TSTP Solution File: SWV845-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV845-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 21:15:01 EDT 2022
% Result : Unsatisfiable 199.32s 199.62s
% Output : Refutation 199.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV845-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jun 15 08:50:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.89/1.23 ============================== Prover9 ===============================
% 0.89/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.23 Process 4156 was started by sandbox on n029.cluster.edu,
% 0.89/1.23 Wed Jun 15 08:50:27 2022
% 0.89/1.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4002_n029.cluster.edu".
% 0.89/1.23 ============================== end of head ===========================
% 0.89/1.23
% 0.89/1.23 ============================== INPUT =================================
% 0.89/1.23
% 0.89/1.23 % Reading from file /tmp/Prover9_4002_n029.cluster.edu
% 0.89/1.23
% 0.89/1.23 set(prolog_style_variables).
% 0.89/1.23 set(auto2).
% 0.89/1.23 % set(auto2) -> set(auto).
% 0.89/1.23 % set(auto) -> set(auto_inference).
% 0.89/1.23 % set(auto) -> set(auto_setup).
% 0.89/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.23 % set(auto) -> set(auto_limits).
% 0.89/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.23 % set(auto) -> set(auto_denials).
% 0.89/1.23 % set(auto) -> set(auto_process).
% 0.89/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.23 % set(auto2) -> assign(stats, some).
% 0.89/1.23 % set(auto2) -> clear(echo_input).
% 0.89/1.23 % set(auto2) -> set(quiet).
% 0.89/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.23 % set(auto2) -> clear(print_given).
% 0.89/1.23 assign(lrs_ticks,-1).
% 0.89/1.23 assign(sos_limit,10000).
% 0.89/1.23 assign(order,kbo).
% 0.89/1.23 set(lex_order_vars).
% 0.89/1.23 clear(print_given).
% 0.89/1.23
% 0.89/1.23 % formulas(sos). % not echoed (499 formulas)
% 0.89/1.23
% 0.89/1.23 ============================== end of input ==========================
% 0.89/1.23
% 0.89/1.23 % From the command line: assign(max_seconds, 300).
% 0.89/1.23
% 0.89/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.23
% 0.89/1.23 % Formulas that are not ordinary clauses:
% 0.89/1.23
% 0.89/1.23 ============================== end of process non-clausal formulas ===
% 0.89/1.23
% 0.89/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.23
% 0.89/1.23 ============================== PREDICATE ELIMINATION =================
% 0.89/1.23 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.89/1.23 2 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.89/1.23 3 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.89/1.23 4 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.89/1.23 5 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.89/1.23 6 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.89/1.23 7 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.89/1.23 8 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.89/1.23 9 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.89/1.23 10 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.92/1.23 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.92/1.23 12 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.92/1.23 13 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.92/1.23 14 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.92/1.23 15 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.92/1.23 16 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.92/1.23 17 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.92/1.23 18 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.92/1.23 19 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.92/1.23 20 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.92/1.23 21 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.92/1.23 22 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,2,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,3,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,4,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(1,a,5,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,6,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,7,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,8,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(1,a,9,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,12,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,13,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(1,a,14,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(1,a,15,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(1,a,16,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,19,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(1,a,20,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(1,a,21,a)].
% 0.92/1.23 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(1,a,22,a)].
% 0.92/1.23 23 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(23,a,2,a)].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(23,a,3,a)].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(23,a,4,a)].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(23,a,5,a)].
% 0.92/1.23 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(23,a,6,a)].
% 0.92/1.23 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(23,a,7,a)].
% 0.92/1.23 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(23,a,8,a)].
% 0.92/1.23 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(23,a,9,a)].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(23,a,12,a)].
% 0.92/1.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(23,a,13,a)].
% 0.92/1.23 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(23,a,14,a)].
% 0.92/1.23 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(23,a,15,a)].
% 0.92/1.23 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(23,a,16,a)].
% 0.92/1.25 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(23,a,19,a)].
% 0.92/1.25 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(23,a,20,a)].
% 0.92/1.25 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(23,a,21,a)].
% 0.92/1.25 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(23,a,22,a)].
% 0.92/1.25 24 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.25 25 -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].
% 0.92/1.25 26 -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].
% 0.92/1.25 27 -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].
% 0.92/1.25 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_sup__least_0) # label(axiom). [assumption].
% 0.92/1.25 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_le__sup__iff_2) # label(axiom). [assumption].
% 0.92/1.25 30 -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].
% 0.92/1.25 31 -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].
% 0.92/1.25 32 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.92/1.25 33 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.92/1.25 34 -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].
% 0.92/1.25 35 -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].
% 0.92/1.25 36 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.92/1.25 37 -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].
% 0.92/1.25 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_1) # label(axiom). [assumption].
% 0.92/1.25 39 -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].
% 0.92/1.25 40 -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].
% 0.92/1.25 41 -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].
% 0.92/1.25 42 -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].
% 0.92/1.25 43 -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].
% 0.92/1.25 44 -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].
% 0.92/1.25 45 -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].
% 0.92/1.25 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(24,a,25,a)].
% 0.92/1.25 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(24,a,26,a)].
% 0.92/1.25 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(24,a,27,a)].
% 0.92/1.25 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(24,a,30,a)].
% 0.92/1.25 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(24,a,31,a)].
% 0.92/1.25 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(24,a,32,a)].
% 0.92/1.25 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(24,a,33,a)].
% 0.92/1.25 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(24,a,34,a)].
% 0.92/1.25 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(24,a,35,a)].
% 0.92/1.25 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(24,a,36,a)].
% 0.92/1.25 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(24,a,37,a)].
% 0.92/1.25 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(24,a,38,a)].
