TSTP Solution File: SCT030-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT030-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 22:03:31 EDT 2022
% Result : Unknown 120.07s 120.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT030-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 00:50:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.40/1.67 ============================== Prover9 ===============================
% 1.40/1.67 Prover9 (32) version 2009-11A, November 2009.
% 1.40/1.67 Process 15191 was started by sandbox on n013.cluster.edu,
% 1.40/1.67 Sat Jul 2 00:50:15 2022
% 1.40/1.67 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15028_n013.cluster.edu".
% 1.40/1.67 ============================== end of head ===========================
% 1.40/1.67
% 1.40/1.67 ============================== INPUT =================================
% 1.40/1.67
% 1.40/1.67 % Reading from file /tmp/Prover9_15028_n013.cluster.edu
% 1.40/1.67
% 1.40/1.67 set(prolog_style_variables).
% 1.40/1.67 set(auto2).
% 1.40/1.67 % set(auto2) -> set(auto).
% 1.40/1.67 % set(auto) -> set(auto_inference).
% 1.40/1.67 % set(auto) -> set(auto_setup).
% 1.40/1.67 % set(auto_setup) -> set(predicate_elim).
% 1.40/1.67 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.40/1.67 % set(auto) -> set(auto_limits).
% 1.40/1.67 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.40/1.67 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.40/1.67 % set(auto) -> set(auto_denials).
% 1.40/1.67 % set(auto) -> set(auto_process).
% 1.40/1.67 % set(auto2) -> assign(new_constants, 1).
% 1.40/1.67 % set(auto2) -> assign(fold_denial_max, 3).
% 1.40/1.67 % set(auto2) -> assign(max_weight, "200.000").
% 1.40/1.67 % set(auto2) -> assign(max_hours, 1).
% 1.40/1.67 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.40/1.67 % set(auto2) -> assign(max_seconds, 0).
% 1.40/1.67 % set(auto2) -> assign(max_minutes, 5).
% 1.40/1.67 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.40/1.67 % set(auto2) -> set(sort_initial_sos).
% 1.40/1.67 % set(auto2) -> assign(sos_limit, -1).
% 1.40/1.67 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.40/1.67 % set(auto2) -> assign(max_megs, 400).
% 1.40/1.67 % set(auto2) -> assign(stats, some).
% 1.40/1.67 % set(auto2) -> clear(echo_input).
% 1.40/1.67 % set(auto2) -> set(quiet).
% 1.40/1.67 % set(auto2) -> clear(print_initial_clauses).
% 1.40/1.67 % set(auto2) -> clear(print_given).
% 1.40/1.67 assign(lrs_ticks,-1).
% 1.40/1.67 assign(sos_limit,10000).
% 1.40/1.67 assign(order,kbo).
% 1.40/1.67 set(lex_order_vars).
% 1.40/1.67 clear(print_given).
% 1.40/1.67
% 1.40/1.67 % formulas(sos). % not echoed (701 formulas)
% 1.40/1.67
% 1.40/1.67 ============================== end of input ==========================
% 1.40/1.67
% 1.40/1.67 % From the command line: assign(max_seconds, 300).
% 1.40/1.67
% 1.40/1.67 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.40/1.67
% 1.40/1.67 % Formulas that are not ordinary clauses:
% 1.40/1.67
% 1.40/1.67 ============================== end of process non-clausal formulas ===
% 1.40/1.67
% 1.40/1.67 ============================== PROCESS INITIAL CLAUSES ===============
% 1.40/1.67
% 1.40/1.67 ============================== PREDICATE ELIMINATION =================
% 1.40/1.67 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.40/1.67 2 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.40/1.67 3 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.40/1.67 4 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.40/1.67 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.40/1.67 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.40/1.67 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.40/1.67 8 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.40/1.67 9 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.40/1.67 10 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.40/1.67 11 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.40/1.67 12 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.40/1.67 13 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.40/1.67 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.40/1.67 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.40/1.67 16 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.40/1.67 17 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.40/1.67 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.40/1.67 19 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.40/1.67 20 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.40/1.67 21 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.40/1.67 22 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(D,A)),E),C,tc_fun(D,A)). [resolve(1,a,2,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(E,tc_fun(D,A)),B),C,tc_fun(D,A)). [resolve(1,a,3,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,4,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,5,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = D | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,8,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) != D | c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,9,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = B | -c_lessequals(D,B,tc_fun(C,A)). [resolve(1,a,10,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),B) = B. [resolve(1,a,11,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)). [resolve(1,a,12,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),E)). [resolve(1,a,13,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,14,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)). [resolve(1,a,15,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),B),tc_fun(D,A)). [resolve(1,a,16,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),B). [resolve(1,a,19,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D). [resolve(1,a,20,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(D,A)). [resolve(1,a,21,a)].
