E,C)),hAPP(E,D))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(E,A,B)) # label(cls_strict__mono__less_0) # label(axiom). [assumption].
% 1.41/1.68 8 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hAPP(C,D) != hAPP(C,E) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) | D = E # label(cls_strict__mono__eq_0) # label(axiom). [assumption].
% 1.41/1.68 9 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.41/1.68 10 -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].
% 1.41/1.68 11 -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].
% 1.41/1.68 12 -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].
% 1.41/1.68 13 -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].
% 1.41/1.68 14 -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].
% 1.41/1.68 15 -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].
% 1.41/1.68 16 -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].
% 1.41/1.68 17 -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].
% 1.41/1.68 18 -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].
% 1.41/1.68 19 -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].
% 1.41/1.68 20 -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].
% 1.41/1.68 21 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMin(B,A)),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 1.41/1.68 22 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Olinorder__class_OMin(B,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 1.41/1.68 23 -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].
% 1.41/1.68 24 -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].
% 1.41/1.68 25 -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].
% 1.41/1.68 26 -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].
% 1.41/1.68 Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),c_Finite__Set_Olinorder__class_OMax(A,tc_nat)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,2,a)].
% 1.41/1.68 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Finite__Set_Olinorder__class_OMax(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,3,a)].
% 1.48/1.77 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)). [resolve(1,a,4,a)].
% 1.48/1.77 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(D,B)),hAPP(D,C))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(D,tc_nat,A)). [resolve(1,a,5,a)].
% 1.48/1.77 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)). [resolve(1,a,6,a)].
% 1.48/1.77 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(D,B)),hAPP(D,C))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(D,tc_nat,A)). [resolve(1,a,7,a)].
% 1.48/1.77 Derived: -class_Orderings_Oorder(A) | hAPP(B,C) != hAPP(B,D) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)) | C = D. [resolve(1,a,8,a)].
% 1.48/1.77 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(1,a,9,a)].
% 1.48/1.77 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,10,a)].
% 1.48/1.77 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,13,a)].
% 1.48/1.77 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,17,a)].
% 1.48/1.77 Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),c_Finite__Set_Olinorder__class_OMin(A,tc_nat)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,21,a)].
% 1.48/1.77 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Olinorder__class_OMin(A,tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,22,a)].
% 1.48/1.77 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,23,a)].
% 1.48/1.77 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(1,a,25,a)].
% 1.48/1.77 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,26,a)].
% 1.48/1.77 27 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.48/1.77 28 -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].
% 1.48/1.77 29 -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].
% 1.48/1.77 30 -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].
% 1.48/1.77 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(27,a,28,a)].
% 1.48/1.77 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(27,a,29,a)].
% 1.48/1.81 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(27,a,30,a)].
% 1.48/1.81 31 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.48/1.81 32 -class_OrderedGroup_Ocomm__monoid__mult(A) | -c_Fun_Oinj__on(B,C,D,E) | c_Finite__Set_Osetprod(F,c_Set_Oimage(B,C,D,E),E,A) = c_Finite__Set_Osetprod(c_Fun_Ocomp(F,B,E,A,D),C,D,A) # label(cls_setprod__reindex__cong_0) # label(axiom). [assumption].
% 1.48/1.81 33 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,c_Set_Oimage(C,D,E,F),F,A) = c_Finite__Set_Osetprod(c_Fun_Ocomp(B,C,F,A,E),D,E,A) | -c_Fun_Oinj__on(C,D,E,F) # label(cls_setprod__reindex_0) # label(axiom). [assumption].
% 1.48/1.81 34 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,C,D,A) = c_Finite__Set_Osetprod(c_Fun_Oid(A),c_Set_Oimage(B,C,D,A),A,A) | -c_Fun_Oinj__on(B,C,D,A) # label(cls_setprod__reindex__id_0) # label(axiom). [assumption].
% 1.48/1.81 35 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),D),E,B,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetprod(C,E,B,A)),c_Finite__Set_Osetprod(D,E,B,A)) # label(cls_setprod__timesf_0) # label(axiom). [assumption].
% 1.48/1.81 Derived: -c_Fun_Oinj__on(A,B,C,D) | c_Finite__Set_Osetprod(E,c_Set_Oimage(A,B,C,D),D,tc_nat) = c_Finite__Set_Osetprod(c_Fun_Ocomp(E,A,D,tc_nat,C),B,C,tc_nat). [resolve(31,a,32,a)].
% 1.48/1.81 Derived: c_Finite__Set_Osetprod(A,B,C,tc_nat) = c_Finite__Set_Osetprod(c_Fun_Oid(tc_nat),c_Set_Oimage(A,B,C,tc_nat),tc_nat,tc_nat) | -c_Fun_Oinj__on(A,B,C,tc_nat). [resolve(31,a,34,a)].
% 1.48/1.81 Derived: c_Finite__Set_Osetprod(hAPP(hAPP(c_COMBS(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B)),C),D,A,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetprod(B,D,A,tc_nat)),c_Finite__Set_Osetprod(C,D,A,tc_nat)). [resolve(31,a,35,a)].
% 1.48/1.81 36 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.48/1.81 37 -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].
% 1.48/1.81 38 -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].
% 1.48/1.81 39 -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].
% 1.48/1.81 40 -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].
% 1.48/1.81 41 -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].
% 1.48/1.81 42 -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].
% 1.48/1.81 43 -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].
% 1.48/1.81 44 -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].
% 1.48/1.81 45 -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].
% 1.48/1.81 46 -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].
% 1.48/1.81 47 -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].
% 1.48/1.81 48 -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].
% 1.48/1.81 49 -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].
% 1.48/1.81 50 -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].
% 1.48/1.81 51 -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].
% 1.48/1.81 52 -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].
% 1.48/1.81 53 -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].
% 1.48/1.81 54 -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].
% 1.48/1.81 55 -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].
% 1.48/1.81 56 -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].
% 1.48/1.81 57 -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].
% 1.48/1.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(36,a,37,a)].
% 1.48/1.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(36,a,39,a)].
% 1.48/1.81 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(36,a,41,a)].
% 1.48/1.81 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(36,a,42,a)].
% 1.48/1.81 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(36,a,43,a)].
% 1.48/1.81 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(36,a,44,a)].
% 1.48/1.81 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(36,a,46,a)].
% 1.48/1.81 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(36,a,47,a)].
% 1.48/1.81 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(36,a,48,a)].
% 1.48/1.81 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(36,a,49,a)].
% 1.48/1.81 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(36,a,50,a)].
% 1.48/1.81 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(36,a,51,a)].
% 1.48/1.81 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(36,a,52,a)].
% 1.48/1.81 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(36,a,53,a)].
% 1.54/1.86 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(36,a,54,a)].
% 1.54/1.86 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(36,a,56,a)].
% 1.54/1.86 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(36,a,57,a)].
