TSTP Solution File: SCT020-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT020-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 : Mon Jul 18 22:03:28 EDT 2022
% Result : Timeout 300.01s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT020-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 06:19:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.00/1.34 ============================== Prover9 ===============================
% 1.00/1.34 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.34 Process 9115 was started by sandbox2 on n015.cluster.edu,
% 1.00/1.34 Sat Jul 2 06:19:15 2022
% 1.00/1.34 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8962_n015.cluster.edu".
% 1.00/1.34 ============================== end of head ===========================
% 1.00/1.34
% 1.00/1.34 ============================== INPUT =================================
% 1.00/1.34
% 1.00/1.34 % Reading from file /tmp/Prover9_8962_n015.cluster.edu
% 1.00/1.34
% 1.00/1.34 set(prolog_style_variables).
% 1.00/1.34 set(auto2).
% 1.00/1.34 % set(auto2) -> set(auto).
% 1.00/1.34 % set(auto) -> set(auto_inference).
% 1.00/1.34 % set(auto) -> set(auto_setup).
% 1.00/1.34 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.34 % set(auto) -> set(auto_limits).
% 1.00/1.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.34 % set(auto) -> set(auto_denials).
% 1.00/1.34 % set(auto) -> set(auto_process).
% 1.00/1.34 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.34 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.34 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.34 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.34 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.34 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.34 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.34 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.34 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.34 % set(auto2) -> assign(stats, some).
% 1.00/1.34 % set(auto2) -> clear(echo_input).
% 1.00/1.34 % set(auto2) -> set(quiet).
% 1.00/1.34 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.34 % set(auto2) -> clear(print_given).
% 1.00/1.34 assign(lrs_ticks,-1).
% 1.00/1.34 assign(sos_limit,10000).
% 1.00/1.34 assign(order,kbo).
% 1.00/1.34 set(lex_order_vars).
% 1.00/1.34 clear(print_given).
% 1.00/1.34
% 1.00/1.34 % formulas(sos). % not echoed (713 formulas)
% 1.00/1.34
% 1.00/1.34 ============================== end of input ==========================
% 1.00/1.34
% 1.00/1.34 % From the command line: assign(max_seconds, 300).
% 1.00/1.34
% 1.00/1.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.34
% 1.00/1.34 % Formulas that are not ordinary clauses:
% 1.00/1.34
% 1.00/1.34 ============================== end of process non-clausal formulas ===
% 1.00/1.34
% 1.00/1.34 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.34
% 1.00/1.34 ============================== PREDICATE ELIMINATION =================
% 1.00/1.34 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.34 2 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.00/1.34 3 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.00/1.34 4 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.00/1.35 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.00/1.35 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.00/1.35 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.00/1.35 8 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.00/1.35 9 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.00/1.35 10 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.00/1.35 11 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.00/1.35 12 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.00/1.35 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.00/1.35 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.00/1.35 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.00/1.35 16 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.00/1.35 17 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.00/1.35 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.00/1.35 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.00/1.35 20 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),B) = B. [resolve(1,a,2,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)). [resolve(1,a,3,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),E)). [resolve(1,a,4,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,5,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)). [resolve(1,a,6,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),B),tc_fun(D,A)). [resolve(1,a,7,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = B | -c_lessequals(D,B,tc_fun(C,A)). [resolve(1,a,10,a)].
% 1.00/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) != D | c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,11,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = D | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,12,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(E,tc_fun(D,A)),B),C,tc_fun(D,A)). [resolve(1,a,13,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(D,A)),E),C,tc_fun(D,A)). [resolve(1,a,14,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,15,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),B). [resolve(1,a,16,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D). [resolve(1,a,17,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,18,a)].
% 1.00/1.39 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),A) = A. [resolve(21,a,2,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)). [resolve(21,a,3,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C)). [resolve(21,a,4,a)].
% 1.00/1.39 Derived: c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,5,a)].
% 1.00/1.39 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool). [resolve(21,a,6,a)].
% 1.00/1.39 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A),tc_bool). [resolve(21,a,7,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,12,a)].
% 1.00/1.39 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_bool),A),B,tc_bool). [resolve(21,a,13,a)].
% 1.00/1.39 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C),B,tc_bool). [resolve(21,a,14,a)].
% 1.00/1.39 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,15,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A). [resolve(21,a,16,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B). [resolve(21,a,17,a)].