% 1.40/1.67 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(1,a,22,a)].
% 1.40/1.67 23 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.40/1.67 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),C),B,tc_nat). [resolve(23,a,2,a)].
% 1.40/1.67 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_nat),A),B,tc_nat). [resolve(23,a,3,a)].
% 1.40/1.67 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,4,a)].
% 1.40/1.67 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,5,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B) = B | -c_lessequals(A,B,tc_nat). [resolve(23,a,8,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B) != B | c_lessequals(A,B,tc_nat). [resolve(23,a,9,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B) = A | -c_lessequals(B,A,tc_nat). [resolve(23,a,10,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),A) = A. [resolve(23,a,11,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B),tc_nat),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C)). [resolve(23,a,12,a)].
% 1.40/1.67 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),C)). [resolve(23,a,13,a)].
% 1.40/1.67 Derived: c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,14,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B),tc_nat). [resolve(23,a,15,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),A),tc_nat). [resolve(23,a,16,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),A). [resolve(23,a,19,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_nat),B). [resolve(23,a,20,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(23,a,21,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_nat),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(23,a,22,a)].
% 1.40/1.69 24 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C),B,tc_bool). [resolve(24,a,2,a)].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_bool),A),B,tc_bool). [resolve(24,a,3,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,4,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,5,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = B | -c_lessequals(A,B,tc_bool). [resolve(24,a,8,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) != B | c_lessequals(A,B,tc_bool). [resolve(24,a,9,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = A | -c_lessequals(B,A,tc_bool). [resolve(24,a,10,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),A) = A. [resolve(24,a,11,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)). [resolve(24,a,12,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C)). [resolve(24,a,13,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,14,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool). [resolve(24,a,15,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A),tc_bool). [resolve(24,a,16,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A). [resolve(24,a,19,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B). [resolve(24,a,20,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(24,a,21,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(24,a,22,a)].
% 1.40/1.69 25 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.40/1.69 26 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.40/1.69 27 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.40/1.69 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.40/1.69 29 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.40/1.69 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.40/1.69 31 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.40/1.69 32 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.40/1.69 33 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.40/1.69 34 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.40/1.69 35 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.40/1.69 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.40/1.69 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.40/1.69 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.40/1.69 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.40/1.69 40 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.40/1.69 41 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.40/1.69 42 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),A),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.40/1.69 43 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.40/1.69 44 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.40/1.69 45 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.40/1.69 46 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),B,tc_fun(C,A)). [resolve(25,a,26,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),D,tc_fun(C,A)). [resolve(25,a,27,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(25,a,28,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = B | -c_lessequals(B,D,tc_fun(C,A)). [resolve(25,a,31,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) != B | c_lessequals(B,D,tc_fun(C,A)). [resolve(25,a,32,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = D | -c_lessequals(D,B,tc_fun(C,A)). [resolve(25,a,33,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)). [resolve(25,a,34,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(E,tc_fun(D,A)),C),tc_fun(D,A)). [resolve(25,a,35,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(25,a,36,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)). [resolve(25,a,37,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),B). [resolve(25,a,40,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),E)). [resolve(25,a,41,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)). [resolve(25,a,42,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_HOL_Oord__class_Oless(D,E,tc_fun(C,A)). [resolve(25,a,43,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(C,A)). [resolve(25,a,44,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D). [resolve(25,a,45,a)].
% 1.40/1.69 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),B) = B. [resolve(25,a,46,a)].
% 1.40/1.69 47 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),A,tc_nat). [resolve(47,a,26,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),B,tc_nat). [resolve(47,a,27,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(47,a,28,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = A | -c_lessequals(A,B,tc_nat). [resolve(47,a,31,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) != A | c_lessequals(A,B,tc_nat). [resolve(47,a,32,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = B | -c_lessequals(B,A,tc_nat). [resolve(47,a,33,a)].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C),tc_nat). [resolve(47,a,34,a)].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_nat),B),tc_nat). [resolve(47,a,35,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(47,a,36,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(47,a,37,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),A). [resolve(47,a,40,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),C)). [resolve(47,a,41,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),tc_nat),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C)). [resolve(47,a,42,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(47,a,43,a)].
% 1.40/1.69 Derived: c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(47,a,44,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B). [resolve(47,a,45,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),A) = A. [resolve(47,a,46,a)].
% 1.40/1.69 48 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),A,tc_bool). [resolve(48,a,26,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),B,tc_bool). [resolve(48,a,27,a)].