% 1.54/1.86 58 class_OrderedGroup_Oordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.54/1.86 59 -class_OrderedGroup_Oordered__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Finite__Set_Olinorder__class_OMax(C,A)) = c_Finite__Set_Olinorder__class_OMax(hAPP(c_Collect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_bool,A),c_Ex(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_fun(A,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(A,tc_bool),tc_fun(A,tc_bool)),A),c_COMBS(A,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_fun(tc_bool,tc_bool)),A),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(tc_fun(A,A),tc_fun(A,tc_bool)),A),c_COMBB(A,tc_bool,A)),c_fequal(A))),hAPP(c_HOL_Oplus__class_Oplus(A),B))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),C)))),A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_add__Max__commute_0) # label(axiom). [assumption].
% 1.54/1.86 60 -class_OrderedGroup_Oordered__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Finite__Set_Olinorder__class_OMin(C,A)) = c_Finite__Set_Olinorder__class_OMin(hAPP(c_Collect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_bool,A),c_Ex(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_fun(A,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(A,tc_bool),tc_fun(A,tc_bool)),A),c_COMBS(A,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_fun(tc_bool,tc_bool)),A),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(tc_fun(A,A),tc_fun(A,tc_bool)),A),c_COMBB(A,tc_bool,A)),c_fequal(A))),hAPP(c_HOL_Oplus__class_Oplus(A),B))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),C)))),A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_add__Min__commute_0) # label(axiom). [assumption].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Finite__Set_Olinorder__class_OMax(B,tc_nat)) = c_Finite__Set_Olinorder__class_OMax(hAPP(c_Collect(tc_nat),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_nat),c_Ex(tc_nat)),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_nat),c_COMBS(tc_nat,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_nat),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_and)),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_fun(tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat),c_COMBB(tc_nat,tc_bool,tc_nat)),c_fequal(tc_nat))),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A))))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_bool),tc_bool),c_in(tc_nat)),B)))),tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(58,a,59,a)].
% 1.59/1.87 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Finite__Set_Olinorder__class_OMin(B,tc_nat)) = c_Finite__Set_Olinorder__class_OMin(hAPP(c_Collect(tc_nat),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_nat),c_Ex(tc_nat)),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_nat),c_COMBS(tc_nat,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_nat),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_and)),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_fun(tc_nat,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat),c_COMBB(tc_nat,tc_bool,tc_nat)),c_fequal(tc_nat))),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A))))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_bool),tc_bool),c_in(tc_nat)),B)))),tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(58,a,60,a)].
% 1.59/1.87 61 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.59/1.87 62 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = hAPP(hAPP(c_Finite__Set_Osetsum(E,A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),A,E),hAPP(c_Finite__Set_Osetsum(B,A),C)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),E),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),E),hAPP(c_COMBS(B,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),D)))),hAPP(c_COMBC(B,E,tc_bool),hAPP(hAPP(c_COMBB(E,tc_fun(E,tc_bool),B),c_fequal(E)),F)))))),c_Set_Oimage(F,D,B,E)) | -c_Finite__Set_Ofinite(D,B) # label(cls_setsum__image__gen_0) # label(axiom). [assumption].
% 1.59/1.87 63 -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].
% 1.59/1.87 64 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,A),c_Fun_Oid(A)),c_Set_Oimage(C,D,B,A)) | -c_Fun_Oinj__on(C,D,B,A) # label(cls_setsum__reindex__id_0) # label(axiom). [assumption].
% 1.59/1.87 65 -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].
% 1.59/1.87 66 -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].
% 1.59/1.87 67 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(A),A,A) # label(cls_comm__monoid__add_Ofun__left__comm_0) # label(axiom). [assumption].
% 1.59/1.87 68 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,tc_fun(C,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),c_Finite__Set_Osetsum(C,A)),D)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),B),c_Collect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),B),hAPP(c_COMBS(C,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),C),c_and),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_bool),tc_bool),c_in(C)),E)))),F)))),V6) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBS(C,tc_fun(B,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),c_Finite__Set_Osetsum(B,A)),hAPP(c_COMBC(B,C,A),D))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),C),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),C),hAPP(c_COMBS(B,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),V6)))),hAPP(c_COMBC(B,C,tc_bool),F))))),E) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(V6,B) # label(cls_setsum__setsum__restrict_0) # label(axiom). [assumption].
% 1.59/1.88 69 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),c_Set_Oimage(D,E,F,B)) = hAPP(hAPP(c_Finite__Set_Osetsum(F,A),c_Fun_Ocomp(C,D,B,A,F)),E) | -c_Fun_Oinj__on(D,E,F,B) # label(cls_setsum__reindex_0) # label(axiom). [assumption].
% 1.59/1.88 70 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C)),D)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.59/1.88 71 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),c_Finite__Set_Osetsum(C,A)),D)),E)),F) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBC(C,tc_fun(B,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),c_Finite__Set_Osetsum(B,A)),hAPP(c_COMBC(B,C,A),D))),F)),E) # label(cls_setsum__commute_0) # label(axiom). [assumption].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_nat,D),hAPP(c_Finite__Set_Osetsum(A,tc_nat),B)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),D),c_Collect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),D),hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),C)))),hAPP(c_COMBC(A,D,tc_bool),hAPP(hAPP(c_COMBB(D,tc_fun(D,tc_bool),A),c_fequal(D)),E)))))),c_Set_Oimage(E,C,A,D)) | -c_Finite__Set_Ofinite(C,A). [resolve(61,a,62,a)].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_Fun_Oid(tc_nat)),c_Set_Oimage(B,C,A,tc_nat)) | -c_Fun_Oinj__on(B,C,A,tc_nat). [resolve(61,a,64,a)].
% 1.59/1.88 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat). [resolve(61,a,67,a)].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBS(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),C)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),A),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),A),hAPP(c_COMBS(B,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),D)))),E)))),F) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBS(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),hAPP(c_COMBC(A,B,tc_nat),C))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),B),c_Collect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),B),hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),F)))),hAPP(c_COMBC(A,B,tc_bool),E))))),D) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(F,A). [resolve(61,a,68,a)].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),c_Set_Oimage(C,D,E,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(E,tc_nat),c_Fun_Ocomp(B,C,A,tc_nat,E)),D) | -c_Fun_Oinj__on(C,D,E,A). [resolve(61,a,69,a)].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBS(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Oplus__class_Oplus(tc_nat)),B)),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),C),D)). [resolve(61,a,70,a)].
% 1.59/1.88 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),hAPP(c_COMBC(A,B,tc_nat),C))),E)),D). [resolve(61,a,71,a)].
% 1.71/2.01 72 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.71/2.01 73 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 1.71/2.01 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(72,a,73,a)].
% 1.71/2.01 74 class_Orderings_Owellorder(tc_nat) # label(clsarity_nat__Orderings_Owellorder) # label(axiom). [assumption].
% 1.71/2.01 75 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_Orderings_Oord__class_OLeast(B,A))) # label(cls_not__less__Least_0) # label(axiom). [assumption].
