TSTP Solution File: SWV878-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV878-1 : 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 21:15:07 EDT 2022
% Result : Timeout 300.07s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV878-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 14:12:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.98/1.34 ============================== Prover9 ===============================
% 0.98/1.34 Prover9 (32) version 2009-11A, November 2009.
% 0.98/1.34 Process 9678 was started by sandbox2 on n016.cluster.edu,
% 0.98/1.34 Wed Jun 15 14:12:33 2022
% 0.98/1.34 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9525_n016.cluster.edu".
% 0.98/1.34 ============================== end of head ===========================
% 0.98/1.34
% 0.98/1.34 ============================== INPUT =================================
% 0.98/1.34
% 0.98/1.34 % Reading from file /tmp/Prover9_9525_n016.cluster.edu
% 0.98/1.34
% 0.98/1.34 set(prolog_style_variables).
% 0.98/1.34 set(auto2).
% 0.98/1.34 % set(auto2) -> set(auto).
% 0.98/1.34 % set(auto) -> set(auto_inference).
% 0.98/1.34 % set(auto) -> set(auto_setup).
% 0.98/1.34 % set(auto_setup) -> set(predicate_elim).
% 0.98/1.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.98/1.34 % set(auto) -> set(auto_limits).
% 0.98/1.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.98/1.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.98/1.34 % set(auto) -> set(auto_denials).
% 0.98/1.34 % set(auto) -> set(auto_process).
% 0.98/1.34 % set(auto2) -> assign(new_constants, 1).
% 0.98/1.34 % set(auto2) -> assign(fold_denial_max, 3).
% 0.98/1.34 % set(auto2) -> assign(max_weight, "200.000").
% 0.98/1.34 % set(auto2) -> assign(max_hours, 1).
% 0.98/1.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.98/1.34 % set(auto2) -> assign(max_seconds, 0).
% 0.98/1.34 % set(auto2) -> assign(max_minutes, 5).
% 0.98/1.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.98/1.34 % set(auto2) -> set(sort_initial_sos).
% 0.98/1.34 % set(auto2) -> assign(sos_limit, -1).
% 0.98/1.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.98/1.34 % set(auto2) -> assign(max_megs, 400).
% 0.98/1.34 % set(auto2) -> assign(stats, some).
% 0.98/1.34 % set(auto2) -> clear(echo_input).
% 0.98/1.34 % set(auto2) -> set(quiet).
% 0.98/1.34 % set(auto2) -> clear(print_initial_clauses).
% 0.98/1.34 % set(auto2) -> clear(print_given).
% 0.98/1.34 assign(lrs_ticks,-1).
% 0.98/1.34 assign(sos_limit,10000).
% 0.98/1.34 assign(order,kbo).
% 0.98/1.34 set(lex_order_vars).
% 0.98/1.34 clear(print_given).
% 0.98/1.34
% 0.98/1.34 % formulas(sos). % not echoed (847 formulas)
% 0.98/1.34
% 0.98/1.34 ============================== end of input ==========================
% 0.98/1.34
% 0.98/1.34 % From the command line: assign(max_seconds, 300).
% 0.98/1.34
% 0.98/1.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.98/1.34
% 0.98/1.34 % Formulas that are not ordinary clauses:
% 0.98/1.34
% 0.98/1.34 ============================== end of process non-clausal formulas ===
% 0.98/1.34
% 0.98/1.34 ============================== PROCESS INITIAL CLAUSES ===============
% 0.98/1.34
% 0.98/1.34 ============================== PREDICATE ELIMINATION =================
% 0.98/1.34 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.98/1.34 2 -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].
% 0.98/1.34 3 -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].
% 0.98/1.34 4 -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].
% 0.98/1.34 5 -class_Orderings_Olinorder(A) | -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(A) = c_Orderings_Oord__class_Omax(A) # label(cls_sup__max_0) # label(axiom). [assumption].
% 0.98/1.34 6 -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].
% 0.98/1.34 7 -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].