% 1.40/1.69 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(48,a,28,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = A | -c_lessequals(A,B,tc_bool). [resolve(48,a,31,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) != A | c_lessequals(A,B,tc_bool). [resolve(48,a,32,a)].
% 1.40/1.69 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = B | -c_lessequals(B,A,tc_bool). [resolve(48,a,33,a)].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool). [resolve(48,a,34,a)].
% 1.40/1.69 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_bool),B),tc_bool). [resolve(48,a,35,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,36,a)].
% 1.40/1.69 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(48,a,37,a)].
% 1.40/1.73 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),A). [resolve(48,a,40,a)].
% 1.40/1.73 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),C)). [resolve(48,a,41,a)].
% 1.40/1.73 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)). [resolve(48,a,42,a)].
% 1.40/1.73 Derived: c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(48,a,43,a)].
% 1.40/1.73 Derived: c_HOL_Oord__class_Oless(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(48,a,44,a)].
% 1.40/1.73 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B). [resolve(48,a,45,a)].
% 1.40/1.73 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),A) = A. [resolve(48,a,46,a)].
% 1.40/1.73 49 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.40/1.73 50 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.40/1.73 51 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.40/1.73 52 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.40/1.73 53 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.40/1.73 54 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.40/1.73 55 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.40/1.73 56 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.40/1.73 57 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.40/1.73 58 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.40/1.73 59 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.40/1.73 60 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.40/1.73 61 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.40/1.73 62 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.40/1.73 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.40/1.73 64 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.40/1.73 65 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.40/1.73 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,50,a)].
% 1.65/1.97 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(49,a,51,a)].
% 1.65/1.97 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(49,a,53,a)].
% 1.65/1.97 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,56,a)].
% 1.65/1.97 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,58,a)].
% 1.65/1.97 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(49,a,60,a)].
% 1.65/1.97 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,61,a)].
% 1.65/1.97 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(49,a,65,a)].
% 1.65/1.97 66 hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_Odictator(A,C) # label(cls_dictator__def_0) # label(axiom). [assumption].
% 1.65/1.97 67 hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(cls_dictator__def_2) # label(axiom). [assumption].
% 1.65/1.97 68 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_dictator__def_1) # label(axiom). [assumption].
% 1.65/1.97 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C),C). [resolve(66,c,67,b)].
% 1.65/1.97 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)),c_Arrow__Order__Mirabelle_OProf)). [resolve(66,c,68,a)].
% 1.65/1.97
% 1.65/1.97 ============================== end predicate elimination =============
% 1.65/1.97
% 1.65/1.97 Auto_denials: (non-Horn, no changes).
% 1.65/1.97
% 1.65/1.97 Term ordering decisions:
% 1.65/1.97 Function symbol KB weights: tc_bool=1. tc_nat=1. tc_Arrow__Order__Mirabelle_Oalt=1. c_Arrow__Order__Mirabelle_OProf=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Not=1. v_P____=1. v_Q____=1. hAPP=1. tc_fun=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Collect=1. tc_prod=1. v_sko__Arrow__Order__Mirabelle__Xdictator__def__1=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_HOL_Ouminus__class_Ouminus=1. c_fequal=1. c_HOL_Oundefined=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_COMBK=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3=1. c_FuncSet_Oextensional=1. c_ATP__Linkup_Osko__Set__XbexCI__1__1=1. c_ATP__Linkup_Osko__Set__XballE__1__1=1. c_ATP__Linkup_Osko__Set__XbexE__1__1=1. c_ATP__Linkup_Osko__Set__XbexI__1__1=1. c_ATP__Linkup_Osko__Set__Xbspec__1__1=1. c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1=1. c_SetInterval_Oord_OatMost=1. c_SetInterval_Oord_OgreaterThan=1. c_SetInterval_Oord_OlessThan=1. c_ATP__Linkup_Osko__Set__Xset__insert__1__1=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_COMBC=1. c_FuncSet_OPi=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1=1. c_ATP__Linkup_Osko__Set__Xbex__Un__1__3=1. c_SetInterval_Oord_OatLeastAtMost=1. c_SetInterval_Oord_OgreaterThanLessThan=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. c_Finite__Set_Osetsum=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_COMBB=1. c_Fun_Ofun__upd=1. c_Fun_Ooverride__on=1. c_FuncSet_Osko__FuncSet__XPi__I_H__1__1=1. c_FuncSet_Osko__FuncSet__XPi__I__1__1=1. c_FuncSet_Osko__FuncSet__XextensionalityI__1__1=1. c_SetInterval_Oord_OatLeastLessThan=1. c_SetInterval_Oord_OgreaterThanAtMost=1. c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1. c_FuncSet_Osko__FuncSet__XfuncsetI__1__1=1.
