TSTP Solution File: SCT008-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT008-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 22:03:24 EDT 2022
% Result : Timeout 300.04s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SCT008-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Fri Jul 1 22:19:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/1.24 ============================== Prover9 ===============================
% 0.94/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.94/1.24 Process 28317 was started by sandbox on n010.cluster.edu,
% 0.94/1.24 Fri Jul 1 22:19:04 2022
% 0.94/1.24 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28164_n010.cluster.edu".
% 0.94/1.24 ============================== end of head ===========================
% 0.94/1.24
% 0.94/1.24 ============================== INPUT =================================
% 0.94/1.24
% 0.94/1.24 % Reading from file /tmp/Prover9_28164_n010.cluster.edu
% 0.94/1.24
% 0.94/1.24 set(prolog_style_variables).
% 0.94/1.24 set(auto2).
% 0.94/1.24 % set(auto2) -> set(auto).
% 0.94/1.24 % set(auto) -> set(auto_inference).
% 0.94/1.24 % set(auto) -> set(auto_setup).
% 0.94/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.94/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.94/1.24 % set(auto) -> set(auto_limits).
% 0.94/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.94/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.94/1.24 % set(auto) -> set(auto_denials).
% 0.94/1.24 % set(auto) -> set(auto_process).
% 0.94/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.94/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.94/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.94/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.94/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.94/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.94/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.94/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.94/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.94/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.94/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.94/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.94/1.24 % set(auto2) -> assign(stats, some).
% 0.94/1.24 % set(auto2) -> clear(echo_input).
% 0.94/1.24 % set(auto2) -> set(quiet).
% 0.94/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.94/1.24 % set(auto2) -> clear(print_given).
% 0.94/1.24 assign(lrs_ticks,-1).
% 0.94/1.24 assign(sos_limit,10000).
% 0.94/1.24 assign(order,kbo).
% 0.94/1.24 set(lex_order_vars).
% 0.94/1.24 clear(print_given).
% 0.94/1.24
% 0.94/1.24 % formulas(sos). % not echoed (582 formulas)
% 0.94/1.24
% 0.94/1.24 ============================== end of input ==========================
% 0.94/1.24
% 0.94/1.24 % From the command line: assign(max_seconds, 300).
% 0.94/1.24
% 0.94/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.94/1.24
% 0.94/1.24 % Formulas that are not ordinary clauses:
% 0.94/1.24
% 0.94/1.24 ============================== end of process non-clausal formulas ===
% 0.94/1.24
% 0.94/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.24
% 0.94/1.24 ============================== PREDICATE ELIMINATION =================
% 0.94/1.24 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.94/1.24 2 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.94/1.24 3 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.94/1.24 4 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.94/1.24 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.94/1.24 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.94/1.24 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.94/1.24 8 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.94/1.24 9 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.94/1.24 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].
% 0.94/1.24 11 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.94/1.24 12 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.94/1.24 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.94/1.24 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.94/1.24 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.94/1.24 16 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.94/1.24 17 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.94/1.24 18 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.94/1.24 19 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.94/1.24 20 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.94/1.24 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,2,a)].
% 0.94/1.24 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,3,a)].
% 0.94/1.24 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,4,a)].
% 0.94/1.24 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,5,a)].
% 0.94/1.24 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,8,a)].
% 0.94/1.24 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,9,a)].
% 0.94/1.24 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)].
% 0.94/1.24 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,11,a)].
% 0.94/1.24 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,12,a)].
% 0.94/1.24 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,13,a)].
% 0.94/1.24 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,16,a)].
% 0.97/1.28 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,17,a)].
% 0.97/1.28 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,18,a)].
% 0.97/1.28 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,19,a)].
% 0.97/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,20,a)].
% 0.97/1.28 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.97/1.28 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,2,a)].
% 0.97/1.28 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,3,a)].
% 0.97/1.28 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,4,a)].
% 0.97/1.28 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,5,a)].
% 0.97/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,8,a)].
% 0.97/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,9,a)].
% 0.97/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 0.97/1.28 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,11,a)].
% 0.97/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,12,a)].
% 0.97/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,13,a)].
% 0.97/1.28 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,16,a)].
% 0.97/1.28 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,17,a)].
% 0.97/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(21,a,18,a)].
% 0.97/1.28 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,19,a)].
% 0.97/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,20,a)].
% 0.97/1.28 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.28 23 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.97/1.28 24 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.97/1.28 25 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.97/1.28 26 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.97/1.28 27 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.97/1.28 28 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.97/1.28 29 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.97/1.28 30 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.97/1.28 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.97/1.28 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.97/1.28 33 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.97/1.28 34 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.97/1.28 35 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.97/1.28 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.97/1.28 37 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.97/1.28 38 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.97/1.28 39 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.97/1.28 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].
