TSTP Solution File: SWV830-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV830-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 21:14:58 EDT 2022
% Result : Timeout 300.10s 300.33s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV830-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 08:01:47 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.10/1.45 ============================== Prover9 ===============================
% 1.10/1.45 Prover9 (32) version 2009-11A, November 2009.
% 1.10/1.45 Process 18686 was started by sandbox2 on n016.cluster.edu,
% 1.10/1.45 Wed Jun 15 08:01:48 2022
% 1.10/1.45 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18533_n016.cluster.edu".
% 1.10/1.45 ============================== end of head ===========================
% 1.10/1.45
% 1.10/1.45 ============================== INPUT =================================
% 1.10/1.45
% 1.10/1.45 % Reading from file /tmp/Prover9_18533_n016.cluster.edu
% 1.10/1.45
% 1.10/1.45 set(prolog_style_variables).
% 1.10/1.45 set(auto2).
% 1.10/1.45 % set(auto2) -> set(auto).
% 1.10/1.45 % set(auto) -> set(auto_inference).
% 1.10/1.45 % set(auto) -> set(auto_setup).
% 1.10/1.45 % set(auto_setup) -> set(predicate_elim).
% 1.10/1.45 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.10/1.45 % set(auto) -> set(auto_limits).
% 1.10/1.45 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.10/1.45 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.10/1.45 % set(auto) -> set(auto_denials).
% 1.10/1.45 % set(auto) -> set(auto_process).
% 1.10/1.45 % set(auto2) -> assign(new_constants, 1).
% 1.10/1.45 % set(auto2) -> assign(fold_denial_max, 3).
% 1.10/1.45 % set(auto2) -> assign(max_weight, "200.000").
% 1.10/1.45 % set(auto2) -> assign(max_hours, 1).
% 1.10/1.45 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.10/1.45 % set(auto2) -> assign(max_seconds, 0).
% 1.10/1.45 % set(auto2) -> assign(max_minutes, 5).
% 1.10/1.45 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.10/1.45 % set(auto2) -> set(sort_initial_sos).
% 1.10/1.45 % set(auto2) -> assign(sos_limit, -1).
% 1.10/1.45 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.10/1.45 % set(auto2) -> assign(max_megs, 400).
% 1.10/1.45 % set(auto2) -> assign(stats, some).
% 1.10/1.45 % set(auto2) -> clear(echo_input).
% 1.10/1.45 % set(auto2) -> set(quiet).
% 1.10/1.45 % set(auto2) -> clear(print_initial_clauses).
% 1.10/1.45 % set(auto2) -> clear(print_given).
% 1.10/1.45 assign(lrs_ticks,-1).
% 1.10/1.45 assign(sos_limit,10000).
% 1.10/1.45 assign(order,kbo).
% 1.10/1.45 set(lex_order_vars).
% 1.10/1.45 clear(print_given).
% 1.10/1.45
% 1.10/1.45 % formulas(sos). % not echoed (720 formulas)
% 1.10/1.45
% 1.10/1.45 ============================== end of input ==========================
% 1.10/1.45
% 1.10/1.45 % From the command line: assign(max_seconds, 300).
% 1.10/1.45
% 1.10/1.45 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.10/1.45
% 1.10/1.45 % Formulas that are not ordinary clauses:
% 1.10/1.45
% 1.10/1.45 ============================== end of process non-clausal formulas ===
% 1.10/1.45
% 1.10/1.45 ============================== PROCESS INITIAL CLAUSES ===============
% 1.10/1.45
% 1.10/1.45 ============================== PREDICATE ELIMINATION =================
% 1.10/1.45 1 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.10/1.45 2 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 1.10/1.45 3 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 1.10/1.45 4 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 1.10/1.45 5 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),C,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__0_0) # label(axiom). [assumption].
% 1.10/1.45 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,2,a)].
% 1.10/1.45 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(1,a,3,a)].
% 1.10/1.45 Derived: c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),B,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,5,a)].
% 1.10/1.45 6 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.10/1.45 7 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.10/1.45 8 -class_Orderings_Olinorder(A) | c_Orderings_Olinorder(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),A) # label(cls_dual__linorder_0) # label(axiom). [assumption].
% 1.10/1.45 9 -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].
% 1.10/1.45 10 -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].
% 1.10/1.45 11 -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].
% 1.10/1.45 12 -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].
% 1.10/1.45 13 -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].
% 1.10/1.45 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__le_1) # label(axiom). [assumption].
% 1.10/1.45 15 -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].
% 1.10/1.45 16 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Olinorder__class_OMax(B,A)),c_Finite__Set_Olinorder__class_OMax(C,A))) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),B),C)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 1.10/1.45 17 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_lessThan__subset__iff_1) # label(axiom). [assumption].
% 1.10/1.45 18 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) # label(cls_lessThan__subset__iff_0) # label(axiom). [assumption].