% 1.71/2.01 76 -class_Orderings_Owellorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Orderings_Oord__class_OLeast(B,A)),C)) | -hBOOL(hAPP(B,C)) # label(cls_Least__le_0) # label(axiom). [assumption].
% 1.71/2.01 77 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI__ex_0) # label(axiom). [assumption].
% 1.71/2.01 78 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI_0) # label(axiom). [assumption].
% 1.71/2.01 Derived: -hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_Orderings_Oord__class_OLeast(A,tc_nat))). [resolve(74,a,75,a)].
% 1.71/2.01 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(A,tc_nat)),B)) | -hBOOL(hAPP(A,B)). [resolve(74,a,76,a)].
% 1.71/2.01 Derived: hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(A,tc_nat))) | -hBOOL(hAPP(A,B)). [resolve(74,a,77,a)].
% 1.71/2.01 79 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.71/2.01 80 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(A),A,A) # label(cls_fun__left__comm_0) # label(axiom). [assumption].
% 1.71/2.01 81 -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].
% 1.71/2.01 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat). [resolve(79,a,80,a)].
% 1.71/2.01 82 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.71/2.01 83 -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].
% 1.71/2.01 84 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.71/2.01 85 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBB(A,A,C),hAPP(c_HOL_Otimes__class_Otimes(A),B)),D)),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.71/2.01 86 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),E)),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.71/2.01 87 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),hAPP(hAPP(c_Finite__Set_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,A),c_Fun_Oid(A)),hAPP(c_Collect(A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_bool,A),c_Ex(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_bool),A),hAPP(c_COMBB(tc_fun(E,tc_bool),tc_bool,B),c_Ex(E))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool))),tc_fun(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_bool))),A),c_COMBS(B,tc_fun(E,tc_bool),tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_fun(tc_bool,tc_bool))),tc_fun(B,tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool))),A),hAPP(c_COMBB(tc_fun(E,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool)),B),c_COMBS(E,tc_bool,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_fun(tc_bool,tc_bool))),A),hAPP(c_COMBB(tc_fun(E,tc_bool),tc_fun(E,tc_fun(tc_bool,tc_bool)),B),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),E),c_and))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(E,A)),tc_fun(B,tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(E,A),tc_fun(E,tc_bool)),tc_fun(tc_fun(B,tc_fun(E,A)),tc_fun(B,tc_fun(E,tc_bool))),A),c_COMBB(tc_fun(E,A),tc_fun(E,tc_bool),B)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(tc_fun(E,A),tc_fun(E,tc_bool)),A),c_COMBB(A,tc_bool,E)),c_fequal(A)))),hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F)))))),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_bool),tc_fun(E,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool)),B),c_COMBB(tc_bool,tc_bool,E)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),D)))),hAPP(hAPP(c_COMBC(E,tc_fun(E,tc_bool),tc_bool),c_in(E)),V6))))))) | -c_Fun_Oinj__on(c_split(hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F),B,E,A),c_Product__Type_OSigma(D,hAPP(c_COMBK(tc_fun(E,tc_bool),B),V6),B,E),tc_prod(B,E),A) # label(cls_setsum__mult__setsum__if__inj_0) # label(axiom). [assumption].
% 1.71/2.01 88 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),hAPP(hAPP(c_Finite__Set_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(E,A),tc_fun(tc_fun(E,tc_bool),A),B),c_Finite__Set_Osetsum(E,A)),hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F))),V6)),D) # label(cls_setsum__product_0) # label(axiom). [assumption].
% 1.71/2.01 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,B),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A)),C)),D). [resolve(84,a,85,a)].
% 1.71/2.01 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B)),D)),C). [resolve(84,a,86,a)].
% 1.71/2.01 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_Fun_Oid(tc_nat)),hAPP(c_Collect(tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_bool,tc_nat),c_Ex(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_bool),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_bool),tc_bool,A),c_Ex(D))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool))),tc_fun(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_bool))),tc_nat),c_COMBS(A,tc_fun(D,tc_bool),tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_fun(tc_bool,tc_bool))),tc_fun(A,tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool))),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool)),A),c_COMBS(D,tc_bool,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_fun(tc_bool,tc_bool))),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_bool),tc_fun(D,tc_fun(tc_bool,tc_bool)),A),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),D),c_and))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(A,tc_fun(D,tc_nat)),tc_fun(A,tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_bool)),tc_fun(tc_fun(A,tc_fun(D,tc_nat)),tc_fun(A,tc_fun(D,tc_bool))),tc_nat),c_COMBB(tc_fun(D,tc_nat),tc_fun(D,tc_bool),A)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_bool)),tc_nat),c_COMBB(tc_nat,tc_bool,D)),c_fequal(tc_nat)))),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E)))))),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_fun(D,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool)),A),c_COMBB(tc_bool,tc_bool,D)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),C)))),hAPP(hAPP(c_COMBC(D,tc_fun(D,tc_bool),tc_bool),c_in(D)),F))))))) | -c_Fun_Oinj__on(c_split(hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E),A,D,tc_nat),c_Product__Type_OSigma(C,hAPP(c_COMBK(tc_fun(D,tc_bool),A),F),A,D),tc_prod(A,D),tc_nat). [resolve(84,a,87,a)].
% 1.71/2.03 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(D,tc_nat),tc_fun(tc_fun(D,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(D,tc_nat)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E))),F)),C). [resolve(84,a,88,a)].
% 1.71/2.03 89 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.71/2.03 90 -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].
% 1.71/2.03 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(89,a,90,a)].
% 1.71/2.03 91 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.71/2.03 92 -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].
% 1.78/2.06 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(91,a,92,a)].
% 1.78/2.06 93 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.78/2.06 94 -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].
% 1.78/2.06 95 -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].
% 1.78/2.06 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(93,a,95,a)].
% 1.78/2.06 96 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.78/2.06 97 -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].
% 1.78/2.06 98 -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].
% 1.78/2.06 99 -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].
% 1.78/2.06 100 -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].
% 1.78/2.06 101 -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].
% 1.78/2.06 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(96,a,97,a)].
% 1.78/2.06 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(96,a,98,a)].
% 1.78/2.06 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(96,a,99,a)].
% 1.78/2.06 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(96,a,100,a)].
% 1.78/2.06 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(96,a,101,a)].
% 1.78/2.11 102 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.78/2.11 103 -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].
% 1.78/2.11 104 -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].
% 1.78/2.11 105 -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].
% 1.78/2.11 106 -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].
% 1.78/2.11 107 -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].
% 1.78/2.11 108 -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].
% 1.78/2.11 109 -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].
% 1.78/2.11 110 -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].
% 1.78/2.11 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(102,a,104,a)].
% 1.78/2.11 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(102,a,106,a)].
% 1.78/2.11 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(102,a,108,a)].
% 1.78/2.11 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(102,a,110,a)].
