TSTP Solution File: SCT011-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT011-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 22:03:25 EDT 2022
% Result : Timeout 300.06s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT011-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 20:38:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.98/1.32 ============================== Prover9 ===============================
% 0.98/1.32 Prover9 (32) version 2009-11A, November 2009.
% 0.98/1.32 Process 25395 was started by sandbox on n017.cluster.edu,
% 0.98/1.32 Fri Jul 1 20:38:25 2022
% 0.98/1.32 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25242_n017.cluster.edu".
% 0.98/1.32 ============================== end of head ===========================
% 0.98/1.32
% 0.98/1.32 ============================== INPUT =================================
% 0.98/1.32
% 0.98/1.32 % Reading from file /tmp/Prover9_25242_n017.cluster.edu
% 0.98/1.32
% 0.98/1.32 set(prolog_style_variables).
% 0.98/1.32 set(auto2).
% 0.98/1.32 % set(auto2) -> set(auto).
% 0.98/1.32 % set(auto) -> set(auto_inference).
% 0.98/1.32 % set(auto) -> set(auto_setup).
% 0.98/1.32 % set(auto_setup) -> set(predicate_elim).
% 0.98/1.32 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.98/1.32 % set(auto) -> set(auto_limits).
% 0.98/1.32 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.98/1.32 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.98/1.32 % set(auto) -> set(auto_denials).
% 0.98/1.32 % set(auto) -> set(auto_process).
% 0.98/1.32 % set(auto2) -> assign(new_constants, 1).
% 0.98/1.32 % set(auto2) -> assign(fold_denial_max, 3).
% 0.98/1.32 % set(auto2) -> assign(max_weight, "200.000").
% 0.98/1.32 % set(auto2) -> assign(max_hours, 1).
% 0.98/1.32 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.98/1.32 % set(auto2) -> assign(max_seconds, 0).
% 0.98/1.32 % set(auto2) -> assign(max_minutes, 5).
% 0.98/1.32 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.98/1.32 % set(auto2) -> set(sort_initial_sos).
% 0.98/1.32 % set(auto2) -> assign(sos_limit, -1).
% 0.98/1.32 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.98/1.32 % set(auto2) -> assign(max_megs, 400).
% 0.98/1.32 % set(auto2) -> assign(stats, some).
% 0.98/1.32 % set(auto2) -> clear(echo_input).
% 0.98/1.32 % set(auto2) -> set(quiet).
% 0.98/1.32 % set(auto2) -> clear(print_initial_clauses).
% 0.98/1.32 % set(auto2) -> clear(print_given).
% 0.98/1.32 assign(lrs_ticks,-1).
% 0.98/1.32 assign(sos_limit,10000).
% 0.98/1.32 assign(order,kbo).
% 0.98/1.32 set(lex_order_vars).
% 0.98/1.32 clear(print_given).
% 0.98/1.32
% 0.98/1.32 % formulas(sos). % not echoed (695 formulas)
% 0.98/1.32
% 0.98/1.32 ============================== end of input ==========================
% 0.98/1.32
% 0.98/1.32 % From the command line: assign(max_seconds, 300).
% 0.98/1.32
% 0.98/1.32 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.98/1.32
% 0.98/1.32 % Formulas that are not ordinary clauses:
% 0.98/1.32
% 0.98/1.32 ============================== end of process non-clausal formulas ===
% 0.98/1.32
% 0.98/1.32 ============================== PROCESS INITIAL CLAUSES ===============
% 0.98/1.32
% 0.98/1.32 ============================== PREDICATE ELIMINATION =================
% 0.98/1.32 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.98/1.32 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 6 -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].
% 0.98/1.32 7 -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].
% 0.98/1.32 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].
% 0.98/1.32 9 -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].
% 0.98/1.32 10 -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].
% 0.98/1.32 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_sup__least_0) # label(axiom). [assumption].
% 0.98/1.32 12 -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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 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].
% 0.98/1.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.98/1.32 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)].
% 0.98/1.32 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)].
% 0.98/1.32 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)].
% 0.98/1.32 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,6,a)].
% 0.98/1.32 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,7,a)].
% 0.98/1.32 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)].
% 0.98/1.32 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,9,a)].
% 0.98/1.32 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,10,a)].
% 0.98/1.32 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,2,a)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(21,a,3,a)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(21,a,4,a)].
% 0.98/1.36 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,5,a)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,6,a)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,7,a)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,8,a)].
% 0.98/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,9,a)].
% 0.98/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,10,a)].
% 0.98/1.36 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)].
% 0.98/1.36 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(21,a,14,a)].
% 0.98/1.36 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(21,a,15,a)].
% 0.98/1.36 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(21,a,16,a)].
% 0.98/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,17,a)].
% 0.98/1.36 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 0.98/1.36 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.98/1.36 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].
% 0.98/1.36 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].
% 0.98/1.36 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].
% 0.98/1.36 26 -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].
% 0.98/1.36 27 -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].
% 0.98/1.36 28 -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].