% 1.00/1.39 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 1.00/1.39 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.39 23 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.00/1.39 24 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.00/1.39 25 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.00/1.39 26 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.00/1.39 27 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),A),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.00/1.39 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.00/1.39 29 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.00/1.39 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.00/1.39 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.00/1.39 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.00/1.39 33 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.00/1.39 34 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.00/1.39 35 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.00/1.39 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.00/1.39 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.00/1.39 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.00/1.39 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.00/1.39 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.00/1.39 41 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = B | -c_lessequals(B,D,tc_fun(C,A)). [resolve(22,a,23,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) != B | c_lessequals(B,D,tc_fun(C,A)). [resolve(22,a,24,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = D | -c_lessequals(D,B,tc_fun(C,A)). [resolve(22,a,25,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),E)). [resolve(22,a,26,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)). [resolve(22,a,27,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(22,a,28,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),D,tc_fun(C,A)). [resolve(22,a,31,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),B,tc_fun(C,A)). [resolve(22,a,32,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D). [resolve(22,a,33,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),B) = B. [resolve(22,a,34,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),B). [resolve(22,a,35,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)). [resolve(22,a,36,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(E,tc_fun(D,A)),C),tc_fun(D,A)). [resolve(22,a,37,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(22,a,38,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)). [resolve(22,a,39,a)].
% 1.00/1.39 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.39 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),C)). [resolve(42,a,26,a)].
% 1.00/1.39 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)). [resolve(42,a,27,a)].
% 1.00/1.39 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(42,a,28,a)].
% 1.00/1.40 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),B,tc_bool). [resolve(42,a,31,a)].
% 1.00/1.40 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),A,tc_bool). [resolve(42,a,32,a)].
% 1.00/1.40 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B). [resolve(42,a,33,a)].
% 1.00/1.40 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),A) = A. [resolve(42,a,34,a)].
% 1.00/1.40 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),A). [resolve(42,a,35,a)].
% 1.00/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool). [resolve(42,a,36,a)].
% 1.00/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_bool),B),tc_bool). [resolve(42,a,37,a)].
% 1.00/1.40 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(42,a,38,a)].
% 1.00/1.40 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(42,a,39,a)].
% 1.00/1.40 43 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oequiv(c_Relation_ODomain(A,B,B),A,B) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 1.00/1.40 44 c_lessequals(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 1.00/1.40 45 c_lessequals(A,c_Product__Type_OSigma(B,c_COMBK(B,tc_fun(C,tc_bool),C),C,C),tc_fun(tc_prod(C,C),tc_bool)) | -c_Equiv__Relations_Oequiv(B,A,C) # label(cls_equiv__type_0) # label(axiom). [assumption].
% 1.00/1.40 46 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(B,E,C)) | -c_lessequals(hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 1.00/1.40 47 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(E,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),tc_fun(C,tc_bool)),hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))))),C)) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 1.00/1.40 48 hBOOL(c_in(A,hAPP(c_Relation_OImage(B,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),C)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 1.00/1.40 49 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 1.00/1.40 50 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 1.00/1.40 51 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 1.00/1.41 52 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -c_Equiv__Relations_Oequiv(E,A,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 1.00/1.41 53 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 1.00/1.41 54 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 1.00/1.41 55 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(43,b,44,c)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(A,c_Product__Type_OSigma(c_Relation_ODomain(A,B,B),c_COMBK(c_Relation_ODomain(A,B,B),tc_fun(B,tc_bool),B),B,B),tc_fun(tc_prod(B,B),tc_bool)). [resolve(43,b,45,b)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -c_lessequals(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)). [resolve(43,b,46,d)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(E,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))),B)). [resolve(43,b,47,c)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(C,hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(43,b,48,c)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(43,b,49,c)].
% 1.00/1.41 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)). [resolve(43,b,51,d)].
% 1.00/1.61 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_Otrans(A,B). [resolve(43,b,55,b)].
% 1.00/1.61 56 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) = A | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 1.00/1.61 57 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 1.00/1.61 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(57,b,43,b)].
% 1.00/1.61 58 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 1.00/1.61 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(58,b,43,b)].
% 1.00/1.61 59 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,F,V6)) | -c_Equiv__Relations_Ocongruent2(V7,A,B,V6,D,E) | -c_Equiv__Relations_Oequiv(F,V7,V6) # label(cls_congruent2__implies__congruent_0) # label(axiom). [assumption].
% 1.00/1.61 Derived: c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,c_Relation_ODomain(F,V6,V6),V6)) | -c_Equiv__Relations_Ocongruent2(F,A,B,V6,D,E) | c_Relation_Orel__comp(c_Relation_Oconverse(F,V6,V6),F,V6,V6,V6) != F. [resolve(59,d,43,b)].
% 1.00/1.61 60 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 1.00/1.61 Derived: hBOOL(c_in(A,c_Relation_ODomain(B,C,C),C)) | -hBOOL(c_in(c_Pair(D,A,C,C),B,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(B,C,C),B,C,C,C) != B. [resolve(60,c,43,b)].
