TSTP Solution File: SWV879-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV879-1 : 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 : Wed Jul 20 21:15:07 EDT 2022
% Result : Unsatisfiable 5.35s 5.61s
% Output : Refutation 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV879-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 01:54:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.33/1.66 ============================== Prover9 ===============================
% 1.33/1.66 Prover9 (32) version 2009-11A, November 2009.
% 1.33/1.66 Process 546 was started by sandbox2 on n013.cluster.edu,
% 1.33/1.66 Wed Jun 15 01:54:45 2022
% 1.33/1.66 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_375_n013.cluster.edu".
% 1.33/1.66 ============================== end of head ===========================
% 1.33/1.66
% 1.33/1.66 ============================== INPUT =================================
% 1.33/1.66
% 1.33/1.66 % Reading from file /tmp/Prover9_375_n013.cluster.edu
% 1.33/1.66
% 1.33/1.66 set(prolog_style_variables).
% 1.33/1.66 set(auto2).
% 1.33/1.66 % set(auto2) -> set(auto).
% 1.33/1.66 % set(auto) -> set(auto_inference).
% 1.33/1.66 % set(auto) -> set(auto_setup).
% 1.33/1.66 % set(auto_setup) -> set(predicate_elim).
% 1.33/1.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.33/1.66 % set(auto) -> set(auto_limits).
% 1.33/1.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.33/1.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.33/1.66 % set(auto) -> set(auto_denials).
% 1.33/1.66 % set(auto) -> set(auto_process).
% 1.33/1.66 % set(auto2) -> assign(new_constants, 1).
% 1.33/1.66 % set(auto2) -> assign(fold_denial_max, 3).
% 1.33/1.66 % set(auto2) -> assign(max_weight, "200.000").
% 1.33/1.66 % set(auto2) -> assign(max_hours, 1).
% 1.33/1.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.33/1.66 % set(auto2) -> assign(max_seconds, 0).
% 1.33/1.66 % set(auto2) -> assign(max_minutes, 5).
% 1.33/1.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.33/1.66 % set(auto2) -> set(sort_initial_sos).
% 1.33/1.66 % set(auto2) -> assign(sos_limit, -1).
% 1.33/1.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.33/1.66 % set(auto2) -> assign(max_megs, 400).
% 1.33/1.66 % set(auto2) -> assign(stats, some).
% 1.33/1.66 % set(auto2) -> clear(echo_input).
% 1.33/1.66 % set(auto2) -> set(quiet).
% 1.33/1.66 % set(auto2) -> clear(print_initial_clauses).
% 1.33/1.66 % set(auto2) -> clear(print_given).
% 1.33/1.66 assign(lrs_ticks,-1).
% 1.33/1.66 assign(sos_limit,10000).
% 1.33/1.66 assign(order,kbo).
% 1.33/1.66 set(lex_order_vars).
% 1.33/1.66 clear(print_given).
% 1.33/1.66
% 1.33/1.66 % formulas(sos). % not echoed (913 formulas)
% 1.33/1.66
% 1.33/1.66 ============================== end of input ==========================
% 1.33/1.66
% 1.33/1.66 % From the command line: assign(max_seconds, 300).
% 1.33/1.66
% 1.33/1.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.33/1.66
% 1.33/1.66 % Formulas that are not ordinary clauses:
% 1.33/1.66
% 1.33/1.66 ============================== end of process non-clausal formulas ===
% 1.33/1.66
% 1.33/1.66 ============================== PROCESS INITIAL CLAUSES ===============
% 1.33/1.66
% 1.33/1.66 ============================== PREDICATE ELIMINATION =================
% 1.33/1.66 1 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.33/1.66 2 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.33/1.66 3 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.33/1.66 4 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.33/1.66 5 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.33/1.66 6 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.33/1.66 7 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.33/1.66 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.33/1.66 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.33/1.66 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.33/1.66 11 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.33/1.66 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.33/1.66 13 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.33/1.66 14 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.33/1.66 15 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.33/1.66 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.33/1.66 17 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.33/1.66 18 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.33/1.66 19 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.33/1.66 20 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.33/1.66 21 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.33/1.66 22 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(1,a,2,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(1,a,3,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(1,a,4,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(1,a,5,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(1,a,7,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(1,a,9,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(1,a,11,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(1,a,12,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(1,a,13,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(1,a,14,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(1,a,15,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(1,a,16,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(1,a,17,a)].
% 1.33/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(1,a,19,a)].