% 0.97/1.28 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.97/1.28 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,23,a)].
% 0.97/1.28 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,24,a)].
% 0.97/1.28 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,25,a)].
% 0.97/1.28 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,28,a)].
% 0.97/1.28 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,29,a)].
% 0.97/1.28 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,30,a)].
% 0.97/1.28 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,31,a)].
% 0.97/1.28 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,32,a)].
% 0.97/1.28 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,33,a)].
% 0.97/1.28 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,34,a)].
% 0.97/1.28 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,37,a)].
% 0.97/1.28 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,38,a)].
% 0.97/1.28 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,39,a)].
% 0.97/1.28 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)].
% 0.97/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 0.97/1.28 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(42,a,23,a)].
% 0.97/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(42,a,24,a)].
% 0.97/1.28 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,25,a)].
% 0.97/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,28,a)].
% 0.97/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,29,a)].
% 0.97/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,30,a)].
% 0.97/1.28 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,31,a)].
% 0.97/1.28 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,32,a)].
% 0.97/1.28 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,33,a)].
% 0.97/1.28 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,34,a)].
% 0.97/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(42,a,37,a)].
% 0.97/1.28 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,38,a)].
% 0.97/1.29 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,39,a)].
% 0.97/1.29 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)].
% 0.97/1.29 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(42,a,41,a)].
% 0.97/1.29 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].
% 0.97/1.29 44 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)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.97/1.29 45 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | -hBOOL(hAPP(hAPP(c_in(A),C),E)) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,A) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.97/1.29 46 hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_OImage(C,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A))) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Equiv__Relations_Oequiv(D,C,A) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.97/1.29 47 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | -hBOOL(hAPP(hAPP(c_in(A),E),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(D,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)))) | -c_Equiv__Relations_Oequiv(F,D,A) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.97/1.29 48 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) | -hBOOL(hAPP(hAPP(c_in(B),D),E)) | -hBOOL(hAPP(hAPP(c_in(B),A),E)) | -c_Equiv__Relations_Oequiv(E,C,B) | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(A,D,B,B)),C)) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 0.97/1.29 49 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(A,D,B,B)),C)) | -hBOOL(hAPP(hAPP(c_in(B),D),E)) | -hBOOL(hAPP(hAPP(c_in(B),A),E)) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 0.97/1.29 50 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 | -hBOOL(hAPP(hAPP(c_in(tc_fun(C,tc_bool)),B),c_Equiv__Relations_Oquotient(D,E,C))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(C,tc_bool)),A),c_Equiv__Relations_Oquotient(D,E,C))) | -c_Equiv__Relations_Oequiv(D,E,C) # label(cls_quotient__disj_0) # label(axiom). [assumption].
% 0.97/1.29 51 A = B | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(D,E,C,C)),F)) | -hBOOL(hAPP(hAPP(c_in(C),E),B)) | -hBOOL(hAPP(hAPP(c_in(C),D),A)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(C,tc_bool)),B),c_Equiv__Relations_Oquotient(V6,F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(C,tc_bool)),A),c_Equiv__Relations_Oquotient(V6,F,C))) | -c_Equiv__Relations_Oequiv(V6,F,C) # label(cls_quotient__eqI_0) # label(axiom). [assumption].
% 0.97/1.29 52 -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(A),D),C)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(A,tc_bool)),C),c_Equiv__Relations_Oquotient(E,F,A))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(A,tc_bool)),C),c_Equiv__Relations_Oquotient(E,F,A))) | -c_Equiv__Relations_Oequiv(E,F,A) | hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),F)) # label(cls_quotient__eq__iff_0) # label(axiom). [assumption].
% 0.97/1.29 53 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.97/1.29 54 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.97/1.29 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) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.97/1.29 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_Equiv__Relations_Oequiv(E,A,C) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.97/1.29 57 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.97/1.29 58 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) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.97/1.29 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)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)). [resolve(43,b,44,c)].
% 0.97/1.29 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,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(43,b,45,d)].
% 0.97/1.29 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B))) | -hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_ODomain(A,B,B))). [resolve(43,b,46,c)].
% 0.97/1.29 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),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)))). [resolve(43,b,47,c)].
% 0.97/1.29 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) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,B,B))) | -hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_ODomain(A,B,B))) | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)). [resolve(43,b,48,d)].
% 0.97/1.30 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,B,B))) | -hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_ODomain(A,B,B))). [resolve(43,b,49,e)].
% 0.97/1.30 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 | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),D),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),C),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))). [resolve(43,b,50,e)].