% 0.92/1.25 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(24,a,39,a)].
% 0.92/1.25 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(24,a,40,a)].
% 0.92/1.25 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(24,a,41,a)].
% 0.92/1.25 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(24,a,42,a)].
% 0.92/1.25 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(24,a,43,a)].
% 0.92/1.36 46 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.36 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,25,a)].
% 0.92/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(46,a,26,a)].
% 0.92/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(46,a,27,a)].
% 0.92/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(46,a,30,a)].
% 0.92/1.36 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,31,a)].
% 0.92/1.36 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(46,a,32,a)].
% 0.92/1.36 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(46,a,33,a)].
% 0.92/1.36 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,34,a)].
% 0.92/1.36 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,35,a)].
% 0.92/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(46,a,36,a)].
% 0.92/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(46,a,37,a)].
% 0.92/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(46,a,38,a)].
% 0.92/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(46,a,39,a)].
% 0.92/1.36 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,40,a)].
% 0.92/1.36 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,41,a)].
% 0.92/1.36 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,42,a)].
% 0.92/1.36 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,43,a)].
% 0.92/1.36
% 0.92/1.36 ============================== end predicate elimination =============
% 0.92/1.36
% 0.92/1.36 Auto_denials: (non-Horn, no changes).
% 0.92/1.36
% 0.92/1.36 Term ordering decisions:
% 0.92/1.36 Function symbol KB weights: tc_bool=1. t_a=1. v_x=1. v_P=1. v_b=1. c_Not=1. tc_Com_Ostate=1. v_c=1. v_G=1. v_xa=1. tc_fun=1. hAPP=1. c_Com_Ocom_OWhile=1. c_Collect=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_fequal=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_ATP__Linkup_Osko__Set__Xequals0I__1__1=1. c_Set_Ocontents=1. v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. v_n=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Com_Ocom_OCond=1. c_COMBK=1. c_Hoare__Mirabelle_Opeek__and=1. c_Finite__Set_Ofold1Set=1. c_Finite__Set_Ofold1=1. c_ATP__Linkup_Osko__Set__Xmk__disjoint__insert__1__1=1. c_ATP__Linkup_Osko__Set__Xset__insert__1__1=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Fun_Ocomp=1.
% 0.92/1.36
% 0.92/1.36 ============================== end of process initial clauses ========
% 199.32/199.62
% 199.32/199.62 ============================== CLAUSES FOR SEARCH ====================
% 199.32/199.62
% 199.32/199.62 ============================== end of clauses for search =============
% 199.32/199.62
% 199.32/199.62 ============================== SEARCH ================================
% 199.32/199.62
% 199.32/199.62 % Starting search at 0.19 seconds.
% 199.32/199.62
% 199.32/199.62 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 0.44 sec).
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=44.000, iters=3373
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=42.000, iters=3379
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=41.000, iters=3388
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=39.000, iters=3335
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=38.000, iters=3393
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=37.000, iters=3352
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=35.000, iters=3335
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=34.000, iters=3341
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=33.000, iters=3417
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=32.000, iters=3430
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=31.000, iters=3361
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=30.000, iters=3369
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=29.000, iters=3514
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=28.000, iters=3351
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=27.000, iters=3359
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=26.000, iters=3363
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=25.000, iters=3391
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=24.000, iters=3350
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=23.000, iters=3355
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=22.000, iters=3351
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=21.000, iters=3360
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=20.000, iters=3339
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=19.000, iters=3349
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=18.000, iters=3341
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=17.000, iters=3333
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11246, wt=60.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11244, wt=58.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11355, wt=55.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11354, wt=53.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11247, wt=51.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11245, wt=49.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12161, wt=42.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=8113, wt=41.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12693, wt=40.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=7311, wt=39.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12168, wt=38.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=10500, wt=37.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12841, wt=36.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12840, wt=35.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12568, wt=34.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=12839, wt=33.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13604, wt=32.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13603, wt=31.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=11498, wt=30.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13954, wt=29.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13605, wt=28.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13839, wt=27.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13474, wt=26.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=13504, wt=25.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=14211, wt=24.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=14455, wt=23.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=15179, wt=22.000
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=15808, wt=16.000
% 199.32/199.62
% 199.32/199.62 Low Water (keep): wt=16.000, iters=3336
% 199.32/199.62
% 199.32/199.62 Low Water (displace): id=174449, wt=15.000
% 199.32/199.62
% 199.32/199.62 ============================== PROOF =================================
% 199.32/199.62 % SZS status Unsatisfiable
% 199.32/199.62 % SZS output start Refutation
% 199.32/199.62
% 199.32/199.62 % Proof 1 at 194.16 (+ 4.29) seconds.
% 199.32/199.62 % Length of proof is 201.
% 199.32/199.62 % Level of proof is 25.
% 199.32/199.62 % Maximum clause weight is 29.000.
% 199.32/199.62 % Given clauses 22625.
% 199.32/199.62
% 199.32/199.62 4 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 199.32/199.62 5 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 199.32/199.62 9 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 199.32/199.62 19 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 199.32/199.62 23 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 199.32/199.62 30 -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].
% 199.32/199.62 33 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 199.32/199.62 39 -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].
% 199.32/199.62 46 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 199.32/199.62 51 c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Un__upper1_0) # label(axiom). [assumption].
% 199.32/199.62 64 c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),B,tc_fun(C,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool)) # label(cls_Un__Diff__cancel2_0) # label(axiom). [assumption].
% 199.32/199.62 86 c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) | -c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Diff__subset__conv_1) # label(axiom). [assumption].
