TSTP Solution File: SCT053-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT053-1 : 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 22:03:38 EDT 2022
% Result : Timeout 300.02s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SCT053-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 04:24:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.11/1.35 ============================== Prover9 ===============================
% 1.11/1.35 Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.35 Process 1984 was started by sandbox on n015.cluster.edu,
% 1.11/1.35 Sat Jul 2 04:24:44 2022
% 1.11/1.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1824_n015.cluster.edu".
% 1.11/1.35 ============================== end of head ===========================
% 1.11/1.35
% 1.11/1.35 ============================== INPUT =================================
% 1.11/1.35
% 1.11/1.35 % Reading from file /tmp/Prover9_1824_n015.cluster.edu
% 1.11/1.35
% 1.11/1.35 set(prolog_style_variables).
% 1.11/1.35 set(auto2).
% 1.11/1.35 % set(auto2) -> set(auto).
% 1.11/1.35 % set(auto) -> set(auto_inference).
% 1.11/1.35 % set(auto) -> set(auto_setup).
% 1.11/1.35 % set(auto_setup) -> set(predicate_elim).
% 1.11/1.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.35 % set(auto) -> set(auto_limits).
% 1.11/1.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.35 % set(auto) -> set(auto_denials).
% 1.11/1.35 % set(auto) -> set(auto_process).
% 1.11/1.35 % set(auto2) -> assign(new_constants, 1).
% 1.11/1.35 % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.35 % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.35 % set(auto2) -> assign(max_hours, 1).
% 1.11/1.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.35 % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.35 % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.35 % set(auto2) -> set(sort_initial_sos).
% 1.11/1.35 % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.35 % set(auto2) -> assign(max_megs, 400).
% 1.11/1.35 % set(auto2) -> assign(stats, some).
% 1.11/1.35 % set(auto2) -> clear(echo_input).
% 1.11/1.35 % set(auto2) -> set(quiet).
% 1.11/1.35 % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.35 % set(auto2) -> clear(print_given).
% 1.11/1.35 assign(lrs_ticks,-1).
% 1.11/1.35 assign(sos_limit,10000).
% 1.11/1.35 assign(order,kbo).
% 1.11/1.35 set(lex_order_vars).
% 1.11/1.35 clear(print_given).
% 1.11/1.35
% 1.11/1.35 % formulas(sos). % not echoed (697 formulas)
% 1.11/1.35
% 1.11/1.35 ============================== end of input ==========================
% 1.11/1.35
% 1.11/1.35 % From the command line: assign(max_seconds, 300).
% 1.11/1.35
% 1.11/1.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.35
% 1.11/1.35 % Formulas that are not ordinary clauses:
% 1.11/1.35
% 1.11/1.35 ============================== end of process non-clausal formulas ===
% 1.11/1.35
% 1.11/1.35 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.35
% 1.11/1.35 ============================== PREDICATE ELIMINATION =================
% 1.11/1.35 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.11/1.35 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.11/1.35 3 -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].
% 1.11/1.35 4 -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].
% 1.11/1.35 5 -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].
% 1.11/1.35 6 -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].
% 1.11/1.35 7 -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].
% 1.11/1.35 8 -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].
% 1.11/1.35 9 -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].
% 1.11/1.35 10 -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].
% 1.11/1.35 11 -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].
% 1.11/1.35 12 -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].
% 1.11/1.35 13 -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].
% 1.11/1.35 14 -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].
% 1.11/1.35 15 -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].
% 1.11/1.35 16 -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].
% 1.11/1.35 17 -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].
% 1.11/1.35 18 -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].
% 1.11/1.35 19 -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].
% 1.11/1.35 20 -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].
% 1.11/1.35 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 1.11/1.35 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(1,a,3,a)].
% 1.11/1.35 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(1,a,4,a)].
% 1.11/1.35 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(1,a,5,a)].
% 1.11/1.35 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(1,a,6,a)].
% 1.11/1.35 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(1,a,7,a)].
% 1.11/1.35 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(1,a,10,a)].
% 1.11/1.35 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(1,a,11,a)].
% 1.11/1.35 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(1,a,12,a)].
% 1.11/1.35 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(1,a,13,a)].
% 1.11/1.40 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(1,a,14,a)].
% 1.11/1.40 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(1,a,15,a)].
% 1.11/1.40 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(1,a,16,a)].
% 1.11/1.40 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(1,a,17,a)].
% 1.11/1.40 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(1,a,18,a)].
% 1.11/1.40 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.11/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,2,a)].
% 1.11/1.40 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(21,a,3,a)].
