TSTP Solution File: SCT062-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT062-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 22:03:41 EDT 2022
% Result : Timeout 300.04s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SCT062-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n026.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sat Jul 2 06:45:35 EDT 2022
% 0.09/0.29 % CPUTime :
% 1.06/1.42 ============================== Prover9 ===============================
% 1.06/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.06/1.42 Process 4043 was started by sandbox2 on n026.cluster.edu,
% 1.06/1.42 Sat Jul 2 06:45:36 2022
% 1.06/1.42 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3889_n026.cluster.edu".
% 1.06/1.42 ============================== end of head ===========================
% 1.06/1.42
% 1.06/1.42 ============================== INPUT =================================
% 1.06/1.42
% 1.06/1.42 % Reading from file /tmp/Prover9_3889_n026.cluster.edu
% 1.06/1.42
% 1.06/1.42 set(prolog_style_variables).
% 1.06/1.42 set(auto2).
% 1.06/1.42 % set(auto2) -> set(auto).
% 1.06/1.42 % set(auto) -> set(auto_inference).
% 1.06/1.42 % set(auto) -> set(auto_setup).
% 1.06/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.06/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.06/1.42 % set(auto) -> set(auto_limits).
% 1.06/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.06/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.06/1.42 % set(auto) -> set(auto_denials).
% 1.06/1.42 % set(auto) -> set(auto_process).
% 1.06/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.06/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.06/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.06/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.06/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.06/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.06/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.06/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.06/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.06/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.06/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.06/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.06/1.42 % set(auto2) -> assign(stats, some).
% 1.06/1.42 % set(auto2) -> clear(echo_input).
% 1.06/1.42 % set(auto2) -> set(quiet).
% 1.06/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.06/1.42 % set(auto2) -> clear(print_given).
% 1.06/1.42 assign(lrs_ticks,-1).
% 1.06/1.42 assign(sos_limit,10000).
% 1.06/1.42 assign(order,kbo).
% 1.06/1.42 set(lex_order_vars).
% 1.06/1.42 clear(print_given).
% 1.06/1.42
% 1.06/1.42 % formulas(sos). % not echoed (701 formulas)
% 1.06/1.42
% 1.06/1.42 ============================== end of input ==========================
% 1.06/1.42
% 1.06/1.42 % From the command line: assign(max_seconds, 300).
% 1.06/1.42
% 1.06/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.06/1.42
% 1.06/1.42 % Formulas that are not ordinary clauses:
% 1.06/1.42
% 1.06/1.42 ============================== end of process non-clausal formulas ===
% 1.06/1.42
% 1.06/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.06/1.42
% 1.06/1.42 ============================== PREDICATE ELIMINATION =================
% 1.06/1.42 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.06/1.42 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 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].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.42 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,2,a)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,6,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,7,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,12,a)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 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].
% 1.06/1.45 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.45 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 1.06/1.46 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.06/1.46 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 1.06/1.46 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 1.06/1.46 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.46 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)].
% 1.06/1.54 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(42,a,38,a)].
% 1.06/1.54 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(42,a,39,a)].
% 1.06/1.54 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)].
% 1.06/1.54 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(42,a,41,a)].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 47 c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_Equiv__Relations_Oequiv(c_Relation_ODomain(B,A,A),B,A) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 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].
% 1.06/1.54 53 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].
% 1.06/1.54 54 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].
% 1.06/1.54 55 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].
% 1.06/1.54 56 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].
% 1.06/1.54 57 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].
% 1.06/1.54 58 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].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) != c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) | c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)) | -c_in(D,c_Relation_ODomain(B,A,A),A). [resolve(47,b,48,d)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) = c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) | -c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)) | -c_in(D,c_Relation_ODomain(B,A,A),A) | -c_in(C,c_Relation_ODomain(B,A,A),A). [resolve(47,b,50,e)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_lessequals(c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)) | -c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)). [resolve(47,b,52,c)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_in(C,c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),A) | -c_in(C,c_Relation_ODomain(B,A,A),A). [resolve(47,b,53,c)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)),A). [resolve(47,b,54,c)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) = c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A) | -c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)). [resolve(47,b,55,c)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_in(c_Pair(C,D,A,A),B,tc_prod(A,A)) | -c_in(D,c_Relation_ODomain(B,A,A),A) | -c_lessequals(c_Relation_OImage(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(B,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)). [resolve(47,b,57,d)].