% 0.98/1.36 29 -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].
% 0.98/1.36 30 -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].
% 0.98/1.36 31 -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].
% 0.98/1.36 32 -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].
% 0.98/1.36 33 -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].
% 0.98/1.36 34 -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].
% 0.98/1.36 35 -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].
% 0.98/1.36 36 -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].
% 0.98/1.36 37 -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].
% 0.98/1.36 38 -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].
% 0.98/1.36 39 -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].
% 0.98/1.36 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].
% 0.98/1.36 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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)].
% 0.98/1.36 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,26,a)].
% 0.98/1.36 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,27,a)].
% 0.98/1.36 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,28,a)].
% 0.98/1.36 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,31,a)].
% 0.98/1.36 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,32,a)].
% 0.98/1.36 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,33,a)].
% 0.98/1.36 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,34,a)].
% 0.98/1.36 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,35,a)].
% 0.98/1.36 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,36,a)].
% 0.98/1.36 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,37,a)].
% 0.98/1.36 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)].
% 0.98/1.36 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 0.98/1.36 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.98/1.36 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 0.98/1.36 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 0.98/1.36 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 0.98/1.36 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,26,a)].
% 0.98/1.36 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,27,a)].
% 0.98/1.36 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,28,a)].
% 0.98/1.36 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(42,a,31,a)].
% 0.98/1.36 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(42,a,32,a)].
% 0.98/1.36 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(42,a,33,a)].
% 0.98/1.36 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,34,a)].
% 0.98/1.36 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,35,a)].
% 0.98/1.36 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,36,a)].
% 0.98/1.39 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,37,a)].
% 0.98/1.39 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)].
% 0.98/1.39 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(42,a,41,a)].
% 0.98/1.39 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].
% 0.98/1.39 44 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].
% 0.98/1.39 45 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].
% 0.98/1.39 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].
% 0.98/1.39 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].
% 0.98/1.39 48 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(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].
% 0.98/1.39 49 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].
% 0.98/1.39 50 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(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].
% 0.98/1.39 51 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(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].
% 0.98/1.39 52 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,F,V6)) | -c_Equiv__Relations_Ocongruent2(V7,A,B,V6,D,E) | -c_Equiv__Relations_Oequiv(F,V7,V6) # label(cls_congruent2__implies__congruent_0) # label(axiom). [assumption].
% 0.98/1.39 53 hBOOL(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)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.98/1.39 54 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(c_in(B,c_Equiv__Relations_Oquotient(D,E,C),tc_fun(C,tc_bool))) | -hBOOL(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].
% 0.98/1.39 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(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].
% 0.98/1.39 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) | -hBOOL(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].
% 0.98/1.39 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(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.98/1.39 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) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.98/1.39 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) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.98/1.39 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) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.98/1.39 61 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(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 0.98/1.39 62 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(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) | hBOOL(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 0.98/1.39 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(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(47,b,48,c)].
% 0.98/1.39 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,49,b)].
% 0.98/1.39 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -c_lessequals(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,50,d)].
% 0.98/1.39 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(E,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,51,c)].
% 0.98/1.39 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Ocongruent(C,hAPP(D,E),F,V6) | -hBOOL(c_in(E,c_Relation_ODomain(A,B,B),B)) | -c_Equiv__Relations_Ocongruent2(A,C,D,B,F,V6). [resolve(47,b,52,d)].
% 0.98/1.40 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(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)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(47,b,53,c)].
% 0.98/1.40 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(c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool))) | -hBOOL(c_in(C,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool))). [resolve(47,b,54,e)].
% 0.98/1.40 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(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(47,b,55,c)].
% 0.98/1.40 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(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)). [resolve(47,b,57,d)].
% 0.98/1.40 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(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(47,b,61,e)].
% 0.98/1.40 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(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(47,b,62,d)].
% 0.98/1.40 63 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].
% 0.98/1.40 64 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.98/1.40 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(64,b,47,b)].
% 0.98/1.40 65 c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(A,B,C),tc_fun(C,tc_bool)) = A | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_Union__quotient_0) # label(axiom). [assumption].
% 0.98/1.40 Derived: c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) = c_Relation_ODomain(A,B,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(65,b,47,b)].
% 0.98/1.40 66 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.98/1.40 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)].
% 0.98/1.40 67 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.98/1.40 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(67,b,47,b)].
% 0.98/1.40 68 A = B | -hBOOL(c_in(c_Pair(C,D,E,E),F,tc_prod(E,E))) | -hBOOL(c_in(D,B,E)) | -hBOOL(c_in(C,A,E)) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(V6,F,E),tc_fun(E,tc_bool))) | -hBOOL(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].