% 1.78/2.11 111 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.78/2.11 112 -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].
% 3.22/3.55
% 3.22/3.55 ============================== end predicate elimination =============
% 3.22/3.55
% 3.22/3.55 Auto_denials: (non-Horn, no changes).
% 3.22/3.55
% 3.22/3.55 Term ordering decisions:
% 3.22/3.55 Function symbol KB weights: tc_bool=1. t_a=1. tc_Com_Ostate=1. tc_nat=1. tc_Com_Ocom=1. t_b=1. c_Natural_Oevaln=1. c_and=1. c_implies=1. v_x=1. v_P=1. v_r=1. v_Q=1. v_A=1. v_f=1. v_R=1. v_n=1. c_or=1. v_c=1. c_Com_Ocom_OSKIP=1. c_HOL_Oinduct__conj=1. v_B=1. v_upd=1. c_Not=1. t_c=1. v_acc=1. v_xa=1. v_xb=1. hAPP=1. tc_fun=1. tc_prod=1. c_Pair=1. c_Finite__Set_Osetsum=1. c_Com_Ocom_OWhile=1. c_COMBK=1. c_Hilbert__Choice_OEps=1. c_Finite__Set_Olattice__class_OInf__fin=1. c_Finite__Set_Olattice__class_OSup__fin=1. c_HOL_Oinduct__forall=1. c_Com_Ocom_OSemi=1. c_Recdef_Ocut=1. c_The=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Hoare__Mirabelle_Otriple__valid=1. c_Orderings_Oord__class_OLeast=1. c_Relation_Oantisym=1. c_Relation_Osym=1. c_Relation_Otrans=1. c_lessequals=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Oplus__class_Oplus=1. c_Orderings_Obot__class_Obot=1. c_HOL_Oord__class_Oless=1. c_HOL_Otimes__class_Otimes=1. c_Collect=1. c_All=1. c_fequal=1. c_HOL_Ouminus__class_Ouminus=1. c_Ex=1. c_Fun_Oid=1. c_Suc=1. c_COMBI=1. c_FunDef_OTHE__default=1. c_HOL_Ominus__class_Ominus=1. c_COMBB=1. c_COMBC=1. c_COMBS=1. c_Com_Ocom_OCond=1. c_Fun_Ofcomp=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_Orderings_Oorder__class_Ostrict__mono=1. c_Finite__Set_Olattice_OInf__fin=1. c_Finite__Set_Olattice_OSup__fin=1. c_Orderings_Oorder__class_Omono=1. c_List_Ofilter=1. c_List_Olistsp=1. c_Orderings_Oorder_Omono=1. c_Orderings_Oorder_Ostrict__mono=1. c_Relation_Ototal__on=1. c_Predicate_OPowp=1. c_Orderings_Oord_OLeast=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Finite__Set_Osetprod=1. c_Product__Type_OSigma=1. c_Record_Oiso__tuple__update__accessor__cong__assist=1. c_split=1. c_List_Omap=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1=1. c_Hilbert__Choice_OGreatestM=1. c_Hilbert__Choice_OLeastM=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_Fun_Ocomp=1. c_List_Ofoldl=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1=1. c_Recdef_Owfrec=1. c_Recdef_Owfrec__rel=1. c_Product__Type_Oscomp=1. c_Natural_Osko__Natural__Xevaln__max2__1__1=1.
% 3.22/3.55
% 3.22/3.55 ============================== end of process initial clauses ========
% 3.22/3.55
% 3.22/3.55 ============================== CLAUSES FOR SEARCH ====================
% 3.22/3.55
% 3.22/3.55 ============================== end of clauses for search =============
% 3.22/3.55
% 3.22/3.55 ============================== SEARCH ================================
% 3.22/3.55
% 3.22/3.55 % Starting search at 0.68 seconds.
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=96.000, iters=3412
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=91.000, iters=3342
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=85.000, iters=3414
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=83.000, iters=3373
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=77.000, iters=3335
% 3.22/3.55
% 3.22/3.55 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 50 (0.00 of 1.67 sec).
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=67.000, iters=3360
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=66.000, iters=3454
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=63.000, iters=3582
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=59.000, iters=3427
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=58.000, iters=3373
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=56.000, iters=3368
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=51.000, iters=3385
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=50.000, iters=3361
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=48.000, iters=3390
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=45.000, iters=3333
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=44.000, iters=3363
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=43.000, iters=3461
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=42.000, iters=3366
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=41.000, iters=3433
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=39.000, iters=3384
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=38.000, iters=3336
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=37.000, iters=3443
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=36.000, iters=3339
% 3.22/3.55
% 3.22/3.55 Low Water (keep): wt=35.000, iters=3431
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=34.000, iters=3510
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=33.000, iters=3472
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=32.000, iters=3362
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=31.000, iters=3389
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=30.000, iters=3335
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=29.000, iters=3359
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=26.000, iters=3683
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=25.000, iters=3511
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=21.000, iters=3647
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=20.000, iters=3458
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=19.000, iters=3358
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=18.000, iters=3366
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=17.000, iters=3472
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=16.000, iters=3357
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=15.000, iters=3334
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=14.000, iters=3342
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4457, wt=199.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3865, wt=196.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4410, wt=189.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4108, wt=187.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3866, wt=186.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3874, wt=184.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4411, wt=183.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4337, wt=174.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3044, wt=172.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4459, wt=171.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3867, wt=168.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4343, wt=166.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3887, wt=165.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4103, wt=164.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4351, wt=161.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3868, wt=160.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4111, wt=159.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4354, wt=158.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3888, wt=157.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4352, wt=156.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4356, wt=153.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4116, wt=150.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4349, wt=148.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4342, wt=147.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3806, wt=145.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4326, wt=143.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=2567, wt=141.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4327, wt=140.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4346, wt=138.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4106, wt=137.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3807, wt=135.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3885, wt=134.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4489, wt=132.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3825, wt=130.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4076, wt=129.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4341, wt=128.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3808, wt=127.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4035, wt=126.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4335, wt=125.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4143, wt=124.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=2375, wt=123.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3818, wt=122.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4453, wt=121.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=1533, wt=120.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4338, wt=119.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4072, wt=118.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4118, wt=117.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4095, wt=116.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4067, wt=115.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=2378, wt=114.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4454, wt=113.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4488, wt=112.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4099, wt=111.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=1883, wt=110.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4484, wt=109.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4140, wt=108.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4120, wt=107.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4479, wt=106.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4177, wt=105.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4030, wt=104.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4091, wt=103.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3826, wt=102.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4436, wt=101.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4110, wt=100.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4485, wt=99.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4070, wt=98.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4406, wt=97.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4481, wt=96.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4456, wt=95.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4323, wt=94.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4499, wt=93.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4458, wt=92.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4426, wt=91.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3854, wt=90.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4508, wt=89.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4482, wt=88.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=4147, wt=87.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6209, wt=78.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=12224, wt=77.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=3853, wt=71.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=6223, wt=68.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=4906, wt=65.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=6169, wt=61.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12203, wt=60.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=6205, wt=55.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=4896, wt=54.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12554, wt=46.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12662, wt=45.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12485, wt=44.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12621, wt=43.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=12647, wt=42.000
% 187.43/187.76
% 187.43/187.76 Low Water (displace): id=13000, wt=12.000
% 187.43/187.76
% 187.43/187.76 ============================== PROOF =================================
% 187.43/187.76 % SZS status Unsatisfiable
% 187.43/187.76 % SZS output start Refutation
% 187.43/187.76
% 187.43/187.76 % Proof 1 at 181.66 (+ 4.56) seconds.