% 120.01/120.40
% 120.01/120.40 ============================== end of process initial clauses ========
% 120.01/120.40
% 120.01/120.40 ============================== CLAUSES FOR SEARCH ====================
% 120.01/120.40
% 120.01/120.40 ============================== end of clauses for search =============
% 120.01/120.40
% 120.01/120.40 ============================== SEARCH ================================
% 120.01/120.40
% 120.01/120.40 % Starting search at 0.37 seconds.
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=97.000, iters=3676
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=79.000, iters=3673
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=64.000, iters=3593
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=55.000, iters=3336
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=53.000, iters=3458
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=51.000, iters=3402
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=50.000, iters=3384
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=48.000, iters=3343
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=46.000, iters=3412
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=44.000, iters=3343
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=43.000, iters=3577
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=41.000, iters=3451
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=39.000, iters=3368
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=37.000, iters=3351
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=36.000, iters=3366
% 120.01/120.40
% 120.01/120.40 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 49 (0.00 of 2.33 sec).
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=35.000, iters=3414
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=34.000, iters=3375
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=33.000, iters=3390
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=32.000, iters=3439
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=31.000, iters=3370
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=30.000, iters=3490
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=29.000, iters=3359
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=28.000, iters=3352
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=27.000, iters=3430
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=26.000, iters=3389
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=25.000, iters=3378
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=24.000, iters=3373
% 120.01/120.40
% 120.01/120.40 Low Water (keep): wt=23.000, iters=3341
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=22.000, iters=3340
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=21.000, iters=3341
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=20.000, iters=3354
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=14349, wt=38.000
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=14459, wt=36.000
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=14477, wt=17.000
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=14631, wt=16.000
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=19.000, iters=3353
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=17733, wt=15.000
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=18.000, iters=3340
% 120.07/120.40
% 120.07/120.40 Low Water (displace): id=26821, wt=14.000
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=17.000, iters=3335
% 120.07/120.40
% 120.07/120.40 Low Water (keep): wt=16.000, iters=3339
% 120.07/120.40
% 120.07/120.40 ============================== STATISTICS ============================
% 120.07/120.40
% 120.07/120.40 Given=14153. Generated=3310633. Kept=471871. proofs=0.
% 120.07/120.40 Usable=13848. Sos=9999. Demods=1366. Limbo=164, Disabled=448673. Hints=0.
% 120.07/120.40 Kept_by_rule=0, Deleted_by_rule=3.
% 120.07/120.40 Forward_subsumed=403182. Back_subsumed=154.
% 120.07/120.40 Sos_limit_deleted=2435576. Sos_displaced=444372. Sos_removed=0.
% 120.07/120.40 New_demodulators=1900 (4 lex), Back_demodulated=3314. Back_unit_deleted=20.
% 120.07/120.40 Demod_attempts=75729434. Demod_rewrites=458079.
% 120.07/120.40 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 120.07/120.40 Nonunit_fsub_feature_tests=421139. Nonunit_bsub_feature_tests=34502.
% 120.07/120.40 Megabytes=419.43.
% 120.07/120.40 User_CPU=116.13, System_CPU=2.61, Wall_clock=119.
% 120.07/120.40
% 120.07/120.40 Megs malloced by palloc(): 400.