% 1.11/1.40 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(21,a,4,a)].
% 1.11/1.40 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(21,a,5,a)].
% 1.11/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,6,a)].
% 1.11/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,7,a)].
% 1.11/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 1.11/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 1.11/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,12,a)].
% 1.11/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(21,a,13,a)].
% 1.11/1.40 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(21,a,14,a)].
% 1.11/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(21,a,15,a)].
% 1.11/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(21,a,16,a)].
% 1.11/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,17,a)].
% 1.11/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 1.11/1.40 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.11/1.40 23 -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].
% 1.11/1.40 24 -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].
% 1.11/1.40 25 -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].
% 1.11/1.40 26 -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].
% 1.11/1.40 27 -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].
% 1.11/1.40 28 -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].
% 1.11/1.40 29 -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].
% 1.11/1.40 30 -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].
% 1.11/1.40 31 -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].
% 1.11/1.40 32 -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].
% 1.11/1.40 33 -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].
% 1.11/1.40 34 -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].
% 1.11/1.40 35 -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].
% 1.11/1.40 36 -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].
% 1.11/1.40 37 -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].
% 1.11/1.40 38 -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].
% 1.11/1.40 39 -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].
% 1.11/1.40 40 -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].
% 1.11/1.40 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.11/1.40 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(22,a,23,a)].
% 1.11/1.40 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(22,a,24,a)].
% 1.11/1.40 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(22,a,25,a)].
% 1.11/1.40 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(22,a,26,a)].
% 1.11/1.40 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(22,a,27,a)].
% 1.11/1.40 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(22,a,28,a)].
% 1.11/1.40 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(22,a,29,a)].
% 1.11/1.40 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(22,a,30,a)].
% 1.11/1.40 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(22,a,31,a)].
% 1.11/1.40 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(22,a,32,a)].
% 1.11/1.40 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(22,a,35,a)].
% 1.11/1.40 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(22,a,38,a)].
% 1.11/1.40 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(22,a,39,a)].
% 1.11/1.40 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(22,a,40,a)].
% 1.11/1.40 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 1.11/1.40 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.11/1.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 1.11/1.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 1.11/1.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 1.11/1.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(42,a,26,a)].
% 1.11/1.40 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(42,a,27,a)].
% 1.11/1.40 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(42,a,28,a)].
% 1.11/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(42,a,29,a)].
% 1.11/1.40 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(42,a,30,a)].
% 1.11/1.40 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(42,a,31,a)].
% 1.11/1.40 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(42,a,32,a)].
% 1.11/1.40 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(42,a,35,a)].
% 1.25/1.48 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(42,a,38,a)].
% 1.25/1.48 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(42,a,39,a)].
% 1.25/1.48 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(42,a,40,a)].
% 1.25/1.48 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(42,a,41,a)].
% 1.25/1.48 43 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].
% 1.25/1.48 44 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].
% 1.25/1.48 45 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].
% 1.25/1.48 46 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].
% 1.25/1.48 47 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].
% 1.25/1.48 48 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 1.25/1.48 49 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_in(B,E,C) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 1.25/1.48 50 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_in(B,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 1.25/1.48 51 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(D,E,C) | -c_in(B,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 1.25/1.48 52 c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 1.25/1.48 53 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -c_in(c_Pair(A,D,B,B),C,tc_prod(B,B)) | -c_in(D,E,B) | -c_in(A,E,B) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 1.25/1.48 54 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -c_in(D,E,B) | -c_in(A,E,B) | -c_Equiv__Relations_Oequiv(E,C,B) | c_in(c_Pair(A,D,B,B),C,tc_prod(B,B)) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 1.25/1.48 55 c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) | -c_in(B,E,C) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 1.25/1.48 56 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) | A = B | -c_in(B,c_Equiv__Relations_Oquotient(D,E,C),tc_fun(C,tc_bool)) | -c_in(A,c_Equiv__Relations_Oquotient(D,E,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(D,E,C) # label(cls_quotient__disj_0) # label(axiom). [assumption].
% 1.25/1.48 57 c_in(A,c_Relation_OImage(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),C) | -c_in(A,D,C) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 1.25/1.48 58 c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 1.25/1.48 59 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 1.25/1.48 60 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 1.25/1.48 61 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].
% 1.25/1.48 62 -c_in(A,B,C) | -c_in(D,B,C) | -c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool)) | -c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,F,C) | c_in(c_Pair(D,A,C,C),F,tc_prod(C,C)) # label(cls_quotient__eq__iff_0) # label(axiom). [assumption].