% 1.43/1.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(1,a,20,a)].
% 1.43/1.73 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(1,a,21,a)].
% 1.43/1.73 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(1,a,22,a)].
% 1.43/1.73 23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.43/1.73 24 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 1.43/1.73 25 -class_Orderings_Olinorder(A) | -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(A) = c_Orderings_Oord__class_Omax(A) # label(cls_sup__max_0) # label(axiom). [assumption].
% 1.43/1.73 26 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 1.43/1.73 27 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),C,A) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 1.43/1.73 28 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B),C,A) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 1.43/1.73 29 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 1.43/1.73 30 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 1.43/1.73 31 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 1.43/1.73 32 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 1.43/1.73 33 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),C,A) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 1.43/1.73 34 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B),C,A) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 1.43/1.73 35 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 1.43/1.73 36 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 1.43/1.73 37 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 1.43/1.73 38 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 1.43/1.73 39 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 1.43/1.73 40 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 1.43/1.73 41 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 1.43/1.73 42 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 1.43/1.73 43 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 1.43/1.73 44 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C),A) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 1.43/1.73 45 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.43/1.73 46 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),B) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 1.43/1.73 47 -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].
% 1.43/1.73 48 -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].
% 1.43/1.73 49 -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].
% 1.43/1.73 50 -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].
% 1.43/1.73 51 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 1.43/1.73 52 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),A) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 1.43/1.73 53 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 1.43/1.73 54 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 1.43/1.73 55 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 1.43/1.73 56 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B),A) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 1.43/1.73 57 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),A) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 1.43/1.73 58 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 1.43/1.73 59 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 1.43/1.73 60 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 1.43/1.73 61 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 1.43/1.73 62 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 1.43/1.73 63 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 1.43/1.73 64 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 1.43/1.73 65 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 1.43/1.73 66 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 1.43/1.73 67 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 1.43/1.73 68 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__atLeastLessThan_0) # label(axiom). [assumption].
% 1.43/1.73 69 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.43/1.73 70 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 1.43/1.73 71 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) != C | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 1.43/1.73 72 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 1.43/1.73 73 -class_Orderings_Olinorder(A) | -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(A) = c_Orderings_Oord__class_Omin(A) # label(cls_inf__min_0) # label(axiom). [assumption].
% 1.43/1.73 74 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 1.43/1.73 75 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 1.43/1.73 76 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 1.43/1.73 77 -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].
% 1.43/1.73 78 -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].
% 1.43/1.73 79 -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].
% 1.43/1.73 80 -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].
% 1.43/1.73 81 -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].
% 1.43/1.73 82 -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].
% 1.43/1.73 83 -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].
% 1.43/1.73 84 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 1.43/1.73 85 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 1.43/1.73 86 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 1.43/1.73 87 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 1.43/1.73 88 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 1.43/1.73 89 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 1.43/1.73 90 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 1.43/1.73 91 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 1.43/1.73 92 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),B),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 1.43/1.73 93 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 1.43/1.73 94 -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].
% 1.43/1.73 95 -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].
% 1.43/1.73 96 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(D,E,A)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__greaterThanAtMost_0) # label(axiom). [assumption].
% 1.43/1.73 97 -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].
% 1.43/1.73 98 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(D,B,A),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom). [assumption].
% 1.43/1.73 99 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom). [assumption].
% 1.43/1.73 100 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OgreaterThanAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I20_J_0) # label(axiom). [assumption].
% 1.43/1.73 101 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 1.43/1.73 102 -class_Orderings_Olinorder(A) | c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(D,C,A) | -c_lessequals(B,D,A) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 1.43/1.73 103 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -hBOOL(c_in(C,D,A)) | -c_HOL_Oord__class_Oless(B,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),D),A) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_strict__below__fold1__iff_0) # label(axiom). [assumption].
% 1.43/1.73 104 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B),C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -hBOOL(c_in(D,B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__strict__below__iff_2) # label(axiom). [assumption].
% 1.43/1.73 105 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(A) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(A),A) # label(cls_Max__def__raw_0) # label(axiom). [assumption].
% 1.43/1.73 106 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(A) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A) # label(cls_linorder__class_OMin__def__raw_0) # label(axiom). [assumption].
% 1.43/1.73 107 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 1.43/1.73 108 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 1.43/1.73 109 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 1.43/1.73 110 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 1.43/1.73 111 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 1.43/1.74 112 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 1.43/1.74 113 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 1.43/1.74 114 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(D,E,A)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E),A) # label(cls_Int__atLeastAtMost_0) # label(axiom). [assumption].