% 199.32/199.62 90 -class_HOL_Oord(A) | c_lessequals(hAPP(B,C),hAPP(D,C),A) | -c_lessequals(B,D,tc_fun(E,A)) # label(cls_le__funD_0) # label(axiom). [assumption].
% 199.32/199.62 97 -hBOOL(c_in(A,c_ATP__Linkup_Osko__Set__Xset__insert__1__1(B,A,C),C)) | -hBOOL(c_in(A,B,C)) # label(cls_set__insert_1) # label(axiom). [assumption].
% 199.32/199.62 103 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 199.32/199.62 106 hAPP(c_COMBK(A,B,C),D) = A # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 199.32/199.62 130 -class_Complete__Lattice_Ocomplete__lattice(A) | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Complete__Lattice_OInf__class_OInf(C,A),A) # label(cls_Inf__insert_0) # label(axiom). [assumption].
% 199.32/199.62 131 -class_Complete__Lattice_Ocomplete__lattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Complete__Lattice_OInf__class_OInf(C,A),A) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(B,C,A),A). [copy(130),flip(b)].
% 199.32/199.62 135 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 199.32/199.62 144 -class_Orderings_Oorder(A) | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),c_SetInterval_Oord__class_OatLeastAtMost(D,E,A),tc_fun(A,tc_bool)) | -c_lessequals(C,E,A) | -c_lessequals(D,B,A) # label(cls_atLeastatMost__subset__iff_3) # label(axiom). [assumption].
% 199.32/199.62 147 c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) | c_lessequals(D,A,tc_fun(C,tc_bool)) # label(cls_Un__Int__assoc__eq_0) # label(axiom). [assumption].
% 199.32/199.62 168 -c_HOL_Oord__class_Oless(A,A,tc_fun(B,tc_bool)) # label(cls_psubset__eq_1) # label(axiom). [assumption].
% 199.32/199.62 179 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 199.32/199.62 181 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(D,B,tc_fun(C,tc_bool)),C)) # label(cls_DiffE_1) # label(axiom). [assumption].
% 199.32/199.62 186 hBOOL(c_in(A,c_Collect(B,C),C)) | -hBOOL(hAPP(B,A)) # label(cls_CollectI_0) # label(axiom). [assumption].
% 199.32/199.62 187 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)). [copy(186),rewrite([135(1)])].
% 199.32/199.62 188 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,c_Collect(A,C),C)) # label(cls_CollectD_0) # label(axiom). [assumption].
% 199.32/199.62 189 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,A,C)). [copy(188),rewrite([135(3)])].
% 199.32/199.62 198 c_HOL_Oord__class_Oless(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) | -c_lessequals(A,C,tc_fun(D,tc_bool)) | hBOOL(c_in(B,A,D)) | hBOOL(c_in(B,C,D)) # label(cls_psubset__insert__iff_3) # label(axiom). [assumption].
% 199.32/199.62 206 -class_Orderings_Obot(A) | c_lessequals(c_Orderings_Obot__class_Obot(A),B,A) # label(cls_bot__least_0) # label(axiom). [assumption].
% 199.32/199.62 215 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) != c_Collect(B,A) | -hBOOL(hAPP(B,C)) # label(cls_empty__Collect__eq_0) # label(axiom). [assumption].
% 199.32/199.62 216 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) != B | -hBOOL(hAPP(B,C)). [copy(215),rewrite([135(4)])].
% 199.32/199.62 224 c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) = B # label(cls_Un__empty__left_0) # label(axiom). [assumption].
% 199.32/199.62 227 c_HOL_Ominus__class_Ominus(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A # label(cls_Diff__empty_0) # label(axiom). [assumption].
% 199.32/199.62 230 c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_Int__empty__left_0) # label(axiom). [assumption].
% 199.32/199.62 231 c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) # label(cls_empty__subsetI_0) # label(axiom). [assumption].
% 199.32/199.62 247 c_lessequals(c_Set_Oinsert(A,B,C),c_Set_Oinsert(A,D,C),tc_fun(C,tc_bool)) | -c_lessequals(B,D,tc_fun(C,tc_bool)) # label(cls_insert__mono_0) # label(axiom). [assumption].
% 199.32/199.62 250 c_lessequals(A,c_Set_Oinsert(B,A,C),tc_fun(C,tc_bool)) # label(cls_subset__insertI_0) # label(axiom). [assumption].
% 199.32/199.62 252 c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) = c_Set_Oinsert(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_fun(D,tc_bool)),D) # label(cls_Un__insert__right_0) # label(axiom). [assumption].
% 199.32/199.62 253 c_Set_Oinsert(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,tc_bool)),D) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Set_Oinsert(A,C,D),tc_fun(D,tc_bool)). [copy(252),flip(a)].
% 199.32/199.62 289 -class_Orderings_Oorder(A) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_atLeastatMost__empty__iff2_0) # label(axiom). [assumption].
% 199.32/199.62 290 -class_Orderings_Oorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,A). [copy(289),flip(b)].
% 199.32/199.62 316 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 199.32/199.62 317 c_lessequals(A,A,tc_fun(B,tc_bool)) # label(cls_equalityE_0) # label(axiom). [assumption].
% 199.32/199.62 319 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(C,B)) | -c_lessequals(C,A,tc_fun(D,tc_bool)) # label(cls_predicate1D_0) # label(axiom). [assumption].
% 199.32/199.62 321 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 199.32/199.62 324 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 199.32/199.62 340 c_The(c_fequal(A,B),B) = A # label(cls_the__sym__eq__trivial_0) # label(axiom). [assumption].
% 199.32/199.62 347 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 199.32/199.62 351 -class_Complete__Lattice_Ocomplete__lattice(A) | c_lessequals(B,c_Complete__Lattice_OSup__class_OSup(C,A),A) | -hBOOL(c_in(B,C,A)) # label(cls_Sup__upper_0) # label(axiom). [assumption].