% 1.00/1.61 61 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(A,D,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 1.00/1.61 62 hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Nitpick_Orefl_H(C,B) # label(cls_Nitpick_Orefl_H__def_0) # label(axiom). [assumption].
% 1.00/1.61 63 c_Nitpick_Orefl_H(A,B) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_Nitpick_Orefl_H__def_1) # label(axiom). [assumption].
% 1.00/1.61 Derived: hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(62,b,63,a)].
% 1.00/1.61 64 c_Order__Relation_Ostrict__linear__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | -c_Relation_Oirrefl(B,C) | -c_Relation_Otrans(B,C) # label(cls_strict__linear__order__on__def_3) # label(axiom). [assumption].
% 1.00/1.61 65 c_Relation_Otrans(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_0) # label(axiom). [assumption].
% 1.00/1.61 66 c_Relation_Ototal__on(A,B,C) | -c_Order__Relation_Ostrict__linear__order__on(A,B,C) # label(cls_strict__linear__order__on__def_2) # label(axiom). [assumption].
% 1.00/1.61 67 c_Relation_Oirrefl(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_1) # label(axiom). [assumption].
% 1.00/1.61 68 hBOOL(c_in(c_Pair(A,B,C,D),E,tc_prod(C,D))) | -c_FunDef_Oin__rel(E,A,B,C,D) # label(cls_in__rel__def_0) # label(axiom). [assumption].
% 1.00/1.61 69 c_FunDef_Oin__rel(A,B,C,D,E) | -hBOOL(c_in(c_Pair(B,C,D,E),A,tc_prod(D,E))) # label(cls_in__rel__def_1) # label(axiom). [assumption].
% 1.00/1.61 70 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.00/1.61 71 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.00/1.61 Derived: A = A. [resolve(70,b,71,a)].
% 1.00/1.61
% 1.00/1.61 ============================== end predicate elimination =============
% 1.00/1.61
% 1.00/1.61 Auto_denials: (non-Horn, no changes).
% 1.00/1.61
% 1.00/1.61 Term ordering decisions:
% 1.00/1.61 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. v_x=1. v_P=1. t_b=1. v_r=1. v_a=1. v_b=1. v_i=1. hAPP=1. tc_fun=1. tc_prod=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_Transitive__Closure_Ortrancl=1. c_HOL_Ominus__class_Ominus=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Complete__Lattice_OSup__class_OSup=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_ATP__Linkup_Osko__Relation__XIdE__1__1=1. c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1=1. c_ATP__Linkup_Osko__Relation__XtransI__1__1=1. c_ATP__Linkup_Osko__Relation__XtransI__1__2=1. c_ATP__Linkup_Osko__Relation__XtransI__1__3=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3=1. c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1=1. c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_Relation_OId=1. v_F=1. v_Pa=1. c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1=1. c_in=1. c_Relation_Oconverse=1. c_Relation_OImage=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1=1. c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2=1. c_ATP__Linkup_Osko__Relation__XId__onE__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1=1. c_List_Osko__Recdef__Xtfl__wf__induct__1__1=1. v_sko__Transitive__Closure__Xtrancl__Xcases__1=1. c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Set_Oimage=1. c_Product__Type_OSigma=1. c_Relation_Oinv__image=1. c_split=1. c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomainE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_Relation_Orel__comp=1. c_COMBB=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 1.98/2.23
% 1.98/2.23 ============================== end of process initial clauses ========
% 1.98/2.23
% 1.98/2.23 ============================== CLAUSES FOR SEARCH ====================
% 1.98/2.23
% 1.98/2.23 ============================== end of clauses for search =============
% 1.98/2.23
% 1.98/2.23 ============================== SEARCH ================================
% 1.98/2.23
% 1.98/2.23 % Starting search at 0.36 seconds.
% 1.98/2.23
% 1.98/2.23 Low Water (keep): wt=60.000, iters=3531
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% 1.98/2.23 Low Water (keep): wt=53.000, iters=3398
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% 1.98/2.23 Low Water (keep): wt=51.000, iters=3333
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% 1.98/2.23 Low Water (keep): wt=50.000, iters=3367
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% 1.98/2.23 Low Water (keep): wt=49.000, iters=3356
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% 1.98/2.23 Low Water (keep): wt=48.000, iters=3380
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% 1.98/2.23 Low Water (keep): wt=47.000, iters=3536
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% 1.98/2.23 Low Water (keep): wt=43.000, iters=3396
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% 1.98/2.23 NOTE: Back_subsumption disabled, ratio of keptCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------