% 0.98/1.58 Derived: A = B | -hBOOL(c_in(c_Pair(C,D,E,E),F,tc_prod(E,E))) | -hBOOL(c_in(D,B,E)) | -hBOOL(c_in(C,A,E)) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(c_Relation_ODomain(F,E,E),F,E),tc_fun(E,tc_bool))) | -hBOOL(c_in(A,c_Equiv__Relations_Oquotient(c_Relation_ODomain(F,E,E),F,E),tc_fun(E,tc_bool))) | c_Relation_Orel__comp(c_Relation_Oconverse(F,E,E),F,E,E,E) != F. [resolve(68,g,47,b)].
% 0.98/1.58 69 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(D,B,C)) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool))) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool))) | -c_Equiv__Relations_Oequiv(E,F,C) | hBOOL(c_in(c_Pair(D,A,C,C),F,tc_prod(C,C))) # label(cls_quotient__eq__iff_0) # label(axiom). [assumption].
% 0.98/1.58 Derived: -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(D,B,C)) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(c_Relation_ODomain(E,C,C),E,C),tc_fun(C,tc_bool))) | -hBOOL(c_in(B,c_Equiv__Relations_Oquotient(c_Relation_ODomain(E,C,C),E,C),tc_fun(C,tc_bool))) | hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(E,C,C),E,C,C,C) != E. [resolve(69,e,47,b)].
% 0.98/1.58 70 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 0.98/1.58 Derived: hBOOL(c_in(A,c_Relation_ODomain(B,C,C),C)) | -hBOOL(c_in(c_Pair(D,A,C,C),B,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(B,C,C),B,C,C,C) != B. [resolve(70,c,47,b)].
% 0.98/1.58 71 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(A,D,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 0.98/1.58 72 -hBOOL(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].
% 0.98/1.58 73 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].
% 0.98/1.58 74 c_Relation_Oirrefl(A,B) | hBOOL(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].
% 0.98/1.58 Derived: -hBOOL(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(72,b,73,a)].
% 0.98/1.58 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | hBOOL(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(72,b,74,a)].
% 0.98/1.58 75 hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Nitpick_Orefl_H(C,B) # label(cls_Nitpick_Orefl_H__def_0) # label(axiom). [assumption].
% 0.98/1.58 76 c_Nitpick_Orefl_H(A,B) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_Nitpick_Orefl_H__def_1) # label(axiom). [assumption].
% 0.98/1.58 Derived: hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(75,b,76,a)].
% 0.98/1.58
% 0.98/1.58 ============================== end predicate elimination =============
% 0.98/1.58
% 0.98/1.58 Auto_denials: (non-Horn, no changes).
% 0.98/1.58
% 0.98/1.58 Term ordering decisions:
% 0.98/1.58 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. v_x=1. v_y=1. v_a=1. v_L=1. v_b=1. c_Arrow__Order__Mirabelle_OLin=1. t_b=1. v_R=1. v_r=1. v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_ATP__Linkup_Osko__Relation__XIdE__1__1=1. c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1=1. c_ATP__Linkup_Osko__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. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_and=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_Relation_Oconverse=1. c_HOL_Ominus__class_Ominus=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Equiv__Relations_Oquotient=1. c_fequal=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__Complete__Lattice__XInterI__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__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_FuncSet_OPi=1. c_Relation_Oinv__image=1. c_Product__Type_OPair__Rep=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_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_Recdef_Ocut=1. c_FunDef_Oin__rel=1. c_FuncSet_Osko__FuncSet__XPi__I_H__1__1=1. c_FuncSet_Osko__FuncSet__XPi__I__1__1=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_Sum__Type_OInl__Rep=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_Predicate_Oinv__imagep=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 2.68/2.99
% 2.68/2.99 ============================== end of process initial clauses ========
% 2.68/2.99
% 2.68/2.99 ============================== CLAUSES FOR SEARCH ====================
% 2.68/2.99
% 2.68/2.99 ============================== end of clauses for search =============
% 2.68/2.99
% 2.68/2.99 ============================== SEARCH ================================
% 2.68/2.99
% 2.68/2.99 % Starting search at 0.37 seconds.
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=56.000, iters=3522
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=53.000, iters=3454
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=51.000, iters=3370
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=49.000, iters=3336
% 2.68/2.99
% 2.68/2.99 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 52 (0.00 of 0.96 sec).
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=48.000, iters=3337
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=47.000, iters=3365
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=46.000, iters=3361
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=45.000, iters=3359
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=44.000, iters=3519
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=43.000, iters=3412
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=42.000, iters=3395
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=41.000, iters=3341
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=40.000, iters=3398
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=39.000, iters=3380
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=37.000, iters=3359
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=36.000, iters=3413
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=35.000, iters=3469
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=34.000, iters=3442
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=33.000, iters=3380
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=32.000, iters=3457
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=31.000, iters=3438
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=30.000, iters=3496
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=29.000, iters=3429
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=28.000, iters=3346
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=27.000, iters=3335
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=26.000, iters=3364
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=25.000, iters=3580
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=24.000, iters=3346
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=23.000, iters=3337
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=22.000, iters=3351
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=21.000, iters=3529
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wt=20.000, iters=3343
% 2.68/2.99
% 2.68/2.99 Low Water (keep): wtCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------