% 1.10/1.45 19 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 1.10/1.45 20 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.10/1.45 21 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.10/1.45 22 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.10/1.45 23 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.10/1.45 24 -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].
% 1.10/1.45 25 -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].
% 1.10/1.45 26 -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].
% 1.10/1.45 27 -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].
% 1.10/1.47 28 -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].
% 1.10/1.47 29 -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].
% 1.10/1.47 30 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 1.10/1.47 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(6,a,7,a)].
% 1.10/1.47 Derived: c_Orderings_Olinorder(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),tc_nat). [resolve(6,a,8,a)].
% 1.10/1.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,9,a)].
% 1.10/1.47 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,12,a)].
% 1.10/1.47 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Olinorder__class_OMax(A,tc_nat)),c_Finite__Set_Olinorder__class_OMax(B,tc_nat))) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),A),B)). [resolve(6,a,16,a)].
% 1.10/1.47 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(6,a,17,a)].
% 1.10/1.47 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))). [resolve(6,a,18,a)].
% 1.10/1.47 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(6,a,19,a)].
% 1.10/1.47 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(6,a,20,a)].
% 1.10/1.47 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(6,a,24,a)].
% 1.10/1.47 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(6,a,26,a)].
% 1.10/1.47 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(6,a,27,a)].
% 1.10/1.47 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,28,a)].
% 1.10/1.47 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(6,a,29,a)].
% 1.10/1.47 Derived: c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_nat) = A. [resolve(6,a,30,a)].
% 1.10/1.47 31 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.10/1.47 32 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.10/1.47 33 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.10/1.47 34 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),D,A))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_below__fold1__iff_0) # label(axiom). [assumption].
% 1.10/1.47 35 -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].
% 1.10/1.47 36 -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].
% 1.10/1.47 37 -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].
% 1.10/1.47 38 -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].
% 1.10/1.47 39 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.10/1.47 40 -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),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.10/1.47 41 -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].
% 1.10/1.47 42 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),B,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 1.10/1.47 43 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.10/1.47 44 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.10/1.47 45 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.10/1.47 46 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.10/1.47 47 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.10/1.47 48 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.10/1.47 49 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.10/1.47 50 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.10/1.47 51 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.10/1.47 52 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.10/1.47 53 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.10/1.47 54 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)). [resolve(31,a,32,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),E)). [resolve(31,a,33,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E,tc_fun(B,A)))) | E = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(B,A),tc_bool)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(31,a,34,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(31,a,35,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(31,a,36,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(31,a,37,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C). [resolve(31,a,38,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))). [resolve(31,a,39,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(31,a,40,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(31,a,41,a)].
% 1.10/1.47 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,tc_fun(B,A))),D)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,A)),D),C)) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(31,a,42,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(31,a,43,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),D)). [resolve(31,a,46,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),C)). [resolve(31,a,47,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D). [resolve(31,a,48,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(31,a,49,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E),D))). [resolve(31,a,50,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(31,a,51,a)].
% 1.10/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(31,a,52,a)].
% 1.10/1.48 55 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)). [resolve(55,a,32,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),C)). [resolve(55,a,33,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C,tc_nat))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(55,a,34,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(55,a,35,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(55,a,36,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(55,a,37,a)].
% 1.10/1.48 Derived: 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(55,a,38,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C))). [resolve(55,a,39,a)].
% 1.10/1.48 Derived: 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),B),C)). [resolve(55,a,40,a)].
% 1.10/1.48 Derived: 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(55,a,41,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A,tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(55,a,42,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(55,a,43,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),B)). [resolve(55,a,46,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),A)). [resolve(55,a,47,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B). [resolve(55,a,48,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),A) = A. [resolve(55,a,49,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C),B))). [resolve(55,a,50,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(55,a,51,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(55,a,52,a)].
% 1.10/1.48 56 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)). [resolve(56,a,32,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),C)). [resolve(56,a,33,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_in(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C,tc_bool))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(56,a,34,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(56,a,35,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(56,a,36,a)].
% 1.10/1.48 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(56,a,37,a)].
% 1.10/1.48 Derived: 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(56,a,38,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))). [resolve(56,a,39,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(56,a,40,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(56,a,41,a)].
% 1.10/1.48 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,tc_bool)),B)) | -hBOOL(hAPP(hAPP(c_in(tc_bool),B),A)) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(56,a,42,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(56,a,43,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),B)). [resolve(56,a,46,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),A)). [resolve(56,a,47,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B). [resolve(56,a,48,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(56,a,49,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B))). [resolve(56,a,50,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(56,a,51,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(56,a,52,a)].
% 1.10/1.61 57 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.10/1.61 58 -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__supE_0) # label(axiom). [assumption].
% 1.10/1.61 59 -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__supE_1) # label(axiom). [assumption].
% 1.10/1.61 60 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.10/1.61 61 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.10/1.61 62 -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].
% 1.10/1.61 63 -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].
% 1.10/1.61 64 -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].