% 1.43/1.74 115 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 1.43/1.74 116 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)),A) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 1.43/1.74 117 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 1.43/1.74 118 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 1.43/1.74 119 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 1.43/1.74 120 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 1.43/1.74 121 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 1.43/1.74 122 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I22_J_0) # label(axiom). [assumption].
% 1.43/1.74 123 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__insert_0) # label(axiom). [assumption].
% 1.43/1.74 124 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Min__insert_0) # label(axiom). [assumption].
% 1.43/1.74 125 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(c_Finite__Set_Olinorder__class_OMin(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__Un_0) # label(axiom). [assumption].
% 1.43/1.74 126 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(c_Finite__Set_Olinorder__class_OMax(A),B)),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__Un_0) # label(axiom). [assumption].
% 1.43/1.74 127 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B),C,A) | -c_lessequals(D,C,A) | -hBOOL(c_in(D,B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__below__iff_2) # label(axiom). [assumption].
% 1.43/1.74 128 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I5_J_0) # label(axiom). [assumption].
% 1.43/1.74 129 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I6_J_0) # label(axiom). [assumption].
% 1.43/1.74 130 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),B),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(A),A),C),A) | -c_Finite__Set_Ofinite(B,A) | -c_lessequals(C,B,tc_fun(A,tc_bool)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_fold1__antimono_0) # label(axiom). [assumption].
% 1.43/1.74 131 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(A),B),hAPP(c_Finite__Set_Olinorder__class_OMax(A),C),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 1.43/1.74 132 -class_Orderings_Olinorder(A) | c_lessequals(B,hAPP(c_Finite__Set_Olinorder__class_OMax(A),C),A) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 1.43/1.74 133 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(A),B),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 1.43/1.74 134 -class_Orderings_Olinorder(A) | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(A),B),hAPP(c_Finite__Set_Olinorder__class_OMin(A),C),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 1.43/1.74 135 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.43/1.74 136 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMin(A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 1.43/1.74 137 -class_Orderings_Olinorder(A) | hAPP(c_Finite__Set_Olinorder__class_OMax(A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 1.43/1.74 138 -class_Orderings_Olinorder(A) | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(A),B),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 1.43/1.74 139 -class_Orderings_Olinorder(A) | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(A),B),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A),B,tc_nat). [resolve(23,a,24,a)].
% 1.43/1.74 Derived: -class_Lattices_Oupper__semilattice(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat). [resolve(23,a,25,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),B),tc_nat). [resolve(23,a,26,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),B,tc_nat). [resolve(23,a,27,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A),B,tc_nat). [resolve(23,a,28,a)].
% 1.43/1.74 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,29,a)].
% 1.43/1.74 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,30,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),A),B,tc_nat). [resolve(23,a,35,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat). [resolve(23,a,36,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B),tc_nat). [resolve(23,a,37,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,38,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(23,a,39,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),B),tc_nat). [resolve(23,a,44,a)].
% 1.43/1.74 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(23,a,45,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),A) = A. [resolve(23,a,46,a)].
% 1.43/1.74 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(23,a,47,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),A) = A. [resolve(23,a,51,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)),tc_nat). [resolve(23,a,52,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)). [resolve(23,a,53,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)). [resolve(23,a,54,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)). [resolve(23,a,55,a)].
% 1.43/1.74 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A),tc_nat). [resolve(23,a,56,a)].
% 1.43/1.74 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B),tc_nat). [resolve(23,a,57,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,58,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),A,tc_nat). [resolve(23,a,61,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),B,tc_nat). [resolve(23,a,62,a)].
% 1.43/1.74 Derived: c_lessequals(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,63,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(23,a,66,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(23,a,67,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(23,a,68,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B). [resolve(23,a,69,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat). [resolve(23,a,70,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat). [resolve(23,a,71,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat). [resolve(23,a,72,a)].
% 1.43/1.74 Derived: -class_Lattices_Olower__semilattice(tc_nat) | c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat). [resolve(23,a,73,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = A | -c_lessequals(A,B,tc_nat). [resolve(23,a,74,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) != A | c_lessequals(A,B,tc_nat). [resolve(23,a,75,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = B | -c_lessequals(B,A,tc_nat). [resolve(23,a,76,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,77,a)].