% 187.43/187.76 % Length of proof is 188.
% 187.43/187.76 % Level of proof is 24.
% 187.43/187.76 % Maximum clause weight is 32.000.
% 187.43/187.76 % Given clauses 23700.
% 187.43/187.76
% 187.43/187.76 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 187.43/187.76 10 -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].
% 187.43/187.76 13 -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].
% 187.43/187.76 74 class_Orderings_Owellorder(tc_nat) # label(clsarity_nat__Orderings_Owellorder) # label(axiom). [assumption].
% 187.43/187.76 76 -class_Orderings_Owellorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Orderings_Oord__class_OLeast(B,A)),C)) | -hBOOL(hAPP(B,C)) # label(cls_Least__le_0) # label(axiom). [assumption].
% 187.43/187.76 77 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI__ex_0) # label(axiom). [assumption].
% 187.43/187.76 121 -class_Lattices_Oboolean__algebra(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_Orderings_Obot__class_Obot(A) # label(cls_compl__inf__bot_0) # label(axiom). [assumption].
% 187.43/187.76 122 -class_Lattices_Oboolean__algebra(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = c_Orderings_Obot__class_Obot(A) # label(cls_inf__compl__bot_0) # label(axiom). [assumption].
% 187.43/187.76 124 hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C))) | hBOOL(hAPP(hAPP(c_in(A),B),C)) # label(cls_ComplI_0) # label(axiom). [assumption].
% 187.43/187.76 125 -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C))) # label(cls_ComplD_0) # label(axiom). [assumption].
% 187.43/187.76 126 -class_Orderings_Obot(A) | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,A)),v_x) = c_Orderings_Obot__class_Obot(A) # label(cls_bot__fun__eq_0) # label(axiom). [assumption].
% 187.43/187.76 148 hAPP(c_Collect(A),B) = B # label(cls_Collect__def_0) # label(axiom). [assumption].
% 187.43/187.76 186 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),D)) | -hBOOL(hAPP(C,D)) # label(cls_sup1CI_0) # label(axiom). [assumption].
% 187.43/187.76 187 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),D)) | -hBOOL(hAPP(B,D)) # label(cls_sup1CI_1) # label(axiom). [assumption].
% 187.43/187.76 204 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom). [assumption].
% 187.43/187.76 221 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_in(C),B),A)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 187.43/187.76 222 hAPP(c_COMBI(A),B) = B # label(cls_COMBI__def_0) # label(axiom). [assumption].
% 187.43/187.76 223 hAPP(hAPP(c_COMBK(A,B),C),D) = C # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 187.43/187.76 233 -class_Lattices_Oboolean__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__eq_0) # label(axiom). [assumption].
% 187.43/187.76 234 -class_Lattices_Oboolean__algebra(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C). [copy(233),flip(b)].
% 187.43/187.76 241 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 187.43/187.76 242 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 187.43/187.76 246 -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),c_Finite__Set_Olattice__class_OSup__fin(C,A)) = B | -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_inf__Sup__absorb_0) # label(axiom). [assumption].
% 187.43/187.76 247 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 187.43/187.76 248 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 187.43/187.76 249 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 187.43/187.76 251 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 187.43/187.76 255 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 187.43/187.76 274 -hBOOL(hAPP(A,B)) | hBOOL(hAPP(A,c_Hilbert__Choice_OEps(A,C))) # label(cls_exE__some_0) # label(axiom). [assumption].
% 187.43/187.76 286 -class_Lattices_Oboolean__algebra(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_compl__eq__compl__iff_0) # label(axiom). [assumption].
% 187.43/187.76 291 A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) # label(cls_le__antisym_0) # label(axiom). [assumption].
% 187.43/187.76 294 -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = B # label(cls_inf__sup__absorb_0) # label(axiom). [assumption].
% 187.43/187.76 296 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 187.43/187.76 299 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 187.43/187.76 301 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 187.43/187.76 332 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Suc(B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) # label(cls_le__SucI_0) # label(axiom). [assumption].
% 187.43/187.76 333 -class_HOL_Ouminus(A) | hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,A)),B),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(B,v_x)) # label(cls_fun__Compl__def_0) # label(axiom). [assumption].
% 187.43/187.76 339 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(A)),A)) # label(cls_Suc__n__not__le__n_0) # label(axiom). [assumption].
% 187.43/187.76 375 hAPP(c_Collect(A),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,A),c_Not),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),hAPP(c_Collect(A),B)) # label(cls_Collect__neg__eq_0) # label(axiom). [assumption].
% 187.43/187.76 376 hAPP(hAPP(c_COMBB(tc_bool,tc_bool,A),c_Not),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B). [copy(375),rewrite([148(8),148(11)])].
% 187.43/187.76 380 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 187.43/187.76 400 -class_Finite__Set_Ofinite_Ofinite(A) | c_Finite__Set_Ofinite(B,A) # label(cls_finite_0) # label(axiom). [assumption].
% 187.43/187.76 409 hAPP(c_Fun_Oid(A),B) = B # label(cls_id__apply_0) # label(axiom). [assumption].
% 187.43/187.76 414 -class_Lattices_Oboolean__algebra(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_double__compl_0) # label(axiom). [assumption].
% 187.43/187.76 427 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B)),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 187.43/187.76 428 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 187.43/187.76 449 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),A)) # label(cls_le__refl_0) # label(axiom). [assumption].
% 187.43/187.76 477 hAPP(c_Collect(A),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B)) = B # label(cls_Collect__mem__eq_0) # label(axiom). [assumption].
% 187.43/187.76 478 hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B) = B. [copy(477),rewrite([148(9)])].
% 187.43/187.76 522 hAPP(c_Collect(A),hAPP(hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_or),B)),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),hAPP(c_Collect(A),B)),hAPP(c_Collect(A),C)) # label(cls_Collect__disj__eq_0) # label(axiom). [assumption].
% 187.43/187.76 523 hAPP(hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_or),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C). [copy(522),rewrite([148(15),148(18),148(19)])].
% 187.43/187.76 538 hAPP(c_Collect(A),hAPP(hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_implies),B)),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),hAPP(c_Collect(A),B))),hAPP(c_Collect(A),C)) # label(cls_Collect__imp__eq_0) # label(axiom). [assumption].
