TSTP Solution File: SWV890-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV890-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 21:15:09 EDT 2022
% Result : Timeout 300.04s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV890-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.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 : Tue Jun 14 15:33:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.86/1.17 ============================== Prover9 ===============================
% 0.86/1.17 Prover9 (32) version 2009-11A, November 2009.
% 0.86/1.17 Process 17621 was started by sandbox2 on n022.cluster.edu,
% 0.86/1.17 Tue Jun 14 15:33:04 2022
% 0.86/1.17 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17468_n022.cluster.edu".
% 0.86/1.17 ============================== end of head ===========================
% 0.86/1.17
% 0.86/1.17 ============================== INPUT =================================
% 0.86/1.17
% 0.86/1.17 % Reading from file /tmp/Prover9_17468_n022.cluster.edu
% 0.86/1.17
% 0.86/1.17 set(prolog_style_variables).
% 0.86/1.17 set(auto2).
% 0.86/1.17 % set(auto2) -> set(auto).
% 0.86/1.17 % set(auto) -> set(auto_inference).
% 0.86/1.17 % set(auto) -> set(auto_setup).
% 0.86/1.17 % set(auto_setup) -> set(predicate_elim).
% 0.86/1.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.86/1.17 % set(auto) -> set(auto_limits).
% 0.86/1.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.86/1.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.86/1.17 % set(auto) -> set(auto_denials).
% 0.86/1.17 % set(auto) -> set(auto_process).
% 0.86/1.17 % set(auto2) -> assign(new_constants, 1).
% 0.86/1.17 % set(auto2) -> assign(fold_denial_max, 3).
% 0.86/1.17 % set(auto2) -> assign(max_weight, "200.000").
% 0.86/1.17 % set(auto2) -> assign(max_hours, 1).
% 0.86/1.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.86/1.17 % set(auto2) -> assign(max_seconds, 0).
% 0.86/1.17 % set(auto2) -> assign(max_minutes, 5).
% 0.86/1.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.86/1.17 % set(auto2) -> set(sort_initial_sos).
% 0.86/1.17 % set(auto2) -> assign(sos_limit, -1).
% 0.86/1.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.86/1.17 % set(auto2) -> assign(max_megs, 400).
% 0.86/1.17 % set(auto2) -> assign(stats, some).
% 0.86/1.17 % set(auto2) -> clear(echo_input).
% 0.86/1.17 % set(auto2) -> set(quiet).
% 0.86/1.17 % set(auto2) -> clear(print_initial_clauses).
% 0.86/1.17 % set(auto2) -> clear(print_given).
% 0.86/1.17 assign(lrs_ticks,-1).
% 0.86/1.17 assign(sos_limit,10000).
% 0.86/1.17 assign(order,kbo).
% 0.86/1.17 set(lex_order_vars).
% 0.86/1.17 clear(print_given).
% 0.86/1.17
% 0.86/1.17 % formulas(sos). % not echoed (488 formulas)
% 0.86/1.17
% 0.86/1.17 ============================== end of input ==========================
% 0.86/1.17
% 0.86/1.17 % From the command line: assign(max_seconds, 300).
% 0.86/1.17
% 0.86/1.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.86/1.17
% 0.86/1.17 % Formulas that are not ordinary clauses:
% 0.86/1.17
% 0.86/1.17 ============================== end of process non-clausal formulas ===
% 0.86/1.17
% 0.86/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.86/1.17
% 0.86/1.17 ============================== PREDICATE ELIMINATION =================
% 0.86/1.17 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.86/1.17 2 -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].
% 0.86/1.17 3 -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].
% 0.86/1.17 4 -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].
% 0.86/1.17 5 -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].
% 0.86/1.17 6 -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].
% 0.86/1.17 7 -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].
% 0.86/1.17 8 -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].
% 0.86/1.17 9 -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].
% 0.86/1.17 10 -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].
% 0.86/1.17 11 -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].
% 0.86/1.17 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -hBOOL(c_in(C,D,A)) | -c_lessequals(B,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),D,A),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].
% 0.86/1.17 13 -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].
% 0.86/1.17 14 -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].
% 0.86/1.17 15 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),B,A),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 0.86/1.17 16 -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].
% 0.86/1.17 17 -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].
% 0.86/1.17 18 -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].
% 0.86/1.17 19 -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].
% 0.86/1.17 20 -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].
% 0.86/1.17 21 -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].
% 0.86/1.17 22 -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].
% 0.86/1.17 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(1,a,2,a)].
% 0.86/1.17 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(1,a,3,a)].
% 0.86/1.17 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(1,a,4,a)].
% 0.86/1.17 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(1,a,5,a)].
% 0.86/1.17 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(1,a,8,a)].
% 0.86/1.17 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(1,a,9,a)].
% 0.86/1.17 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(1,a,10,a)].