% 1.43/1.74 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(23,a,80,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)). [resolve(23,a,84,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)). [resolve(23,a,85,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = A. [resolve(23,a,86,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(23,a,87,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(23,a,88,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),B,tc_nat). [resolve(23,a,91,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),C),A),B,tc_nat). [resolve(23,a,92,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)). [resolve(23,a,93,a)].
% 1.43/1.74 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(23,a,94,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,tc_nat)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(23,a,96,a)].
% 1.43/1.74 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(23,a,97,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(23,a,98,a)].
% 1.43/1.74 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(23,a,99,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,100,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,101,a)].
% 1.43/1.74 Derived: c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,102,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -hBOOL(c_in(B,C,tc_nat)) | -c_HOL_Oord__class_Oless(A,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),C),tc_nat) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(23,a,103,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A),B,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat) | -hBOOL(c_in(C,A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,104,a)].
% 1.43/1.74 Derived: c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat). [resolve(23,a,105,a)].
% 1.43/1.74 Derived: c_Finite__Set_Olinorder__class_OMin(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat). [resolve(23,a,106,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),A). [resolve(23,a,107,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(23,a,108,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(23,a,109,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),C),tc_nat). [resolve(23,a,110,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),C),B),tc_nat). [resolve(23,a,111,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),B),D),tc_nat). [resolve(23,a,114,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),A). [resolve(23,a,115,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)),tc_nat). [resolve(23,a,116,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)) = A. [resolve(23,a,117,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)). [resolve(23,a,118,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),C)). [resolve(23,a,119,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B). [resolve(23,a,120,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,121,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,122,a)].
% 1.43/1.74 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(23,a,123,a)].
% 1.43/1.74 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(23,a,124,a)].
% 1.43/1.74 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,125,a)].
% 1.43/1.74 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A)),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,126,a)].
% 1.43/1.74 Derived: c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A),B,tc_nat) | -c_lessequals(C,B,tc_nat) | -hBOOL(c_in(C,A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,127,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,128,a)].
% 1.43/1.77 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,129,a)].
% 1.43/1.77 Derived: c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat),B),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(23,a,130,a)].
% 1.43/1.77 Derived: c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)). [resolve(23,a,131,a)].
% 1.43/1.77 Derived: c_lessequals(A,hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B),tc_nat) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(23,a,132,a)].
% 1.43/1.77 Derived: c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A),B,tc_nat) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,133,a)].
% 1.43/1.77 Derived: c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A),hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),B),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)). [resolve(23,a,134,a)].
% 1.43/1.77 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,135,a)].
% 1.43/1.77 Derived: hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = A. [resolve(23,a,136,a)].
% 1.43/1.77 Derived: hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = A. [resolve(23,a,137,a)].
% 1.43/1.77 Derived: hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),A),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,138,a)].
% 1.43/1.77 Derived: hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),A),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,139,a)].
% 1.43/1.77 140 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.43/1.77 141 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,tc_bool)),C),D) != c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B) | c_Finite__Set_Osetsum(E,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(E,C,B,A)),c_Finite__Set_Osetsum(E,D,B,A)) # label(cls_setsum__Un__disjoint_0) # label(axiom). [assumption].
% 1.43/1.77 142 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.43/1.77 143 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),D),E),C,A)),c_Finite__Set_Osetsum(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,tc_bool)),D),E),C,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,D,C,A)),c_Finite__Set_Osetsum(B,E,C,A)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__Un__Int_0) # label(axiom). [assumption].
% 1.43/1.77 144 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.43/1.77 145 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.43/1.77 146 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oinsert(C,D,E),E,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,D,E,A)) | hBOOL(c_in(C,D,E)) | -c_Finite__Set_Ofinite(D,E) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.43/1.77 147 -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,c_Set_Oinsert(C,c_HOL_Ominus__class_Ominus(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)),A),A,A),E)) | hBOOL(c_in(C,D,A)) | -hBOOL(c_in(B,D,A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,A,A),E)) # label(cls_comm__monoid__add_Ofold__graph__permute__diff_0) # label(axiom). [assumption].
% 1.43/1.77 148 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),c_Set_Oinsert(B,C,A)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(A),B,C,A,A) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_comm__monoid__add_Ofold1__eq__fold_0) # label(axiom). [assumption].
% 1.43/1.77 149 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),C)) # label(cls_comm__monoid__add_Ofold1__Un_0) # label(axiom). [assumption].
% 1.43/1.77 150 -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),B,c_Set_Oinsert(C,D,A),A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),E))) | hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(A),C,D,A,A),E)) # label(cls_comm__monoid__add_Ofold__graph__insert__swap_0) # label(axiom). [assumption].