% 199.32/199.62 354 A = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xequals0I__1__1(A,B),A,B)) # label(cls_equals0I_0) # label(axiom). [assumption].
% 199.32/199.62 355 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xequals0I__1__1(B,A),B,A)). [copy(354),flip(a)].
% 199.32/199.62 358 c_lessequals(c_Set_Oinsert(A,B,C),D,tc_fun(C,tc_bool)) | -c_lessequals(B,D,tc_fun(C,tc_bool)) | -hBOOL(c_in(A,D,C)) # label(cls_insert__subset_2) # label(axiom). [assumption].
% 199.32/199.62 366 A = c_Set_Oinsert(B,c_ATP__Linkup_Osko__Set__Xset__insert__1__1(A,B,C),C) | -hBOOL(c_in(B,A,C)) # label(cls_set__insert_0) # label(axiom). [assumption].
% 199.32/199.62 367 c_Set_Oinsert(A,c_ATP__Linkup_Osko__Set__Xset__insert__1__1(B,A,C),C) = B | -hBOOL(c_in(A,B,C)). [copy(366),flip(a)].
% 199.32/199.62 368 hBOOL(c_in(A,B,C)) | -c_lessequals(c_Set_Oinsert(A,D,C),B,tc_fun(C,tc_bool)) # label(cls_insert__subset_0) # label(axiom). [assumption].
% 199.32/199.62 376 c_Collect(c_fequal(A,B),B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 199.32/199.62 377 c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = c_fequal(A,B). [copy(376),rewrite([135(2)]),flip(a)].
% 199.32/199.62 382 hBOOL(hAPP(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B))) # label(cls_Nitpick_OEx1__def_2) # label(axiom). [assumption].
% 199.32/199.62 383 hBOOL(hAPP(c_fequal(A,B),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(A,B),B))). [copy(382),rewrite([377(4),377(5)])].
% 199.32/199.62 389 c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)),D),tc_fun(D,tc_bool)),C,tc_fun(D,tc_bool)) # label(cls_Diff__insert2_0) # label(axiom). [assumption].
% 199.32/199.62 390 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_fequal(B,C),tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,D,C),tc_fun(C,tc_bool)). [copy(389),rewrite([377(8)]),flip(a)].
% 199.32/199.62 401 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = c_Set_Oinsert(A,B,C) # label(cls_insert__Diff__single_0) # label(axiom). [assumption].
% 199.32/199.62 402 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_fequal(A,C),tc_fun(C,tc_bool)),C) = c_Set_Oinsert(A,B,C). [copy(401),rewrite([377(4)])].
% 199.32/199.62 403 -class_Orderings_Oorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(B,B,A) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_atLeastAtMost__singleton_0) # label(axiom). [assumption].
% 199.32/199.62 404 -class_Orderings_Oorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(B,B,A) = c_fequal(B,A). [copy(403),rewrite([377(6)])].
% 199.32/199.62 407 -class_Complete__Lattice_Ocomplete__lattice(A) | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Inf__singleton_0) # label(axiom). [assumption].
% 199.32/199.62 408 -class_Complete__Lattice_Ocomplete__lattice(A) | c_Complete__Lattice_OInf__class_OInf(c_fequal(B,A),A) = B. [copy(407),rewrite([377(5)])].
% 199.32/199.62 416 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = B | -hBOOL(c_in(A,B,C)) # label(cls_insert__Diff_0) # label(axiom). [assumption].
% 199.32/199.62 417 c_Set_Oinsert(A,B,C) = B | -hBOOL(c_in(A,B,C)). [copy(416),rewrite([377(4),402(5)])].
% 199.32/199.62 434 hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)) # label(cls_insert__code_1) # label(axiom). [assumption].
% 199.32/199.62 460 -class_Orderings_Obot(A) | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,A)),v_x) = c_Orderings_Obot__class_Obot(A) # label(cls_bot__fun__eq_0) # label(axiom). [assumption].
% 199.32/199.62 461 A = B | -hBOOL(c_in(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C)) # label(cls_singletonE_0) # label(axiom). [assumption].
% 199.32/199.62 462 A = B | -hBOOL(c_in(A,c_fequal(B,C),C)). [copy(461),rewrite([377(5)])].
% 199.32/199.62 470 c_Set_Oinsert(A,B,C) != c_Set_Oinsert(A,D,C) | hBOOL(c_in(A,D,C)) | hBOOL(c_in(A,B,C)) | B = D # label(cls_insert__ident_0) # label(axiom). [assumption].
% 199.32/199.62 490 class_Complete__Lattice_Ocomplete__lattice(tc_bool) # label(clsarity_bool__Complete__Lattice_Ocomplete__lattice) # label(axiom). [assumption].
% 199.32/199.62 493 class_Orderings_Opreorder(tc_bool) # label(clsarity_bool__Orderings_Opreorder) # label(axiom). [assumption].
% 199.32/199.62 495 class_Orderings_Oorder(tc_bool) # label(clsarity_bool__Orderings_Oorder) # label(axiom). [assumption].
% 199.32/199.62 496 class_Orderings_Obot(tc_bool) # label(clsarity_bool__Orderings_Obot) # label(axiom). [assumption].
% 199.32/199.62 498 class_HOL_Oord(tc_bool) # label(clsarity_bool__HOL_Oord) # label(axiom). [assumption].
% 199.32/199.62 499 hBOOL(hAPP(c_fequal(A,B),A)) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 199.32/199.62 520 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(23,a,4,a)].
% 199.32/199.62 521 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(23,a,5,a)].