% 0.86/1.17 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(1,a,11,a)].
% 0.86/1.17 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -hBOOL(c_in(C,E,tc_fun(D,A))) | -c_lessequals(B,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E,tc_fun(D,A)),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(1,a,12,a)].
% 0.86/1.17 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(1,a,13,a)].
% 0.86/1.17 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(1,a,14,a)].
% 0.86/1.17 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,tc_fun(B,A)),D,tc_fun(B,A)) | -hBOOL(c_in(D,C,tc_fun(B,A))) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(1,a,15,a)].
% 0.86/1.17 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(1,a,16,a)].
% 0.86/1.17 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(1,a,19,a)].
% 0.86/1.17 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(1,a,20,a)].
% 0.86/1.17 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(1,a,21,a)].
% 0.86/1.17 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(1,a,22,a)].
% 0.86/1.17 23 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.86/1.17 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(23,a,2,a)].
% 0.86/1.17 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(23,a,3,a)].
% 0.86/1.17 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(23,a,4,a)].
% 0.86/1.17 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(23,a,5,a)].
% 0.86/1.17 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(23,a,8,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -c_lessequals(B,A,tc_nat). [resolve(23,a,9,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | c_lessequals(A,B,tc_nat). [resolve(23,a,10,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = A | -c_lessequals(A,B,tc_nat). [resolve(23,a,11,a)].
% 0.86/1.17 Derived: c_lessequals(A,B,tc_nat) | -hBOOL(c_in(B,C,tc_nat)) | -c_lessequals(A,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C,tc_nat),tc_nat) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(23,a,12,a)].
% 0.86/1.17 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(23,a,13,a)].
% 0.86/1.17 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(23,a,14,a)].
% 0.86/1.17 Derived: c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A,tc_nat),B,tc_nat) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,15,a)].
% 0.86/1.17 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(23,a,16,a)].
% 0.86/1.17 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),B,tc_nat). [resolve(23,a,19,a)].
% 0.86/1.17 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),A,tc_nat). [resolve(23,a,20,a)].
% 0.86/1.17 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(23,a,21,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),A) = A. [resolve(23,a,22,a)].
% 0.86/1.17 24 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.86/1.17 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(24,a,2,a)].
% 0.86/1.17 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(24,a,3,a)].
% 0.86/1.17 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(24,a,4,a)].
% 0.86/1.17 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(24,a,5,a)].
% 0.86/1.17 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(24,a,8,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -c_lessequals(B,A,tc_bool). [resolve(24,a,9,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | c_lessequals(A,B,tc_bool). [resolve(24,a,10,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -c_lessequals(A,B,tc_bool). [resolve(24,a,11,a)].
% 0.86/1.17 Derived: c_lessequals(A,B,tc_bool) | -hBOOL(c_in(B,C,tc_bool)) | -c_lessequals(A,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C,tc_bool),tc_bool) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(24,a,12,a)].
% 0.86/1.17 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(24,a,13,a)].
% 0.86/1.17 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(24,a,14,a)].
% 0.86/1.18 Derived: c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,tc_bool),B,tc_bool) | -hBOOL(c_in(B,A,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(24,a,15,a)].
% 0.86/1.18 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(24,a,16,a)].
% 0.86/1.18 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(24,a,19,a)].
% 0.86/1.18 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(24,a,20,a)].
% 0.86/1.18 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(24,a,21,a)].
% 0.86/1.18 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(24,a,22,a)].
% 0.86/1.18 25 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.86/1.18 26 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.86/1.18 27 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.86/1.18 28 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.86/1.18 29 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.86/1.18 30 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.86/1.18 31 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.86/1.18 32 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.86/1.18 33 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.86/1.18 34 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.86/1.18 35 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.86/1.18 36 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.86/1.18 37 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.86/1.18 38 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.86/1.18 39 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.86/1.19 40 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.86/1.19 41 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.86/1.19 42 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.86/1.19 43 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.86/1.19 44 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(25,a,26,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(25,a,27,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(25,a,28,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,30,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,31,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(25,a,33,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,34,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(25,a,35,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(25,a,36,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(25,a,37,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(25,a,38,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(25,a,39,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(25,a,40,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(25,a,41,a)].
% 0.86/1.19 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(25,a,42,a)].
% 0.86/1.19 45 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(45,a,26,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(45,a,27,a)].
% 0.86/1.19 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(45,a,28,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(45,a,30,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(45,a,31,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(45,a,33,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(45,a,34,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(45,a,35,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(45,a,36,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(45,a,37,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(45,a,38,a)].
% 0.86/1.19 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(45,a,39,a)].
% 0.86/1.19 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(45,a,40,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(45,a,41,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(45,a,42,a)].
% 0.86/1.19 46 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(46,a,26,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(46,a,27,a)].
% 0.86/1.19 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(46,a,28,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(46,a,30,a)].