% 1.25/1.48 63 A = B | -c_in(c_Pair(C,D,E,E),F,tc_prod(E,E)) | -c_in(D,B,E) | -c_in(C,A,E) | -c_in(B,c_Equiv__Relations_Oquotient(V6,F,E),tc_fun(E,tc_bool)) | -c_in(A,c_Equiv__Relations_Oquotient(V6,F,E),tc_fun(E,tc_bool)) | -c_Equiv__Relations_Oequiv(V6,F,E) # label(cls_quotient__eqI_0) # label(axiom). [assumption].
% 1.25/1.48 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B). [resolve(47,b,48,d)].
% 1.25/1.48 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B). [resolve(47,b,50,e)].
% 1.25/1.48 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(47,b,52,c)].
% 1.25/1.48 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B). [resolve(47,b,53,e)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B) | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(47,b,54,d)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)). [resolve(47,b,55,d)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | C = D | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(C,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)). [resolve(47,b,56,e)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(C,c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B). [resolve(47,b,57,c)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)),B). [resolve(47,b,58,c)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(47,b,59,c)].
% 1.25/1.49 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(47,b,61,b)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | -c_in(C,D,B) | -c_in(E,D,B) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | c_in(c_Pair(E,C,B,B),A,tc_prod(B,B)). [resolve(47,b,62,e)].
% 1.25/1.49 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | C = D | -c_in(c_Pair(E,F,B,B),A,tc_prod(B,B)) | -c_in(F,D,B) | -c_in(E,C,B) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(C,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)). [resolve(47,b,63,g)].
% 1.25/1.49 64 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].
% 1.25/1.49 65 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 1.25/1.49 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(65,b,47,b)].
% 1.25/1.49 66 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 1.25/1.49 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(66,b,47,b)].
% 1.25/1.49 67 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -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].
% 1.41/1.68 Derived: c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -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(67,d,47,b)].
% 1.41/1.68 68 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 1.41/1.68 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(68,b,47,b)].
% 1.41/1.68 69 c_in(A,B,C) | -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].
% 1.41/1.68 Derived: c_in(A,c_Relation_ODomain(B,C,C),C) | -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(69,c,47,b)].
% 1.41/1.68 70 c_in(A,B,C) | -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].
% 1.41/1.68 71 -c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | -c_Relation_Oirrefl(C,B) # label(cls_irrefl__def_0) # label(axiom). [assumption].
% 1.41/1.68 72 c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(A,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),B) # label(cls_irrefl__diff__Id_0) # label(axiom). [assumption].
% 1.41/1.68 73 c_Relation_Oirrefl(A,B) | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),B,B),A,tc_prod(B,B)) # label(cls_irrefl__def_1) # label(axiom). [assumption].
% 1.41/1.68 Derived: -c_in(c_Pair(A,A,B,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),tc_prod(B,B)). [resolve(71,b,72,a)].
% 1.41/1.68 Derived: -c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),B,B),C,tc_prod(B,B)). [resolve(71,b,73,a)].
% 1.41/1.68 74 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].
% 1.41/1.68 75 c_Nitpick_Orefl_H(A,B) | -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].
% 1.41/1.68 Derived: c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | -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(74,b,75,a)].
% 1.41/1.68 76 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].
% 1.41/1.68 77 c_FunDef_Oin__rel(A,B,C,D,E) | -c_in(c_Pair(B,C,D,E),A,tc_prod(D,E)) # label(cls_in__rel__def_1) # label(axiom). [assumption].
% 1.41/1.68 78 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.41/1.68 79 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.41/1.68 Derived: A = A. [resolve(78,b,79,a)].
% 1.41/1.68
% 1.41/1.68 ============================== end predicate elimination =============
% 1.41/1.68
% 1.41/1.68 Auto_denials: (non-Horn, no changes).
% 1.41/1.68
% 1.41/1.68 Term ordering decisions:
% 1.41/1.68 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Arrow__Order__Mirabelle_OLin=1. v_b____=1. t_a=1. v_a____=1. v_c____=1. v_P____=1. t_b=1. c_Arrow__Order__Mirabelle_OProf=1. v_r=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_HOL_Ouminus__class_Ouminus=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=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__Xirrefl__def__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__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_Relation_OId=1. v_F=1. v_P_H____=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Equiv__Relations_Oquotient=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__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Product__Type_OSigma=1. c_Relation_OImage=1. c_Set_Oimage=1. c_Relation_Oinv__image=1. c_split=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__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_COMBC=1. c_COMBB=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1=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.