% 199.32/199.62 525 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(23,a,9,a)].
% 199.32/199.62 532 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(23,a,19,a)].
% 199.32/199.62 556 c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(46,a,30,a)].
% 199.32/199.62 559 c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(46,a,33,a)].
% 199.32/199.62 566 c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(46,a,39,a)].
% 199.32/199.62 584 c_HOL_Oord__class_Oless(A,c_Set_Oinsert(B,A,C),tc_fun(C,tc_bool)) | hBOOL(c_in(B,A,C)). [factor(198,c,d),unit_del(b,317)].
% 199.32/199.62 634 c_lessequals(c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),C,tc_fun(D,tc_bool)) | -c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)). [para(64(a,1),86(b,2))].
% 199.32/199.62 876 hBOOL(c_in(A,c_COMBK(B,C,D),E)) | -hBOOL(B). [para(106(a,1),187(b,1))].
% 199.32/199.62 913 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) != B | c_lessequals(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),tc_fun(A,tc_bool)). [para(230(a,1),147(a,1,1)),rewrite([224(6),230(9)]),flip(a)].
% 199.32/199.62 919 c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),hAPP(C,B),tc_bool). [resolve(231,a,90,c),unit_del(a,498)].
% 199.32/199.62 934 c_lessequals(c_fequal(A,B),c_Set_Oinsert(A,C,B),tc_fun(B,tc_bool)). [resolve(247,b,231,a),rewrite([377(4)])].
% 199.32/199.62 962 c_lessequals(hAPP(A,B),hAPP(c_Set_Oinsert(C,A,D),B),tc_bool). [resolve(250,a,90,c),unit_del(a,498)].
% 199.32/199.62 1561 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | hBOOL(hAPP(B,c_ATP__Linkup_Osko__Set__Xequals0I__1__1(B,A))). [resolve(355,b,189,b)].
% 199.32/199.62 1579 c_lessequals(c_fequal(A,B),C,tc_fun(B,tc_bool)) | -hBOOL(c_in(A,C,B)). [resolve(358,b,231,a),rewrite([377(4)])].
% 199.32/199.62 1713 c_fequal(A,B) != c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)). [resolve(383,a,216,b),flip(a)].
% 199.32/199.62 1735 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(D,c_Set_Oinsert(E,B,C),tc_fun(C,tc_bool)),C)). [para(390(a,1),181(b,1,2))].
% 199.32/199.62 1921 hBOOL(c_in(A,c_Set_Oinsert(A,B,C),D)). [resolve(434,a,187,b)].
% 199.32/199.62 2028 c_Complete__Lattice_OInf__class_OInf(c_fequal(A,tc_bool),tc_bool) = A. [resolve(490,a,408,a)].
% 199.32/199.62 2031 c_lessequals(A,c_Complete__Lattice_OSup__class_OSup(B,tc_bool),tc_bool) | -hBOOL(c_in(A,B,tc_bool)). [resolve(490,a,351,a)].
% 199.32/199.62 2034 c_Lattices_Olower__semilattice__class_Oinf(A,c_Complete__Lattice_OInf__class_OInf(B,tc_bool),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(A,B,tc_bool),tc_bool). [resolve(490,a,131,a)].
% 199.32/199.62 2048 c_lessequals(A,A,tc_bool). [resolve(493,a,321,a)].
% 199.32/199.62 2055 c_SetInterval_Oord__class_OatLeastAtMost(A,A,tc_bool) = c_fequal(A,tc_bool). [resolve(495,a,404,a)].
% 199.32/199.62 2103 hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(496,a,460,a)].
% 199.32/199.62 2104 c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool). [resolve(496,a,206,a)].
% 199.32/199.62 2115 hBOOL(c_in(A,c_fequal(A,B),C)). [resolve(499,a,187,b)].
% 199.32/199.62 2144 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(532,a,347,d),unit_del(a,495)].
% 199.32/199.62 2464 c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_bool),tc_fun(tc_bool,tc_bool)) | -c_lessequals(B,C,tc_bool). [resolve(2048,a,144,d),unit_del(a,495)].
% 199.32/199.62 2522 c_Orderings_Obot__class_Obot(tc_bool) = A | -c_lessequals(A,c_Orderings_Obot__class_Obot(tc_bool),tc_bool). [resolve(2104,a,179,d),unit_del(a,495)].
% 199.32/199.62 2689 c_Set_Oinsert(A,c_fequal(A,B),C) = c_fequal(A,B). [resolve(2115,a,417,b)].
% 199.32/199.62 2718 c_Set_Oinsert(A,c_ATP__Linkup_Osko__Set__Xset__insert__1__1(c_Set_Oinsert(A,B,C),A,D),D) = c_Set_Oinsert(A,B,C). [resolve(1921,a,367,b)].
% 199.32/199.63 2850 -hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xequals0I__1__1(c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)),D),C,D)) | c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)). [resolve(1735,b,355,b),flip(b)].
% 199.32/199.63 2937 -hBOOL(c_Orderings_Obot__class_Obot(tc_bool)). [para(2103(a,1),216(b,1)),flip(a),xx(a)].
% 199.32/199.63 3072 hBOOL(c_in(A,c_COMBK(hAPP(c_fequal(B,C),B),D,E),F)). [resolve(876,b,499,a)].
% 199.32/199.63 3467 hBOOL(c_in(A,B,C)) | -c_lessequals(c_fequal(A,D),B,tc_fun(C,tc_bool)). [para(2689(a,1),368(b,1))].
% 199.32/199.63 3676 c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),C,tc_bool). [para(106(a,1),919(a,2))].
% 199.32/199.63 3699 hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(3676,a,2522,b),flip(a)].