% 1.43/1.77 151 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),c_Finite__Set_Osetsum(B,c_HOL_Ominus__class_Ominus(C,c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)),D),tc_fun(D,tc_bool)),D,A)) | -hBOOL(c_in(E,C,D)) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 1.43/1.77 152 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(A),A),C)) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_comm__monoid__add_Ofold1__insert_0) # label(axiom). [assumption].
% 1.43/1.77 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | -c_Finite__Set_Ofinite(B,A) | c_Finite__Set_Osetsum(D,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(D,B,A,tc_nat)),c_Finite__Set_Osetsum(D,C,A,tc_nat)). [resolve(140,a,141,a)].
% 1.43/1.77 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),B,tc_nat)),c_Finite__Set_Osetsum(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,tc_bool)),C),D),B,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,C,B,tc_nat)),c_Finite__Set_Osetsum(A,D,B,tc_nat)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(140,a,143,a)].
% 1.58/1.87 Derived: c_Finite__Set_Osetsum(A,c_Set_Oinsert(B,C,D),D,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,C,D,tc_nat)) | hBOOL(c_in(B,C,D)) | -c_Finite__Set_Ofinite(C,D). [resolve(140,a,146,a)].
% 1.58/1.87 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,c_Set_Oinsert(B,c_HOL_Ominus__class_Ominus(C,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat,tc_nat),D)) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(c_in(A,C,tc_nat)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(140,a,147,a)].
% 1.58/1.87 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(140,a,148,a)].
% 1.58/1.87 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),A),B) != c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat) | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B)). [resolve(140,a,149,a)].
% 1.58/1.87 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),A,c_Set_Oinsert(B,C,tc_nat),tc_nat,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),D))) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(140,a,150,a)].
% 1.58/1.87 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),c_Finite__Set_Osetsum(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C,tc_nat)) | -hBOOL(c_in(D,B,C)) | -c_Finite__Set_Ofinite(B,C). [resolve(140,a,151,a)].
% 1.58/1.87 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B)) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(140,a,152,a)].
% 1.58/1.87 153 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.58/1.87 154 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.58/1.87 155 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.58/1.87 156 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.58/1.87 157 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.67/1.93 158 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(153,a,154,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(153,a,155,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(153,a,156,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(153,a,157,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(153,a,158,a)].
% 1.67/1.93 159 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.67/1.93 160 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.67/1.93 161 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.67/1.93 162 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.67/1.93 163 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.67/1.93 164 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.67/1.93 165 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.67/1.93 166 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.67/1.93 167 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.67/1.93 168 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 1.87/2.20 169 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 1.87/2.20 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(159,a,160,a)].
% 1.87/2.20 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(159,a,161,a)].
% 1.87/2.20 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(159,a,162,a)].
% 1.87/2.20 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(159,a,163,a)].
% 1.87/2.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(159,a,165,a)].
% 1.87/2.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(159,a,167,a)].
% 1.87/2.20 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(159,a,168,a)].
% 1.87/2.20 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(159,a,169,a)].
% 1.87/2.20 170 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.20 171 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.87/2.20 172 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.87/2.20 173 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.87/2.20 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(170,a,173,a)].
% 1.87/2.20 174 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.20 175 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.87/2.20 176 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.87/2.20 177 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.87/2.20 178 -class_OrderedGroup_Oab__semigroup__mult(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,c_HOL_Ominus__class_Ominus(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)),A),A,A),E)) | hBOOL(c_in(C,D,A)) | -hBOOL(c_in(B,D,A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,A,A),E)) # label(cls_fold__graph__permute__diff_0) # label(axiom). [assumption].
% 1.87/2.20 179 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),c_Set_Oinsert(B,C,A)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(A),B,C,A,A) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_fold1__eq__fold_0) # label(axiom). [assumption].
% 1.87/2.20 180 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(A,tc_bool)),B),C) != c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),B)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),C)) # label(cls_fold1__Un_0) # label(axiom). [assumption].
% 1.87/2.20 181 -class_OrderedGroup_Oab__semigroup__mult(A) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,D,A),A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E))) | hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,A,A),E)) # label(cls_fold__graph__insert__swap_0) # label(axiom). [assumption].
% 1.87/2.20 182 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),c_Set_Oinsert(B,C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(A),A),C)) | hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_fold1__insert_0) # label(axiom). [assumption].