% 2.96/3.27
% 2.96/3.27 ============================== end of process initial clauses ========
% 2.96/3.27
% 2.96/3.27 ============================== CLAUSES FOR SEARCH ====================
% 2.96/3.27
% 2.96/3.27 ============================== end of clauses for search =============
% 2.96/3.27
% 2.96/3.27 ============================== SEARCH ================================
% 2.96/3.27
% 2.96/3.27 % Starting search at 0.44 seconds.
% 2.96/3.27
% 2.96/3.27 Low Water (keep): wt=63.000, iters=3404
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% 2.96/3.27 Low Water (keep): wt=61.000, iters=3446
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% 2.96/3.27 Low Water (keep): wt=58.000, iters=3367
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% 2.96/3.27 Low Water (keep): wt=55.000, iters=3387
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% 2.96/3.27 Low Water (keep): wt=52.000, iters=3343
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% 2.96/3.27 Low Water (keep): wt=50.000, iters=3394
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% 2.96/3.27 Low Water (keep): wt=49.000, iters=3349
% 2.96/3.27
% 2.96/3.27 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 48 (0.00 of 1.03 sec).
% 2.96/3.27
% 2.96/3.27 Low Water (keep): wt=48.000, iters=3421
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% 2.96/3.27 Low Water (keep): wt=47.000, iters=3402
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% 2.96/3.27 Low Water (keep): wt=45.000, iters=3353
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% 2.96/3.27 Low Water (keep): wt=44.000, iters=3404
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% 2.96/3.27 Low Water (keep): wt=41.000, iters=3349
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% 2.96/3.27 Low Water (keep): wt=40.000, iters=3335
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% 2.96/3.27 Low Water (keep): wt=39.000, iters=3368
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% 2.96/3.27 Low Water (keep): wt=38.000, iters=3379
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% 2.96/3.27 Low Water (keep): wt=37.000, iters=3351
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% 2.96/3.27 Low Water (keep): wt=35.000, iters=3344
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% 2.96/3.27 Low Water (keep): wt=34.000, iters=3386
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% 2.96/3.27 Low Water (keep): wt=33.000, iters=3342
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% 2.96/3.27 Low Water (keep): wt=32.000, iters=3345
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% 2.96/3.27 Low Water (keep): wt=31.000, iters=3376
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% 2.96/3.27 Low Water (keep): wt=30.000, iters=3360
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% 2.96/3.27 Low Water (keep): wt=29.000, iters=3540
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% 2.96/3.27 Low Water (keep): wt=28.000, iters=3346
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% 2.96/3.27 Low Water (keep): wt=27.000, iters=3355
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% 2.96/3.27 Low Water (keep): wt=26.000, iters=3336
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% 2.96/3.27 Low Water (keep): wt=25.000, iters=3378
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% 2.96/3.27 Low Water (keep): wt=24.000, iters=3364
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% 2.96/3.27 Low Water (keep): wt=23.000, iters=3409
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% 2.96/3.27 Low Water (keep): wt=22.000, iters=3379
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% 2.96/3.27 Low Water (keep): wt=21.000, iters=3348
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% 2.96/3.27 Low Water (keep): wt=20.000, iters=3339
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=3878, wt=165.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=3868, wt=163.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=2860, wt=162.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=2858, wt=160.000
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% 2.96/3.27 Low Water (displace): id=3863, wt=146.000
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% 2.96/3.27 Low Water (displace): id=2849, wt=143.000
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% 2.96/3.27 Low Water (displace): id=3788, wt=140.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=3783, wt=139.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=3890, wt=138.000
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% 2.96/3.27 Low Water (displace): id=2914, wt=137.000
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% 2.96/3.27 Low Water (displace): id=3888, wt=136.000
% 2.96/3.27
% 2.96/3.27 Low Water (displace): id=3793, wt=135.000
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% 2.96/3.27 Low Water (displace): id=2870, wt=133.000
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% 2.96/3.27 Low Water (displace): id=3900, wt=132.000
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% 2.96/3.27 Low Water (displace): id=3904, wt=130.000
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% 2.96/3.27 Low Water (displace): id=2888, wt=129.000
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% 2.96/3.27 Low Water (displace): id=3789, wt=126.000
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% 2.96/3.27 Low Water (displace): id=2851, wt=125.000
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% 2.96/3.27 Low Water (displace): id=3261, wt=119.000
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% 2.96/3.27 Low Water (displace): id=3876, wt=117.000
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% 2.96/3.27 Low Water (displace): id=3801, wt=115.000
% 2.96/3.27
% 2.96/3.27 Low Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------