% 199.32/199.63 3746 c_lessequals(hAPP(c_fequal(A,B),C),hAPP(c_Set_Oinsert(A,D,B),C),tc_bool). [resolve(934,a,90,c),unit_del(a,498)].
% 199.32/199.63 3754 c_lessequals(c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),B,tc_fun(C,tc_bool)). [resolve(634,b,51,a)].
% 199.32/199.63 3828 c_lessequals(A,hAPP(c_Set_Oinsert(B,c_COMBK(A,C,D),E),F),tc_bool). [para(106(a,1),962(a,1))].
% 199.32/199.63 3880 c_lessequals(A,c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool),tc_bool). [resolve(2031,b,2115,a)].
% 199.32/199.63 3895 c_Lattices_Olower__semilattice__class_Oinf(A,c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool),tc_bool) = A. [resolve(3880,a,520,b),rewrite([521(5)])].
% 199.32/199.63 4666 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_COMBK(B,C,D) | hBOOL(B). [para(106(a,1),1561(b,1))].
% 199.32/199.63 4668 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)). [para(3699(a,1),1561(b,1)),unit_del(b,2937)].
% 199.32/199.63 4669 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_0. [new_symbol(4668)].
% 199.32/199.63 4671 c_COMBK(A,B,C) = c_0 | hBOOL(A). [back_rewrite(4666),rewrite([4669(3)]),flip(a)].
% 199.32/199.63 4863 hAPP(c_0,A) = c_Orderings_Obot__class_Obot(tc_bool). [back_rewrite(3699),rewrite([4669(3)])].
% 199.32/199.63 5025 -hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xequals0I__1__1(c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)),D),C,D)) | c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) = c_0. [back_rewrite(2850),rewrite([4669(14)])].
% 199.32/199.63 5193 c_fequal(A,B) != c_0. [back_rewrite(1713),rewrite([4669(4)])].
% 199.32/199.63 5277 c_0 != A | c_lessequals(A,c_0,tc_fun(B,tc_bool)). [back_rewrite(913),rewrite([4669(3),4669(5)])].
% 199.32/199.63 5312 c_Set_Oinsert(A,c_0,B) = c_fequal(A,B). [back_rewrite(377),rewrite([4669(3)])].
% 199.32/199.63 5314 -class_Orderings_Oorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) != c_0 | -c_lessequals(B,C,A). [back_rewrite(290),rewrite([4669(5)])].
% 199.32/199.63 5327 c_HOL_Ominus__class_Ominus(A,c_0,tc_fun(B,tc_bool)) = A. [back_rewrite(227),rewrite([4669(3)])].
% 199.32/199.63 5446 c_COMBK(hAPP(A,B),C,D) = c_0 | hBOOL(c_in(B,A,E)). [resolve(4671,b,187,b)].
% 199.32/199.63 6377 c_Set_Oinsert(A,c_COMBK(hAPP(c_fequal(B,C),B),D,E),F) = c_COMBK(hAPP(c_fequal(B,C),B),D,E). [resolve(3072,a,417,b)].
% 199.32/199.63 6511 c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Set_Oinsert(C,c_COMBK(A,D,E),F),V6),B,tc_bool). [resolve(3828,a,316,d),unit_del(a,493)].
% 199.32/199.63 7743 c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(A,B,tc_bool),tc_bool),c_Complete__Lattice_OInf__class_OInf(B,tc_bool),tc_bool). [para(2034(a,1),532(a,1))].
% 199.32/199.63 7789 c_lessequals(A,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool). [para(5312(a,1),7743(a,1,1)),rewrite([2028(4)])].
% 199.32/199.63 7794 c_Lattices_Oupper__semilattice__class_Osup(A,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool). [resolve(7789,a,566,b)].
% 199.32/199.63 7796 c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) = A | c_HOL_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool). [resolve(7789,a,347,d),flip(b),unit_del(a,495)].
% 199.32/199.63 7798 c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) = A | -c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),A,tc_bool). [resolve(7789,a,179,d),flip(b),unit_del(a,495)].
% 199.32/199.63 7851 c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) = A | c_HOL_Oord__class_Oless(B,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool) | -c_lessequals(B,A,tc_bool). [resolve(7796,b,324,c),unit_del(b,493)].
% 199.32/199.63 7877 hAPP(c_Set_Oinsert(A,c_COMBK(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),B,C),D),E) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool). [resolve(7798,b,3828,a),flip(a)].
% 199.32/199.63 7988 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(2144,b,559,b),rewrite([556(7)])].
% 199.32/199.63 8748 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,hAPP(c_fequal(B,C),D),tc_bool),hAPP(c_Set_Oinsert(B,E,C),D),tc_bool). [resolve(3746,a,525,b)].
% 199.32/199.63 9413 c_COMBK(hAPP(c_fequal(A,B),C),D,E) = c_0 | C = A. [resolve(5446,b,462,b)].
% 199.32/199.63 9417 c_COMBK(hAPP(A,B),C,D) = c_0 | c_Set_Oinsert(B,A,E) = A. [resolve(5446,b,417,b)].
% 199.32/199.63 11398 A = B | c_lessequals(c_COMBK(hAPP(c_fequal(B,C),A),D,E),c_0,tc_fun(F,tc_bool)). [resolve(9413,a,5277,a(flip))].
% 199.32/199.63 15225 c_Set_Oinsert(A,B,C) = B | hAPP(B,A) = c_Orderings_Obot__class_Obot(tc_bool). [para(9417(a,1),106(a,1,1)),rewrite([4863(4)]),flip(b)].
% 199.32/199.63 15242 hAPP(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | hBOOL(hAPP(A,B)). [para(15225(a,1),434(a,1,1))].