% 0.97/1.30 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | C = D | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(E,F,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),F),D)) | -hBOOL(hAPP(hAPP(c_in(B),E),C)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),D),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),C),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))). [resolve(43,b,51,g)].
% 0.97/1.30 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | -hBOOL(hAPP(hAPP(c_in(B),C),D)) | -hBOOL(hAPP(hAPP(c_in(B),E),D)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),D),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,tc_bool)),D),c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B))) | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(E,C,B,B)),A)). [resolve(43,b,52,e)].
% 0.97/1.30 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) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)). [resolve(43,b,53,c)].
% 0.97/1.30 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) | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,B,B))). [resolve(43,b,55,d)].
% 0.97/1.30 59 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].
% 0.97/1.30 60 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.97/1.30 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(60,b,43,b)].
% 0.97/1.30 61 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.97/1.30 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(61,b,43,b)].
% 0.97/1.30 62 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(hAPP(hAPP(c_in(F),C),V6)) | -c_Equiv__Relations_Ocongruent2(V7,A,B,F,D,E) | -c_Equiv__Relations_Oequiv(V6,V7,F) # label(cls_congruent2__implies__congruent_0) # label(axiom). [assumption].
% 0.97/1.30 Derived: c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(hAPP(hAPP(c_in(F),C),c_Relation_ODomain(V6,F,F))) | -c_Equiv__Relations_Ocongruent2(V6,A,B,F,D,E) | c_Relation_Orel__comp(c_Relation_Oconverse(V6,F,F),V6,F,F,F) != V6. [resolve(62,d,43,b)].
% 1.81/2.10 63 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 1.81/2.10 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(63,b,43,b)].
% 1.81/2.10 64 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 1.81/2.10 Derived: hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ODomain(C,A,A))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),C)) | c_Relation_Orel__comp(c_Relation_Oconverse(C,A,A),C,A,A,A) != C. [resolve(64,c,43,b)].
% 1.81/2.10 65 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 1.81/2.10
% 1.81/2.10 ============================== end predicate elimination =============
% 1.81/2.10
% 1.81/2.10 Auto_denials: (non-Horn, no changes).
% 1.81/2.10
% 1.81/2.10 Term ordering decisions:
% 1.81/2.10 Function symbol KB weights: tc_bool=1. t_a=1. v_x=1. tc_Arrow__Order__Mirabelle_Oalt=1. v_y=1. t_b=1. v_z=1. v_f=1. v_L=1. v_g=1. v_r=1. t_c=1. c_Arrow__Order__Mirabelle_OLin=1. v_R=1. v_c=1. hAPP=1. tc_fun=1. tc_prod=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Relation_OField=1. c_Arrow__Order__Mirabelle_Omktop=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_and=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_Fun_Oid=1. c_HOL_Oundefined=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Equiv__Relations_Oquotient=1. c_fequal=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_Relation_OImage=1. c_Set_Oimage=1. c_Product__Type_OSigma=1. c_Relation_Oinv__image=1. c_split=1. c_Product__Type_OPair__Rep=1. c_FuncSet_Orestrict=1. c_curry=1. c_HOL_OIf=1. c_List_Osko__Equiv__Relations__XquotientE__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_Fun_Ocomp=1. c_COMBC=1. c_Fun_Ofcomp=1. c_Recdef_Ocut=1. c_Record_Oiso__tuple__surjective__proof__assist=1. c_FunDef_Oin__rel=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_Predicate_Oinv__imagep=1.
% 1.81/2.10
% 1.81/2.10 ============================== end of process initial clauses ========
% 1.81/2.10
% 1.81/2.10 ============================== CLAUSES FOR SEARCH ====================
% 1.81/2.10
% 1.81/2.10 ============================== end of clauses for search =============
% 1.81/2.10
% 1.81/2.10 ============================== SEARCH ================================
% 1.81/2.10
% 1.81/2.10 % Starting search at 0.25 seconds.
% 1.81/2.10
% 1.81/2.10 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 90 (0.00 of 0.62 sec).
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=69.000, iters=3625
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=54.000, iters=3532
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=49.000, iters=3376
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=46.000, iters=3339
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=45.000, iters=3362
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=43.000, iters=3398
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=42.000, iters=3407
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=41.000, iters=3497
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=40.000, iters=3467
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=39.000, iters=3387
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=38.000, iters=3452
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=37.000, iters=3517
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=36.000, iters=3438
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=35.000, iters=3550
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=33.000, iters=3375
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=32.000, iters=3429
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=31.000, iters=3386
% 1.81/2.10
% 1.81/2.10 Low Water (keep): wt=29.000, iters=3346
% 1.81/2.10
% 1.81/2.10 Low Water (keCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------