% 0.98/1.34 8 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.98/1.34 9 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.98/1.34 10 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.98/1.34 11 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.98/1.34 12 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.98/1.34 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.98/1.34 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.98/1.34 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.98/1.34 16 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.98/1.34 17 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.98/1.34 18 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.98/1.34 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.98/1.34 20 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.98/1.34 21 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.98/1.34 22 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.98/1.34 23 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(1,a,2,a)].
% 0.98/1.34 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(1,a,3,a)].
% 0.98/1.34 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(1,a,4,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | -class_Orderings_Olinorder(tc_fun(B,A)) | c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)) = c_Orderings_Oord__class_Omax(tc_fun(B,A)). [resolve(1,a,5,b)].
% 0.98/1.34 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(1,a,6,a)].
% 0.98/1.34 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(1,a,7,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(C,A)). [resolve(1,a,8,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(C,A)). [resolve(1,a,9,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),B),E),C,tc_fun(D,A)). [resolve(1,a,10,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),E),B),C,tc_fun(D,A)). [resolve(1,a,11,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,12,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,13,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,16,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,17,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -c_lessequals(D,C,tc_fun(B,A)). [resolve(1,a,18,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(1,a,19,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),B),D),tc_fun(C,A)). [resolve(1,a,20,a)].
% 0.98/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),B),tc_fun(C,A)). [resolve(1,a,21,a)].
% 0.98/1.34 24 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.98/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(24,a,2,a)].
% 0.98/1.34 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(24,a,3,a)].
% 0.98/1.34 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(24,a,4,a)].
% 0.98/1.34 Derived: -class_Orderings_Olinorder(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat). [resolve(24,a,5,b)].
% 0.98/1.34 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(24,a,6,a)].
% 0.98/1.34 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(24,a,7,a)].
% 0.98/1.34 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(24,a,8,a)].
% 0.98/1.34 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(24,a,9,a)].
% 0.98/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C),B,tc_nat). [resolve(24,a,10,a)].
% 0.98/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A),B,tc_nat). [resolve(24,a,11,a)].
% 0.98/1.34 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(24,a,12,a)].
% 0.98/1.34 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(24,a,13,a)].
% 0.98/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat). [resolve(24,a,16,a)].
% 0.98/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat). [resolve(24,a,17,a)].
% 0.98/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat). [resolve(24,a,18,a)].
% 0.98/1.34 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(24,a,19,a)].
% 0.98/1.34 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat). [resolve(24,a,20,a)].
% 0.98/1.34 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat). [resolve(24,a,21,a)].
% 0.98/1.34 25 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.98/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(25,a,2,a)].
% 0.98/1.34 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(25,a,3,a)].
% 0.98/1.34 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(25,a,4,a)].
% 0.98/1.34 Derived: -class_Orderings_Olinorder(tc_bool) | c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Orderings_Oord__class_Omax(tc_bool). [resolve(25,a,5,b)].
% 0.98/1.34 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(25,a,6,a)].
% 0.98/1.34 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(25,a,7,a)].
% 0.98/1.34 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(25,a,8,a)].
% 0.98/1.34 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(25,a,9,a)].
% 0.98/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C),B,tc_bool). [resolve(25,a,10,a)].
% 0.98/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A),B,tc_bool). [resolve(25,a,11,a)].
% 0.98/1.40 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(25,a,12,a)].
% 0.98/1.40 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(25,a,13,a)].
% 0.98/1.40 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(25,a,16,a)].
% 0.98/1.40 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(25,a,17,a)].
% 0.98/1.40 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(25,a,18,a)].
% 0.98/1.40 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(25,a,19,a)].
% 0.98/1.40 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(25,a,20,a)].
% 0.98/1.40 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(25,a,21,a)].
% 0.98/1.40 26 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.98/1.40 27 -class_Orderings_Olinorder(A) | -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(A) = c_Orderings_Oord__class_Omin(A) # label(cls_inf__min_0) # label(axiom). [assumption].
% 0.98/1.40 28 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.98/1.40 29 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.98/1.40 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),A),B),C,A) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 0.98/1.40 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.98/1.40 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.98/1.40 33 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.98/1.40 34 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_in(C,D,A) | -c_lessequals(B,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),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].