% 0.86/1.19 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(46,a,31,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(46,a,33,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(46,a,34,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(46,a,35,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(46,a,36,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(46,a,37,a)].
% 0.86/1.19 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(46,a,38,a)].
% 0.86/1.19 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(46,a,39,a)].
% 0.86/1.22 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(46,a,40,a)].
% 0.86/1.22 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(46,a,41,a)].
% 0.86/1.22 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(46,a,42,a)].
% 0.86/1.22 47 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.86/1.22 48 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 0.86/1.22 49 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 0.86/1.22 50 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 0.86/1.22 51 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 0.86/1.22 52 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 0.86/1.22 53 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 0.86/1.22 54 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.86/1.22 55 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 0.86/1.22 56 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 0.86/1.22 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)). [resolve(47,a,48,a)].
% 0.86/1.22 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(47,a,49,a)].
% 0.86/1.22 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(47,a,50,a)].
% 0.86/1.22 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),c_Finite__Set_Olinorder__class_OMin(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)). [resolve(47,a,51,a)].
% 0.86/1.22 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(47,a,52,a)].
% 0.86/1.22 Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(47,a,53,a)].
% 0.86/1.22 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(47,a,54,a)].
% 0.86/1.22 Derived: c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(47,a,55,a)].
% 2.51/2.79 Derived: c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(47,a,56,a)].
% 2.51/2.79
% 2.51/2.79 ============================== end predicate elimination =============
% 2.51/2.79
% 2.51/2.79 Auto_denials: (non-Horn, no changes).
% 2.51/2.79
% 2.51/2.79 Term ordering decisions:
% 2.51/2.79 Function symbol KB weights: tc_bool=1. tc_nat=1. tc_Com_Ostate=1. v_x=1. c_Com_Obody=1. tc_Com_Ocom=1. t_a=1. tc_Com_Opname=1. v_G=1. v_c=1. v_ca=1. tc_fun=1. hAPP=1. c_Option_Ooption_OSome=1. c_Collect=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Option_Othe=1. c_fequal=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Set_Ocontents=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. c_Com_Ocom_OBODY=1. c_Option_Ooption_ONone=1. c_Hoare__Mirabelle_OMGT=1. v_sko__Hoare__Mirabelle__XMGF__lemma1__1=1. tc_Option_Ooption=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_Map_Odom=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Com_Ocom_OCall=1. c_Finite__Set_Ofold1=1. c_Finite__Set_Ofold1Set=1. c_ATP__Linkup_Osko__Set__Xset__insert__1__1=1. c_Set_Oimage=1. c_Map_Omap__add=1. c_Set_Ovimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple=1.
% 2.51/2.79
% 2.51/2.79 ============================== end of process initial clauses ========
% 2.51/2.79
% 2.51/2.79 ============================== CLAUSES FOR SEARCH ====================
% 2.51/2.79
% 2.51/2.79 ============================== end of clauses for search =============
% 2.51/2.79
% 2.51/2.79 ============================== SEARCH ================================
% 2.51/2.79
% 2.51/2.79 % Starting search at 0.20 seconds.
% 2.51/2.79
% 2.51/2.79 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 85 (0.00 of 0.55 sec).
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=53.000, iters=3395
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=47.000, iters=3385
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=45.000, iters=3367
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=44.000, iters=3361
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=43.000, iters=3334
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=42.000, iters=3341
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=39.000, iters=3402
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=37.000, iters=3373
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=36.000, iters=3396
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=35.000, iters=3387
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=34.000, iters=3346
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=33.000, iters=3359
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=32.000, iters=3396
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=31.000, iters=3352
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=30.000, iters=3350
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=28.000, iters=3504
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=27.000, iters=3407
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=26.000, iters=3530
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=24.000, iters=3375
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=23.000, iters=3481
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=22.000, iters=3409
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=21.000, iters=3357
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=18.000, iters=3345
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=16.000, iters=3547
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=14.000, iters=3350
% 2.51/2.79
% 2.51/2.79 Low Water (keep): wt=13.000, iters=3337
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=3909, wt=79.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11317, wt=62.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=10173, wt=61.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11650, wt=60.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=9702, wt=59.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=9694, wt=58.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=9703, wt=57.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=9700, wt=56.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11890, wt=54.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11884, wt=53.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11871, wt=52.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11866, wt=51.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11858, wt=50.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11867, wt=49.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=11864, wt=48.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12333, wt=47.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12296, wt=46.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12211, wt=45.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12548, wt=44.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12679, wt=43.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=12993, wt=42.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=13150, wt=41.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=13247, wt=40.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=13372, wt=39.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=13729, wt=38.000
% 2.51/2.79
% 2.51/2.79 Low Water (displace): id=13278, wt=37.000
% 2.51/2.79
% 2.51/2.79 Low Water (displacCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------