% 187.43/187.76 539 hAPP(hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_implies),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B)),C). [copy(538),rewrite([148(15),148(21),148(23)])].
% 187.43/187.76 548 c_lessequals(tc_bool) = c_implies # label(cls_le__bool__def__raw_0) # label(axiom). [assumption].
% 187.43/187.76 549 c_implies = c_lessequals(tc_bool). [copy(548),flip(a)].
% 187.43/187.76 608 hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 187.43/187.76 609 hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F) = hAPP(hAPP(D,F),E) # label(cls_COMBC__def_0) # label(axiom). [assumption].
% 187.43/187.76 610 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 187.43/187.76 634 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 187.43/187.76 635 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 187.43/187.76 638 class_Lattices_Olattice(tc_nat) # label(clsarity_nat__Lattices_Olattice) # label(axiom). [assumption].
% 187.43/187.76 643 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 187.43/187.76 644 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 187.43/187.76 647 class_Lattices_Oboolean__algebra(tc_bool) # label(clsarity_bool__Lattices_Oboolean__algebra) # label(axiom). [assumption].
% 187.43/187.76 648 class_Finite__Set_Ofinite_Ofinite(tc_bool) # label(clsarity_bool__Finite__Set_Ofinite_Ofinite) # label(axiom). [assumption].
% 187.43/187.76 650 class_Lattices_Olattice(tc_bool) # label(clsarity_bool__Lattices_Olattice) # label(axiom). [assumption].
% 187.43/187.76 652 class_Orderings_Obot(tc_bool) # label(clsarity_bool__Orderings_Obot) # label(axiom). [assumption].
% 187.43/187.76 653 class_HOL_Ouminus(tc_bool) # label(clsarity_bool__HOL_Ouminus) # label(axiom). [assumption].
% 187.43/187.76 657 hBOOL(hAPP(hAPP(c_fequal(A),B),B)) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 187.43/187.76 668 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,10,a)].
% 187.43/187.76 669 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,13,a)].
% 187.43/187.76 724 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(A,tc_nat)),B)) | -hBOOL(hAPP(A,B)). [resolve(74,a,76,a)].
% 187.43/187.76 725 hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(A,tc_nat))) | -hBOOL(hAPP(A,B)). [resolve(74,a,77,a)].
% 187.43/187.76 775 hAPP(hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_lessequals(tc_bool)),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B)),C). [back_rewrite(539),rewrite([549(9)])].
% 187.43/187.76 813 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),c_Collect(C)),D)) | -hBOOL(D). [para(148(a,1),186(b,1))].
% 187.43/187.76 836 hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),C)) | hBOOL(hAPP(hAPP(c_in(A),C),B)). [resolve(221,b,124,a)].
% 187.43/187.76 839 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_COMBI(B)),C),D)) | -hBOOL(D). [para(222(a,1),187(b,1))].
% 187.43/187.76 908 -hBOOL(A) | hBOOL(c_Hilbert__Choice_OEps(c_Collect(B),C)). [para(148(a,1),274(a,1)),rewrite([148(5)])].
% 187.43/187.76 913 -hBOOL(A) | hBOOL(c_Hilbert__Choice_OEps(c_COMBI(B),C)). [para(222(a,1),274(a,1)),rewrite([222(5)])].
% 187.43/187.76 1100 -hBOOL(A) | hBOOL(c_Hilbert__Choice_OEps(c_Fun_Oid(B),C)). [para(409(a,1),274(a,1)),rewrite([409(5)])].
% 187.43/187.76 1238 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Suc(A))). [resolve(449,a,332,b)].
% 187.43/187.76 2390 hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),C) = hAPP(c_Not,hAPP(B,C)). [para(376(a,1),608(a,1,1))].
% 187.43/187.76 2420 hBOOL(hAPP(c_Not,hAPP(A,B))) | hBOOL(hAPP(hAPP(c_in(C),B),A)). [back_rewrite(836),rewrite([2390(5)])].
% 187.43/187.76 2442 hAPP(hAPP(c_in(A),B),C) = hAPP(C,B). [para(478(a,1),609(a,1,1)),flip(a)].
% 187.43/187.76 2464 hBOOL(hAPP(c_Not,hAPP(A,B))) | hBOOL(hAPP(A,B)). [back_rewrite(2420),rewrite([2442(7)])].
% 187.43/187.76 2656 -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),c_Finite__Set_Olattice__class_OSup__fin(C,A)) = B | -hBOOL(hAPP(C,B)) | -c_Finite__Set_Ofinite(C,A). [back_rewrite(246),rewrite([2442(9)])].
% 187.43/187.76 2664 -hBOOL(hAPP(A,B)) | -hBOOL(hAPP(c_Not,hAPP(A,B))). [back_rewrite(125),rewrite([2442(3),2442(9),2390(7)])].
% 187.43/187.76 2836 hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),D) = hAPP(hAPP(c_or,hAPP(B,D)),hAPP(C,D)). [para(523(a,1),610(a,1,1)),rewrite([608(15)])].
% 187.43/187.76 3070 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A). [resolve(634,a,380,a)].
% 187.43/187.76 3073 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(634,a,301,a)].
% 187.43/187.76 3075 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(634,a,299,a)].
% 187.43/187.76 3077 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B))). [resolve(634,a,251,a)].
% 187.43/187.76 3079 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)). [resolve(634,a,242,a)].
% 187.43/187.76 3080 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)). [resolve(634,a,241,a)].
% 187.43/187.76 3095 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(635,a,296,a)].
% 187.43/187.76 3097 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),A). [resolve(635,a,255,a)].
% 187.43/187.76 3098 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(635,a,249,a)].
% 187.43/187.76 3099 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(635,a,248,a)].
% 187.43/187.76 3117 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = A. [resolve(638,a,294,a)].
% 187.43/187.76 3137 hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)),B)). [resolve(643,a,428,a)].
% 187.43/187.76 3138 hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A)),B)). [resolve(643,a,427,a)].
% 187.43/187.76 3169 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A). [resolve(644,a,255,a)].
% 187.43/187.76 3172 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(644,a,247,a)].
% 187.43/187.76 3189 hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),A)) = A. [resolve(647,a,414,a)].
% 187.43/187.76 3192 hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),B) | A = B. [resolve(647,a,286,a)].
% 187.43/187.76 3193 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),A),B). [resolve(647,a,234,a)].
% 187.43/187.76 3194 hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),A),A) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(647,a,122,a),rewrite([3193(7)])].
% 187.43/187.76 3195 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),A)),A) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(647,a,121,a)].
% 187.43/187.76 3201 c_Finite__Set_Ofinite(A,tc_bool). [resolve(648,a,400,a)].
% 187.43/187.76 3232 hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(652,a,126,a)].
% 187.43/187.76 3254 hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(A,v_x)) = hAPP(c_Not,hAPP(A,v_x)). [resolve(653,a,333,a),rewrite([2390(7)]),flip(a)].