% 0.98/1.40 35 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.98/1.40 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.98/1.40 37 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.98/1.40 38 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.98/1.40 39 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.98/1.41 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.98/1.41 41 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.98/1.41 42 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.98/1.41 43 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.98/1.41 44 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.98/1.41 45 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.98/1.41 46 -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].
% 0.98/1.41 47 -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].
% 0.98/1.41 48 -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].
% 0.98/1.41 49 -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].
% 0.98/1.41 50 -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].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | -class_Orderings_Olinorder(tc_fun(B,A)) | c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)) = c_Orderings_Oord__class_Omin(tc_fun(B,A)). [resolve(26,a,27,b)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_HOL_Oord__class_Oless(D,E,tc_fun(B,A)). [resolve(26,a,28,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(B,A)). [resolve(26,a,29,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A)),C),D,tc_fun(B,A)) | -c_in(D,C,tc_fun(B,A)) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(26,a,30,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(26,a,31,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),D,tc_fun(B,A)). [resolve(26,a,32,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),C,tc_fun(B,A)). [resolve(26,a,33,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_in(C,E,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),tc_fun(D,A)),E),tc_fun(D,A)) | E = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(D,A),tc_bool)) | -c_Finite__Set_Ofinite(E,tc_fun(D,A)). [resolve(26,a,34,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -c_lessequals(C,D,tc_fun(B,A)). [resolve(26,a,37,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | c_lessequals(C,D,tc_fun(B,A)). [resolve(26,a,38,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -c_lessequals(D,C,tc_fun(B,A)). [resolve(26,a,39,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),C),E),tc_fun(D,A)). [resolve(26,a,40,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E),C),tc_fun(D,A)). [resolve(26,a,41,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(26,a,42,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)). [resolve(26,a,43,a)].
% 0.98/1.41 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(26,a,46,a)].
% 0.98/1.41 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(26,a,47,a)].
% 0.98/1.41 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(26,a,48,a)].
% 0.98/1.41 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(26,a,49,a)].
% 0.98/1.41 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(26,a,50,a)].
% 0.98/1.41 51 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.98/1.41 Derived: -class_Orderings_Olinorder(tc_nat) | c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat). [resolve(51,a,27,b)].
% 0.98/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(51,a,28,a)].
% 0.98/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(51,a,29,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),tc_nat),A),B,tc_nat) | -c_in(B,A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(51,a,30,a)].
% 0.98/1.41 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(51,a,31,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),B,tc_nat). [resolve(51,a,32,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),A,tc_nat). [resolve(51,a,33,a)].
% 0.98/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_in(B,C,tc_nat) | -c_lessequals(A,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),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(51,a,34,a)].
% 0.98/1.41 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = A | -c_lessequals(A,B,tc_nat). [resolve(51,a,37,a)].
% 0.98/1.41 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | c_lessequals(A,B,tc_nat). [resolve(51,a,38,a)].
% 0.98/1.41 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -c_lessequals(B,A,tc_nat). [resolve(51,a,39,a)].
% 0.98/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C),tc_nat). [resolve(51,a,40,a)].
% 0.98/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C),B),tc_nat). [resolve(51,a,41,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(51,a,42,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(51,a,43,a)].
% 0.98/1.41 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(51,a,46,a)].
% 0.98/1.41 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(51,a,47,a)].
% 0.98/1.41 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(51,a,48,a)].
% 0.98/1.41 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(51,a,49,a)].
% 0.98/1.41 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),A) = A. [resolve(51,a,50,a)].
% 0.98/1.41 52 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.98/1.41 Derived: -class_Orderings_Olinorder(tc_bool) | c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = c_Orderings_Oord__class_Omin(tc_bool). [resolve(52,a,27,b)].
% 0.98/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(52,a,28,a)].
% 0.98/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(52,a,29,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool),A),B,tc_bool) | -c_in(B,A,tc_bool) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(52,a,30,a)].
% 0.98/1.41 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(52,a,31,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(52,a,32,a)].
% 0.98/1.41 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(52,a,33,a)].
% 0.98/1.41 Derived: c_lessequals(A,B,tc_bool) | -c_in(B,C,tc_bool) | -c_lessequals(A,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),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(52,a,34,a)].
% 0.98/1.59 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -c_lessequals(A,B,tc_bool). [resolve(52,a,37,a)].