% 199.32/199.63 15243 hAPP(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | hBOOL(c_in(B,A,C)). [para(15225(a,1),584(a,2)),unit_del(b,168)].
% 199.32/199.63 15360 c_Orderings_Obot__class_Obot(tc_bool) = A | hBOOL(A). [para(106(a,1),15242(b,1)),rewrite([106(2)]),flip(a)].
% 199.32/199.63 15410 c_Orderings_Obot__class_Obot(tc_bool) = A | hBOOL(c_in(B,c_COMBK(A,C,D),E)). [resolve(15360,b,876,b)].
% 199.32/199.63 15419 c_in(A,B,C) = c_Orderings_Obot__class_Obot(tc_bool) | hBOOL(hAPP(B,A)). [resolve(15360,b,189,b),flip(a)].
% 199.32/199.63 15432 hAPP(c_ATP__Linkup_Osko__Set__Xset__insert__1__1(A,B,C),B) = c_Orderings_Obot__class_Obot(tc_bool) | -hBOOL(c_in(B,A,C)). [resolve(15243,b,97,a)].
% 199.32/199.63 15456 c_in(A,B,C) = c_Orderings_Obot__class_Obot(tc_bool) | hBOOL(c_in(A,B,D)). [resolve(15419,b,187,b)].
% 199.32/199.63 15514 c_Orderings_Obot__class_Obot(tc_bool) = A | c_lessequals(c_fequal(B,C),c_COMBK(A,D,E),tc_fun(C,tc_bool)). [resolve(15410,b,1579,b)].
% 199.32/199.63 15543 c_in(A,B,C) = c_Orderings_Obot__class_Obot(tc_bool) | c_Set_Oinsert(A,B,D) = B. [resolve(15456,b,417,b)].
% 199.32/199.63 19735 hAPP(c_ATP__Linkup_Osko__Set__Xset__insert__1__1(c_Set_Oinsert(A,B,C),A,D),A) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(15432,b,1921,a)].
% 199.32/199.63 19889 c_in(A,c_ATP__Linkup_Osko__Set__Xset__insert__1__1(c_Set_Oinsert(A,B,C),A,D),E) = c_Orderings_Obot__class_Obot(tc_bool). [para(19735(a,1),15419(b,1)),unit_del(b,2937)].
% 199.32/199.63 22697 hBOOL(c_in(A,B,C)) | c_ATP__Linkup_Osko__Set__Xset__insert__1__1(c_Set_Oinsert(A,B,C),A,C) = B. [resolve(2718,a,470,a),rewrite([19889(5)]),unit_del(b,2937)].
% 199.32/199.63 22775 c_Set_Oinsert(A,B,C) = B | c_ATP__Linkup_Osko__Set__Xset__insert__1__1(c_Set_Oinsert(A,B,D),A,D) = B. [para(15543(a,1),22697(a,1)),unit_del(b,2937)].
% 199.32/199.63 28852 c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) | c_HOL_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool). [resolve(7851,c,3880,a),flip(a)].
% 199.32/199.63 28916 hBOOL(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool)). [para(7877(a,1),434(a,1))].
% 199.32/199.63 39475 c_Orderings_Obot__class_Obot(tc_bool) = A | c_lessequals(hAPP(c_fequal(B,C),D),A,tc_bool). [resolve(15514,b,90,c),rewrite([106(9)]),unit_del(b,498)].
% 199.32/199.63 39488 c_Orderings_Obot__class_Obot(tc_bool) = A | c_lessequals(B,A,tc_bool) | -c_lessequals(B,hAPP(c_fequal(C,D),E),tc_bool). [resolve(39475,b,316,c),unit_del(b,493)].
% 199.32/199.63 44772 c_Set_Oinsert(A,B,C) = B | -hBOOL(c_in(A,B,D)). [para(22775(b,1),97(a,1,2)),unit_del(c,1921)].
% 199.32/199.63 46695 c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) | -c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),A,tc_bool). [resolve(28852,b,103,c),unit_del(b,493)].
% 199.32/199.63 54829 c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(A,c_Orderings_Obot__class_Obot(tc_bool),tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_bool),tc_fun(tc_bool,tc_bool)). [resolve(2464,b,2104,a)].
% 199.32/199.63 54870 c_lessequals(c_fequal(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool),tc_fun(tc_bool,tc_bool)). [para(2055(a,1),54829(a,1))].
% 199.32/199.63 55022 hBOOL(c_in(c_Orderings_Obot__class_Obot(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool),tc_bool)). [resolve(54870,a,3467,b)].
% 199.32/199.63 55034 c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool),B) = c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool). [resolve(55022,a,44772,b)].
% 199.32/199.63 137549 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool). [para(7794(a,1),7988(b,2))].
% 199.32/199.63 137554 c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool) = A | c_HOL_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),tc_bool). [para(3895(a,1),137549(b,1)),rewrite([3895(5)]),flip(a)].
% 199.32/199.63 137577 c_Complete__Lattice_OSup__class_OSup(c_fequal(A,B),tc_bool) = A | -c_lessequals(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),A,tc_bool). [resolve(137554,b,103,c),unit_del(b,493)].
% 199.32/199.63 150473 c_SetInterval_Oord__class_OatLeastAtMost(c_Lattices_Olower__semilattice__class_Oinf(A,hAPP(c_fequal(B,C),D),tc_bool),hAPP(c_Set_Oinsert(B,E,C),D),tc_bool) != c_0. [resolve(8748,a,5314,c),unit_del(a,495)].