% 187.43/187.76 3318 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(A))). [resolve(668,b,339,a)].
% 187.43/187.76 3909 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(c_Collect(A),tc_nat)),B)) | -hBOOL(B). [para(148(a,1),724(b,1))].
% 187.43/187.76 3927 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat)),B)) | -hBOOL(B). [para(409(a,1),724(b,1))].
% 187.43/187.76 3964 hBOOL(c_Orderings_Oord__class_OLeast(c_Collect(A),tc_nat)) | -hBOOL(B). [para(148(a,1),725(b,1)),rewrite([148(5)])].
% 187.43/187.76 3969 hBOOL(c_Orderings_Oord__class_OLeast(c_COMBI(A),tc_nat)) | -hBOOL(B). [para(222(a,1),725(b,1)),rewrite([222(5)])].
% 187.43/187.76 3979 hBOOL(c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat)) | -hBOOL(B). [para(409(a,1),725(b,1)),rewrite([409(5)])].
% 187.43/187.76 4490 hAPP(hAPP(c_lessequals(tc_bool),hAPP(A,B)),hAPP(C,B)) = hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool)),A)),C),B). [para(775(a,1),610(a,1,1)),rewrite([608(20)]),flip(a)].
% 187.43/187.76 4889 -hBOOL(A) | -hBOOL(hAPP(c_Not,A)). [para(148(a,1),2664(b,1,2)),rewrite([148(2)])].
% 187.43/187.76 6091 hBOOL(c_Hilbert__Choice_OEps(c_Collect(A),B)). [resolve(908,a,657,a)].
% 187.43/187.76 6239 hBOOL(c_Hilbert__Choice_OEps(c_COMBI(A),B)). [resolve(913,a,6091,a)].
% 187.43/187.76 6250 hBOOL(c_Hilbert__Choice_OEps(c_Fun_Oid(A),B)). [resolve(1100,a,6239,a)].
% 187.43/187.76 6370 hBOOL(c_Orderings_Oord__class_OLeast(c_Collect(A),tc_nat)). [resolve(3964,b,6250,a)].
% 187.43/187.76 6400 hBOOL(c_Orderings_Oord__class_OLeast(c_COMBI(A),tc_nat)). [resolve(3969,b,6370,a)].
% 187.43/187.76 6413 hBOOL(c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat)). [resolve(3979,b,6400,a)].
% 187.43/187.76 6425 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),c_Collect(C)),c_Orderings_Oord__class_OLeast(c_Fun_Oid(D),tc_nat))). [resolve(6413,a,813,b)].
% 187.43/187.76 6426 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_COMBI(B)),C),c_Orderings_Oord__class_OLeast(c_Fun_Oid(D),tc_nat))). [resolve(839,b,6413,a)].
% 187.43/187.76 6545 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Suc(c_Suc(A)))). [resolve(1238,a,332,b)].
% 187.43/187.76 8253 -hBOOL(c_Orderings_Obot__class_Obot(tc_bool)). [para(3232(a,1),204(a,1))].
% 187.43/187.76 8394 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Suc(c_Suc(c_Suc(A))))). [resolve(6545,a,332,b)].
% 187.43/187.76 8885 hBOOL(hAPP(c_Not,A)) | hBOOL(A). [para(148(a,1),2464(a,1,2)),rewrite([148(5)])].
% 187.43/187.76 8895 hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))). [para(3194(a,1),2464(a,1,2)),rewrite([3194(9)]),unit_del(b,8253)].
% 187.43/187.76 8949 hBOOL(A) | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),c_Not),A)). [resolve(8885,a,186,b)].
% 187.43/187.76 17678 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)))). [resolve(3077,a,332,b)].
% 187.43/187.76 18058 hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),A) != B | hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),B) = A. [para(3189(a,1),3192(a,1)),flip(a)].
% 187.43/187.76 18076 hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),A) = hAPP(c_Not,A). [para(223(a,1),3254(a,1,2)),rewrite([223(8)])].
% 187.43/187.76 18087 hAPP(c_Not,A) != B | hAPP(c_Not,B) = A. [back_rewrite(18058),rewrite([18076(3),18076(6)])].
% 187.43/187.76 18172 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_Not,A)),A) = c_Orderings_Obot__class_Obot(tc_bool). [back_rewrite(3195),rewrite([18076(5)])].
% 187.43/187.76 18173 hAPP(c_Not,A) != hAPP(c_Not,B) | A = B. [back_rewrite(3192),rewrite([18076(3),18076(5)])].
% 187.43/187.76 18174 hAPP(c_Not,hAPP(c_Not,A)) = A. [back_rewrite(3189),rewrite([18076(5),18076(5)])].
% 187.43/187.76 18223 A != B | hAPP(c_Not,B) = hAPP(c_Not,A). [para(18174(a,1),18087(a,1))].
% 187.43/187.76 18225 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(c_Not,A)) = c_Orderings_Obot__class_Obot(tc_bool). [para(18174(a,1),18172(a,1,1,2))].
% 187.43/187.76 18451 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(c_Collect(A),tc_nat)),c_Orderings_Oord__class_OLeast(c_Fun_Oid(B),tc_nat))). [resolve(3909,b,6413,a)].
% 187.43/187.76 18467 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat)),c_Orderings_Oord__class_OLeast(c_Collect(B),tc_nat))). [resolve(3927,b,6370,a)].
% 187.43/187.76 36911 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),A) = A. [para(3117(a,1),3097(a,1)),flip(a)].
% 187.43/187.76 42351 c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat) = c_Orderings_Oord__class_OLeast(c_Collect(B),tc_nat). [resolve(18451,a,291,c),flip(a),unit_del(b,18467)].
% 187.43/187.76 42352 c_Orderings_Oord__class_OLeast(c_Fun_Oid(A),tc_nat) = c_0. [new_symbol(42351)].
% 187.43/187.76 42478 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_COMBI(B)),C),c_0)). [back_rewrite(6426),rewrite([42352(9)])].
% 187.43/187.76 42479 hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),c_Collect(C)),c_0)). [back_rewrite(6425),rewrite([42352(9)])].
% 187.43/187.76 94047 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),c_Finite__Set_Olattice__class_OSup__fin(B,tc_bool)) = A | -hBOOL(hAPP(B,A)). [resolve(2656,d,3201,a),unit_del(a,650)].
% 187.43/187.76 96605 hBOOL(hAPP(hAPP(c_or,c_0),hAPP(A,c_0))). [para(2836(a,1),42478(a,1)),rewrite([222(4)])].
% 187.43/187.76 96786 hBOOL(hAPP(hAPP(c_or,c_0),A)). [para(223(a,1),96605(a,1,2))].
% 187.43/187.76 158070 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),c_Finite__Set_Olattice__class_OSup__fin(hAPP(c_or,c_0),tc_bool)) = A. [resolve(94047,b,96786,a)].