% 1.06/1.54 Derived: c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) != B | c_lessequals(B,c_Product__Type_OSigma(c_Relation_ODomain(B,A,A),c_COMBK(c_Relation_ODomain(B,A,A),tc_fun(A,tc_bool),A),A,A),tc_fun(tc_prod(A,A),tc_bool)). [resolve(47,b,58,b)].
% 1.06/1.54 59 c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(A,A),B),B,A,A,A) = B | -c_Equiv__Relations_Oequiv(C,B,A) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 1.06/1.54 60 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 1.06/1.54 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(B,B),A),A,B,B,B) != A. [resolve(60,b,47,b)].
% 1.46/1.77 61 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 1.46/1.77 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(B,B),A),A,B,B,B) != A. [resolve(61,b,47,b)].
% 1.46/1.77 62 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].
% 1.46/1.77 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(hAPP(c_Relation_Oconverse(V6,V6),F),F,V6,V6,V6) != F. [resolve(62,d,47,b)].
% 1.46/1.77 63 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 1.46/1.77 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(B,B),A),A,B,B,B) != A. [resolve(63,b,47,b)].
% 1.46/1.77 64 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].
% 1.46/1.77 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(hAPP(c_Relation_Oconverse(C,C),B),B,C,C,C) != B. [resolve(64,c,47,b)].
% 1.46/1.77 65 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].
% 1.46/1.77 66 -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].
% 1.46/1.77 67 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].
% 1.46/1.77 68 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].
% 1.46/1.77 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(66,b,67,a)].
% 1.46/1.77 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(66,b,68,a)].
% 1.46/1.77 69 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].
% 1.46/1.77 70 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].
% 1.46/1.77 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(69,b,70,a)].
% 1.46/1.77 71 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].
% 1.46/1.77 72 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].
% 1.46/1.77 73 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.46/1.77 74 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.46/1.77 Derived: A = A. [resolve(73,b,74,a)].
% 1.46/1.77
% 1.46/1.77 ============================== end predicate elimination =============
% 1.46/1.77
% 1.46/1.77 Auto_denials: (non-Horn, no changes).
% 1.46/1.77
% 1.46/1.77 Term ordering decisions:
% 1.46/1.77 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. v_b____=1. v_P____=1. v_P_H____=1. v_a____=1. v_c____=1. t_b=1. v_r=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Relation_Oconverse=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. c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1=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__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. v_F=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_ODomain=1. c_COMBK=1. c_Relation_ORange=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_Product__Type_OSigma=1. c_Relation_OImage=1. c_Set_Oimage=1. v_sko__local__X3__1=1. c_Relation_Oinv__image=1. c_split=1. c_ATP__Linkup_Osko__Relation__XconverseE__1__1=1. c_ATP__Linkup_Osko__Relation__XconverseE__1__2=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_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1=1. c_Relation_Orel__comp=1. c_Fun_Ocomp=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. v_sko__local__X2__1=1. v_sko__local__X1__1=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 3.28/3.69
% 3.28/3.69 ============================== end of process initial clauses ========
% 3.28/3.69
% 3.28/3.69 ============================== CLAUSES FOR SEARCH ====================
% 3.28/3.69
% 3.28/3.69 ============================== end of clauses for search =============
% 3.28/3.69
% 3.28/3.69 ============================== SEARCH ================================
% 3.28/3.69
% 3.28/3.69 % Starting search at 0.42 seconds.
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=60.000, iters=3358
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=53.000, iters=3337
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=52.000, iters=3358
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=49.000, iters=3355
% 3.28/3.69
% 3.28/3.69 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 72 (0.00 of 1.47 sec).
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=48.000, iters=3423
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=47.000, iters=3397
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=44.000, iters=3355
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=43.000, iters=3355
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=42.000, iters=3341
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=41.000, iters=3353
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=40.000, iters=3346
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=39.000, iters=3420
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=38.000, iters=3355
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=37.000, iters=3353
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=36.000, iters=3340
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=35.000, iters=3341
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=34.000, iters=3345
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=33.000, iters=3346
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=32.000, iters=3544
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=31.000, iters=3426
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=30.000, iters=3375
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=29.000, iters=3350
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=28.000, iters=3348
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=27.000, iters=3361
% 3.28/3.69
% 3.28/3.69 Low Water (keep): wt=26.Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------