% 199.32/199.63 160784 A = B | -hBOOL(hAPP(c_fequal(B,C),A)). [resolve(11398,b,319,c),rewrite([4863(3),106(8)]),unit_del(b,2937)].
% 199.32/199.63 169096 c_HOL_Ominus__class_Ominus(A,c_COMBK(hAPP(c_fequal(B,C),B),D,E),tc_fun(F,tc_bool)) = c_0. [resolve(5025,a,3072,a),rewrite([6377(4)])].
% 199.32/199.63 169111 c_lessequals(A,c_COMBK(hAPP(c_fequal(B,C),B),D,E),tc_fun(F,tc_bool)). [para(169096(a,1),3754(a,1,2)),rewrite([5327(4)])].
% 199.32/199.63 169116 c_lessequals(hAPP(A,B),hAPP(c_fequal(C,D),C),tc_bool). [resolve(169111,a,90,c),rewrite([106(7)]),unit_del(a,498)].
% 199.32/199.63 169122 c_lessequals(A,hAPP(c_fequal(B,C),B),tc_bool). [resolve(169116,a,6511,b)].
% 199.32/199.63 169146 c_Complete__Lattice_OSup__class_OSup(c_fequal(hAPP(c_fequal(A,B),A),C),tc_bool) = hAPP(c_fequal(A,B),A). [resolve(169122,a,137577,b)].
% 199.32/199.63 169151 hAPP(c_fequal(A,B),A) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool). [resolve(169122,a,46695,b),rewrite([169146(5)])].
% 199.32/199.63 169152 c_Orderings_Obot__class_Obot(tc_bool) = A | c_lessequals(B,A,tc_bool). [resolve(169122,a,39488,c)].
% 199.32/199.63 169288 c_Orderings_Obot__class_Obot(tc_bool) = A | c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) = A. [resolve(169152,b,7798,b)].
% 199.32/199.63 169536 c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(c_Set_Oinsert(B,C,D),B),tc_bool) != c_0. [para(169151(a,1),150473(a,1,1,2)),rewrite([2034(5),5312(3),2028(4)])].
% 199.32/199.63 169904 c_fequal(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool) != c_0. [para(169288(b,2),5193(a,1)),flip(a)].
% 199.32/199.63 170800 c_fequal(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | C = A | -hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),C)). [para(169288(b,2),160784(b,1,1)),flip(a)].
% 199.32/199.63 170986 c_fequal(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | hAPP(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),A) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool). [para(169288(b,2),169151(a,1,1)),flip(a)].
% 199.32/199.63 171023 c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,c_Set_Oinsert(C,D,E),tc_fun(E,tc_bool)),C),tc_bool) != c_0. [para(253(a,1),169536(a,1,2,1))].
% 199.32/199.63 171650 c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,c_SetInterval_Oord__class_OatLeastAtMost(c_Orderings_Obot__class_Obot(tc_bool),C,tc_bool),tc_fun(D,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) != c_0. [para(55034(a,1),171023(a,1,2,1,2))].
% 199.32/199.63 173943 c_fequal(A,B) = c_Orderings_Obot__class_Obot(tc_bool) | c_Orderings_Obot__class_Obot(tc_bool) = c_0. [resolve(169904,b,169288,b)].
% 199.32/199.63 173949 c_Orderings_Obot__class_Obot(tc_bool) = c_0 | c_The(c_Orderings_Obot__class_Obot(tc_bool),A) = B. [para(173943(a,1),340(a,1,1))].
% 199.32/199.63 174691 c_Orderings_Obot__class_Obot(tc_bool) = c_0 | A = B. [para(173949(b,1),173949(b,1)),merge(b)].
% 199.32/199.63 174694 c_Orderings_Obot__class_Obot(tc_bool) = c_0. [factor(174691,a,b)].
% 199.32/199.63 174935 c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,c_SetInterval_Oord__class_OatLeastAtMost(c_0,C,tc_bool),tc_fun(D,tc_bool)),c_0),tc_bool) != c_0. [back_rewrite(171650),rewrite([174694(2),174694(8)])].
% 199.32/199.63 175109 hAPP(c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool),A) = c_Complete__Lattice_OInf__class_OInf(c_0,tc_bool). [back_rewrite(170986),rewrite([174694(3)]),unit_del(a,5193)].
% 199.32/199.63 175156 A = B. [back_rewrite(170800),rewrite([174694(3),175109(8)]),unit_del(a,5193),unit_del(c,28916)].
% 199.32/199.63 175157 $F. [resolve(175156,a,174935,a)].
% 199.32/199.63
% 199.32/199.63 % SZS output end Refutation
% 199.32/199.63 ============================== end of proof ==========================
% 199.32/199.63
% 199.32/199.63 ============================== STATISTICS ============================
% 199.32/199.63
% 199.32/199.63 Given=22625. Generated=7650832. Kept=175011. proofs=1.
% 199.32/199.63 Usable=21450. Sos=8720. Demods=1995. Limbo=462, Disabled=144945. Hints=0.
% 199.32/199.63 Megabytes=157.78.
% 199.32/199.63 User_CPU=194.16, System_CPU=4.29, Wall_clock=198.
% 199.32/199.63
% 199.32/199.63 ============================== end of statistics =====================
% 199.32/199.63
% 199.32/199.63 ============================== end of search =========================
% 199.32/199.63
% 199.32/199.63 THEOREM PROVED
% 199.32/199.63 % SZS status Unsatisfiable
% 199.32/199.63
% 199.32/199.63 Exiting with 1 proof.
% 199.32/199.63
% 199.32/199.63 Process 4156 exit (max_proofs) Wed Jun 15 08:53:45 2022
% 199.32/199.63 Prover9 interrupted
%------------------------------------------------------------------------------