% 0.98/1.59 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | c_lessequals(A,B,tc_bool). [resolve(52,a,38,a)].
% 0.98/1.59 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -c_lessequals(B,A,tc_bool). [resolve(52,a,39,a)].
% 0.98/1.59 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool). [resolve(52,a,40,a)].
% 0.98/1.59 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B),tc_bool). [resolve(52,a,41,a)].
% 0.98/1.59 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(52,a,42,a)].
% 0.98/1.59 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(52,a,43,a)].
% 0.98/1.59 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(52,a,46,a)].
% 0.98/1.59 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(52,a,47,a)].
% 0.98/1.59 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(52,a,48,a)].
% 0.98/1.59 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(52,a,49,a)].
% 0.98/1.59 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(52,a,50,a)].
% 0.98/1.59 53 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.98/1.59 54 -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].
% 0.98/1.59 55 -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].
% 0.98/1.59 56 -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].
% 0.98/1.59 57 -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].
% 0.98/1.59 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(53,a,54,a)].
% 0.98/1.59 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(53,a,56,a)].
% 0.98/1.59 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(53,a,57,a)].
% 0.98/1.59 58 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 0.98/1.59 59 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -c_in(C,D,E) | -c_Finite__Set_Ofinite(D,E) | c_Finite__Set_Osetprod(B,D,E,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_2) # label(axiom). [assumption].
% 0.98/1.59 Derived: -class_Ring__and__Field_Ocomm__semiring__1(tc_nat) | hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(B,C,D) | -c_Finite__Set_Ofinite(C,D) | c_Finite__Set_Osetprod(A,C,D,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(58,a,59,a)].
% 1.52/1.76 60 hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(B),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | c_in(v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname) | -v_wt(B) # label(cls_assms_I3_J_0) # label(axiom). [assumption].
% 1.52/1.76 61 v_wt(c_Option_Othe(hAPP(c_Com_Obody,A),tc_Com_Ocom)) | -c_in(A,v_U,tc_Com_Opname) # label(cls_assms_I4_J_0) # label(axiom). [assumption].
% 1.52/1.76 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(c_Option_Othe(hAPP(c_Com_Obody,B),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | c_in(v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname) | -c_in(B,v_U,tc_Com_Opname). [resolve(60,c,61,a)].
% 1.52/1.76 62 hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(B),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -v_wt(B) # label(cls_assms_I3_J_1) # label(axiom). [assumption].
% 1.52/1.76 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(c_Option_Othe(hAPP(c_Com_Obody,B),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -c_in(B,v_U,tc_Com_Opname). [resolve(62,c,61,a)].
% 1.52/1.76 63 v_wt(v_c) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 1.52/1.76 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | c_in(v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname). [resolve(63,a,60,c)].
% 1.52/1.76 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))). [resolve(63,a,62,c)].
% 1.52/1.76 64 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.52/1.76 65 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.52/1.76 Derived: A = A. [resolve(64,b,65,a)].
% 1.52/1.76
% 1.52/1.76 ============================== end predicate elimination =============
% 1.52/1.76
% 1.52/1.76 Auto_denials: (non-Horn, no changes).
% 1.52/1.76
% 1.52/1.76 Term ordering decisions:
% 1.52/1.76 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_P=1. v_U=1. v_mgt__call=1. tc_Com_Opname=1. c_Com_Obody=1. tc_Com_Ocom=1. v_G=1. v_c=1. hAPP=1. tc_fun=1. c_Finite__Set_Ocard=1. c_HOL_Ouminus__class_Ouminus=1. c_Finite__Set_Ofold1=1. c_Option_Othe=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_Orderings_Oord__class_Omin=1. c_Suc=1. c_Orderings_Oord__class_Omax=1. c_HOL_Ozero__class_Ozero=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. v_mgt=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_COMBK=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2=1. c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2=1. c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1=1. c_Map_Odom=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Finite__Set_Osetsum=1. c_Fun_Othe__inv__into=1. v_sko__local__Xassms__3__1=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. c_Finite__Set_Osetprod=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_Fun_Ofun__upd=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1. c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1=1.
% 1.52/1.76
% 1.52/1.76 =================Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------