% 120.07/120.40 type (bytes each) gets frees in use bytes
% 120.07/120.40 chunk ( 104) 22044 22044 0 0.0 K
% 120.07/120.40 string_buf ( 8) 20555 20555 0 0.0 K
% 120.07/120.40 token ( 20) 45769 45769 0 0.0 K
% 120.07/120.40 pterm ( 16) 32609 32609 0 0.0 K
% 120.07/120.40 hashtab ( 8) 0 0 0 0.0 K
% 120.07/120.40 hashnode ( 8) 0 0 0 0.0 K
% 120.07/120.40 term ( 20) 123214405 114080937 9133468 178388.0 K
% 120.07/120.40 term arg arrays: 47969.3 K
% 120.07/120.40 attribute ( 12) 2340 130 2210 25.9 K
% 120.07/120.40 ilist ( 8) 534849371 532922871 1926500 15050.8 K
% 120.07/120.40 plist ( 8) 12548433 12032071 516362 4034.1 K
% 120.07/120.40 i2list ( 12) 26360707 26360707 0 0.0 K
% 120.07/120.40 just ( 12) 3751857 3265190 486667 5703.1 K
% 120.07/120.40 parajust ( 16) 979442 932277 47165 737.0 K
% 120.07/120.40 instancejust ( 8) 0 0 0 0.0 K
% 120.07/120.40 ivyjust ( 24) 0 0 0 0.0 K
% 120.07/120.40 formula ( 28) 3458 3458 0 0.0 K
% 120.07/120.40 formula arg arrays: 0.0 K
% 120.07/120.40 topform ( 52) 3311478 2838761 472717 24005.2 K
% 120.07/120.40 clist_pos ( 20) 1409710 935660 474050 9258.8 K
% 120.07/120.40 clist ( 16) 8 1 7 0.1 K
% 120.07/120.40 context ( 808) 17165940 17165938 2 1.6 K
% 120.07/120.40 trail ( 12) 11297597 11297594 3 0.0 K
% 120.07/120.40 ac_match_pos (70044) 0 0 0 0.0 K
% 120.07/120.40 ac_match_free_vars_pos (20020)
% 120.07/120.40 0 0 0 0.0 K
% 120.07/120.40 btm_state ( 60) 0 0 0 0.0 K
% 120.07/120.40 btu_state ( 60) 0 0 0 0.0 K
% 120.07/120.40 ac_position (285432) 0 0 0 0.0 K
% 120.07/120.40 fpa_trie ( 20) 5668330 5013128 655202 12796.9 K
% 120.07/120.40 fpa_state ( 28) 4101873 4101873 0 0.0 K
% 120.07/120.40 fpa_index ( 12) 10 0 10 0.1 K
% 120.07/120.40 fpa_chunk ( 20) 7008025 6891261 116764 2280.5 K
% 120.07/120.40 fpa_list ( 16) 5084902 0 5084902 79451.6 K
% 120.07/120.40 fpa_list chunks: 5729.0 K
% 120.07/120.40 discrim ( 12) 4962885 4829164 133721 1567.0 K
% 120.07/120.40 discrim_pos ( 16) 917875 917875 0 0.0 K
% 120.07/120.40 flat2 ( 32) 48981191 48981191 0 0.0 K
% 120.07/120.40 flat ( 48) 0 0 0 0.0 K
% 120.07/120.40 flatterm ( 32) 119579099 119579099 0 0.0 K
% 120.07/120.40 mindex ( 28) 13 0 13 0.4 K
% 120.07/120.40 mindex_pos ( 56) 8805942 8805942 0 0.0 K
% 120.07/120.40 lindex ( 12) 5 0 5 0.1 K
% 120.07/120.40 clash ( 40) 0 0 0 0.0 K
% 120.07/120.40 di_tree ( 12) 5789720 4459244 1330476 15591.5 K
% 120.07/120.40 avl_node ( 20) 942715 922717 19998 390.6 K
% 120.07/120.40
% 120.07/120.40 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 120.07/120.40 List 1, length 761, 3.0 K
% 120.07/120.40 List 2, length 271, 2.1 K
% 120.07/120.40 List 3, length 30021, 351.8 K
% 120.07/120.40 List 8, length 89, 2.8 K
% 120.07/120.40 List 9, length 15, 0.5 K
% 120.07/120.40 List 10, length 6, 0.2 K
% 120.07/120.40 List 11, length 2, 0.1 K
% 120.07/120.40 List 14, length 2, 0.1 K
% 120.07/120.40 List 16, length 271, 16.9 K
% 120.07/120.40 List 26, length 77, 7.8 K
% 120.07/120.40 List 32, length 67, 8.4 K
% 120.07/120.40 List 64, length 282, 70.5 K
% 120.07/120.40 List 128, length 43, 21.5 K
% 120.07/120.40 List 202, length 2, 1.6 K
% 120.07/120.40
% 120.07/120.40 ============================== SELECTOR REPORT =======================
% 120.07/120.40 Sos_deleted=2435576, Sos_displaced=444372, Sos_size=9999
% 120.07/120.40 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 120.07/120.40 I 2147483647 high age 0 499
% 120.07/120.40 H 1 high weight 0 0
% 120.07/120.40 A 1 low age 9999 1518
% 120.07/120.40 F 4 low weight 1005 6068
% 120.07/120.40 T 4 low weight 8994 6068
% 120.07/120.40 ============================== end of selector report ================
% 120.07/120.40
% 120.07/120.40 ============================== end of statistics =====================
% 120.07/120.40
% 120.07/120.40 Exiting with failure.
% 120.07/120.40
% 120.07/120.40 Process 15191 exit (max_megs) Sat Jul 2 00:52:14 2022
% 120.07/120.40 Prover9 interrupted
%------------------------------------------------------------------------------