% 187.43/187.76 158085 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),c_Finite__Set_Olattice__class_OSup__fin(c_Collect(B),tc_bool)) = A | -hBOOL(A). [para(148(a,1),94047(b,1))].
% 187.43/187.76 158109 hAPP(c_Not,c_Finite__Set_Olattice__class_OSup__fin(hAPP(c_or,c_0),tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool). [para(158070(a,1),18172(a,1))].
% 187.43/187.76 158110 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Finite__Set_Olattice__class_OSup__fin(hAPP(c_or,c_0),tc_bool)),A) = A. [para(158070(a,1),3169(a,1)),flip(a)].
% 187.43/187.76 158118 c_Finite__Set_Olattice__class_OSup__fin(hAPP(c_or,c_0),tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)). [resolve(158109,a,18087,a),flip(a)].
% 187.43/187.76 158125 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),A) = A. [back_rewrite(158110),rewrite([158118(7)])].
% 187.43/187.76 158239 c_Finite__Set_Olattice__class_OSup__fin(c_Collect(A),tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)). [resolve(158085,b,8895,a),rewrite([158125(11)])].
% 187.43/187.76 158240 hAPP(c_Not,c_Finite__Set_Olattice__class_OSup__fin(c_Collect(A),tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(158239,a,18223,a),rewrite([18174(6)]),flip(a)].
% 187.43/187.76 158439 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Finite__Set_Olattice__class_OSup__fin(c_Collect(A),tc_bool)),B) = B. [para(158239(a,2),158125(a,1,1,2))].
% 187.43/187.76 158600 hAPP(c_Not,A) != c_Orderings_Obot__class_Obot(tc_bool) | c_Finite__Set_Olattice__class_OSup__fin(c_Collect(B),tc_bool) = A. [para(158240(a,1),18173(a,1)),flip(a)].
% 187.43/187.76 222028 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),c_Suc(c_Suc(A))) = c_Suc(c_Suc(A)). [resolve(3073,b,6545,a)].
% 187.43/187.76 223528 hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(c_Suc(c_Suc(A)))),A) = c_Suc(c_Suc(c_Suc(A))). [resolve(3075,b,8394,a)].
% 187.43/187.76 232743 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),c_Suc(A))). [resolve(3095,b,3318,a)].
% 187.43/187.76 232999 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)))). [para(36911(a,1),232743(a,1,1,2))].
% 187.43/187.76 234017 -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B))),A)). [resolve(232999,a,669,a)].
% 187.43/187.76 234848 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B))),A) = A. [resolve(3098,b,17678,a)].
% 187.43/187.76 317888 c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) != A. [para(234848(a,1),3099(a,1)),flip(a),unit_del(b,234017)].
% 187.43/187.76 318207 c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) != B. [para(3079(a,1),317888(a,1,1))].
% 187.43/187.76 339457 c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),c_Suc(c_Suc(B)))) != B. [para(222028(a,1),318207(a,1,1,2))].
% 187.43/187.76 339490 c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),c_Suc(c_Suc(C))))) != C. [para(3080(a,1),339457(a,1,1))].
% 187.43/187.76 344016 c_Suc(c_Suc(c_Suc(c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),c_Suc(c_Suc(B))))))) != B. [para(223528(a,1),339490(a,1,1))].
% 187.43/187.76 344017 c_Suc(c_Suc(c_Suc(c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(c_Suc(A))),B))))) != A. [para(3070(a,1),344016(a,1,1,1,1,1))].
% 187.43/187.76 344050 c_Suc(c_Suc(c_Suc(c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(c_Suc(B))),C)))))) != B. [para(3079(a,1),344017(a,1,1,1,1,1))].
% 187.43/187.76 344834 hBOOL(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(B,A)),hAPP(c_Not,A))). [para(4490(a,2),8949(b,1))].
% 187.43/187.76 344837 hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(A,c_0)),c_0)). [para(4490(a,2),42479(a,1)),rewrite([148(8)])].
% 187.43/187.76 344902 hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_0)). [resolve(344837,a,3137,b)].
% 187.43/187.76 344969 hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),c_0) = A. [resolve(344902,a,3172,b)].
% 187.43/187.76 345102 c_Finite__Set_Olattice__class_OSup__fin(c_Collect(A),tc_bool) = c_0. [para(344969(a,1),158439(a,1))].
% 187.43/187.76 345245 hAPP(c_Not,A) != c_Orderings_Obot__class_Obot(tc_bool) | c_0 = A. [back_rewrite(158600),rewrite([345102(8)])].
% 187.43/187.76 350467 hBOOL(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(c_Not,A))). [resolve(344834,b,3138,b)].
% 187.43/187.76 350482 hBOOL(A) | c_Orderings_Obot__class_Obot(tc_bool) = A. [resolve(350467,b,3172,b),rewrite([18225(7)])].
% 187.43/187.76 351246 hAPP(c_Not,A) = c_Orderings_Obot__class_Obot(tc_bool) | -hBOOL(A). [resolve(350482,a,4889,b),flip(a)].
% 187.43/187.76 351484 hAPP(c_Not,A) = c_Orderings_Obot__class_Obot(tc_bool) | c_Orderings_Obot__class_Obot(tc_bool) = A. [resolve(351246,b,350482,a)].
% 187.43/187.76 352387 c_Orderings_Obot__class_Obot(tc_bool) = A | c_0 = A. [resolve(351484,a,345245,a)].
% 187.43/187.76 352418 c_Suc(c_Suc(c_Suc(c_Suc(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(c_Suc(c_Orderings_Obot__class_Obot(tc_bool)))),A))))) = c_0. [resolve(352387,a,344017,a(flip)),flip(a)].
% 187.43/187.76 352419 $F. [resolve(352418,a,344050,a)].
% 187.43/187.76
% 187.43/187.76 % SZS output end Refutation
% 187.43/187.76 ============================== end of proof ==========================
% 187.43/187.76
% 187.43/187.76 ============================== STATISTICS ============================
% 187.43/187.76
% 187.43/187.76 Given=23700. Generated=8213074. Kept=352163. proofs=1.
% 187.43/187.76 Usable=17001. Sos=9571. Demods=1847. Limbo=14, Disabled=326353. Hints=0.
% 187.43/187.76 Megabytes=298.41.
% 187.43/187.76 User_CPU=181.66, System_CPU=4.56, Wall_clock=186.
% 187.43/187.76
% 187.43/187.76 ============================== end of statistics =====================
% 187.43/187.76
% 187.43/187.76 ============================== end of search =========================
% 187.43/187.76
% 187.43/187.76 THEOREM PROVED
% 187.43/187.76 % SZS status Unsatisfiable
% 187.43/187.76
% 187.43/187.76 Exiting with 1 proof.
% 187.43/187.76
% 187.43/187.76 Process 27401 exit (max_proofs) Thu Jun 16 06:52:58 2022
% 187.43/187.76 Prover9 interrupted
%------------------------------------------------------------------------------