% 1.10/1.61 65 -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_1) # label(axiom). [assumption].
% 1.10/1.61 66 -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].
% 1.10/1.61 67 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.10/1.61 68 -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].
% 1.10/1.61 69 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.10/1.61 70 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.10/1.61 71 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.10/1.61 72 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.10/1.61 73 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.10/1.61 74 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.10/1.61 75 -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].
% 1.10/1.61 76 -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].
% 1.10/1.61 77 -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].
% 1.10/1.61 78 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)),D)). [resolve(57,a,58,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),E),C)),D)). [resolve(57,a,59,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(57,a,60,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(57,a,61,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(57,a,64,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(57,a,65,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(57,a,66,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(57,a,67,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D))). [resolve(57,a,68,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C))). [resolve(57,a,69,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),D)). [resolve(57,a,72,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(57,a,73,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(57,a,74,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)). [resolve(57,a,75,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)). [resolve(57,a,76,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C). [resolve(57,a,77,a)].
% 1.10/1.61 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(57,a,78,a)].
% 1.10/1.61 79 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)),B)). [resolve(79,a,58,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A)),B)). [resolve(79,a,59,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(79,a,60,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(79,a,61,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(79,a,64,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(79,a,65,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(79,a,66,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(79,a,67,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B))). [resolve(79,a,68,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A))). [resolve(79,a,69,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(79,a,72,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(79,a,73,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(79,a,74,a)].
% 1.10/1.61 Derived: 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(79,a,75,a)].
% 1.10/1.61 Derived: 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(79,a,76,a)].
% 1.10/1.61 Derived: 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(79,a,77,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B). [resolve(79,a,78,a)].
% 1.10/1.61 80 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.10/1.61 Derived: 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(80,a,58,a)].
% 1.10/1.61 Derived: 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(80,a,59,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(80,a,60,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(80,a,61,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(80,a,64,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(80,a,65,a)].
% 1.10/1.61 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(80,a,66,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(80,a,67,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B))). [resolve(80,a,68,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A))). [resolve(80,a,69,a)].
% 1.10/1.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),B)). [resolve(80,a,72,a)].
% 1.10/1.73 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(80,a,73,a)].
% 1.10/1.73 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(80,a,74,a)].
% 1.10/1.73 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)). [resolve(80,a,75,a)].
% 1.10/1.73 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)). [resolve(80,a,76,a)].
% 1.10/1.73 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [resolve(80,a,77,a)].
% 1.10/1.73 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(80,a,78,a)].
% 1.10/1.73 81 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.10/1.73 82 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.10/1.73 Derived: A = A. [resolve(81,b,82,a)].
% 1.10/1.73
% 1.10/1.73 ============================== end predicate elimination =============
% 1.10/1.73
% 1.10/1.73 Auto_denials: (non-Horn, no changes).
% 1.10/1.73
% 1.10/1.73 Term ordering decisions:
% 1.10/1.73 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. tc_Com_Opname=1. tc_Com_Ocom=1. tc_Com_Ostate=1. v_x=1. c_Com_Ocom_OBODY=1. v_P=1. v_Q=1. c_Com_Obody=1. v_R=1. c_Com_Ocom_OSKIP=1. t_b=1. t_c=1. v_pn=1. v_G=1. v_Procs=1. hAPP=1. tc_fun=1. c_Finite__Set_Ocard=1. c_SetInterval_Oord__class_OlessThan=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_Com_Ocom_OSemi=1. c_Finite__Set_Olinorder__class_OMax=1. c_List_Oset=1. v_sko__Hoare__Mirabelle__Xconseq1__1=1. v_sko__Hoare__Mirabelle__Xconseq1__2=1. v_sko__Hoare__Mirabelle__Xconseq2__1=1. v_sko__Hoare__Mirabelle__Xconseq2__2=1. c_lessequals=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_Orderings_Obot__class_Obot=1. c_in=1. c_HOL_Oord__class_Oless=1. c_HOL_Ominus__class_Ominus=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Otop__class_Otop=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Suc=1. c_HOL_Ozero__class_Ozero=1. c_Option_Othe=1. tc_Option_Ooption=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_COMBK=1. c_Finite__Set_Ofold1=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_COMBC=1. c_Fun_Othe__inv__into=1. c_Finite__Set_Osetsum=1. c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1. v_sko__Hoare__Mirabelle__Xconseq12__2=1. v_sko__Hoare__Mirabelle__Xconseq12__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2=1. c_COMBB=1. c_Fun_Ofun__upd=1. c_COMBS=1. c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1=1. c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2=1. c_List_Ofoldl=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 1.10/1.73
% 1.10/1.73 ============================== end of process initial clauses ========
% 1.10/1.73
% 1.10/1.73 ============================== CLAUSES FOR SEARCH ====================
% 1.10/1.73
% 1.10/1.73 ============================== end of clauses for search =============
% 1.10/1.73
% 1.10/1.73 ============================== SEARCH ==Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------