% 1.87/2.20 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,c_HOL_Ominus__class_Ominus(C,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat,tc_nat),D)) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(c_in(A,C,tc_nat)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(176,a,178,a)].
% 1.87/2.20 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(tc_nat),A,B,tc_nat,tc_nat) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(176,a,179,a)].
% 1.87/2.20 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_nat,tc_bool)),A),B) != c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat) | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),B)). [resolve(176,a,180,a)].
% 1.87/2.20 Derived: hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,C,tc_nat),tc_nat,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D))) | hBOOL(c_in(B,C,tc_nat)) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,tc_nat,tc_nat),D)). [resolve(176,a,181,a)].
% 2.25/2.51 Derived: hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),c_Set_Oinsert(A,B,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat),B)) | hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)). [resolve(176,a,182,a)].
% 2.25/2.51 183 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.25/2.51 184 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.25/2.51 185 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.25/2.51 186 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 2.25/2.51 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(185,a,186,a)].
% 2.25/2.51 187 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.25/2.51 188 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.25/2.51 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(187,a,188,a)].
% 2.25/2.51 189 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.25/2.51 190 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.25/2.51 191 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.25/2.51 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(189,a,191,a)].
% 2.25/2.51
% 2.25/2.51 ============================== end predicate elimination =============
% 2.25/2.51
% 2.25/2.51 Auto_denials: (non-Horn, no changes).
% 2.25/2.51
% 2.25/2.51 Term ordering decisions:
% 2.25/2.51 Function symbol KB weights: tc_bool=1. tc_nat=1. v_x=1. t_a=1. tc_Com_Opname=1. v_U=1. v_G=1. v_P=1. v_mgt__call=1. hAPP=1. tc_fun=1. c_Finite__Set_Ocard=1. c_Finite__Set_Ofold1=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_Collect=1. c_The=1. c_fequal=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Set_Ocontents=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Orderings_Obot__class_Obot=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Otimes__class_Otimes=1. c_Orderings_Oord__class_Omin=1. c_Orderings_Otop__class_Otop=1. c_Orderings_Oord__class_Omax=1. c_Suc=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_in=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_COMBK=1. c_Finite__Set_Ofold1Set=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hilbert__Choice_Oinv__into=1. c_Finite__Set_Osetsum=1. c_Fun_Ofun__upd=1. c_Finite__Set_Ofold__graph=1. c_Finite__Set_Ofold=1. c_ATP__Linkup_Osko__Set__Ximage__cong__1__1=1. c_ATP__Linkup_Osko__Set__XimageE__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__iff__1__1=1.
% 5.35/5.61
% 5.35/5.61 ============================== end of process initial clauses ========
% 5.35/5.61
% 5.35/5.61 ============================== CLAUSES FOR SEARCH ====================
% 5.35/5.61
% 5.35/5.61 ============================== end of clauses for search =============
% 5.35/5.61
% 5.35/5.61 ============================== SEARCH ================================
% 5.35/5.61
% 5.35/5.61 % Starting search at 0.93 seconds.
% 5.35/5.61
% 5.35/5.61 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 1.55 sec).
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=56.000, iters=3586
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=48.000, iters=3365
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=45.000, iters=3334
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=44.000, iters=3350
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=43.000, iters=3460
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=42.000, iters=3481
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=41.000, iters=3439
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=40.000, iters=3432
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=39.000, iters=3365
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=38.000, iters=3374
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=37.000, iters=3392
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=36.000, iters=3342
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=35.000, iters=3376
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=34.000, iters=3360
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=33.000, iters=3379
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=32.000, iters=3432
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=31.000, iters=3369
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=30.000, iters=3407
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=29.000, iters=3467
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=28.000, iters=3483
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=27.000, iters=3379
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=26.000, iters=3355
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=25.000, iters=3337
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=24.000, iters=3340
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=23.000, iters=3345
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=22.000, iters=3337
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=21.000, iters=3343
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=20.000, iters=3346
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=19.000, iters=3345
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=18.000, iters=3351
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=17.000, iters=3334
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=16.000, iters=3350
% 5.35/5.61
% 5.35/5.61 Low Water (keep): wt=15.000, iters=3336
% 5.35/5.61
% 5.35/5.61 Low Water (displace): id=3286, wt=124.000
% 5.35/5.61
% 5.35/5.61 Low Water (displace): id=3283, wt=106.000
% 5.35/5.61
% 5.35/5.61 Low Water (displace): id=12901, wt=14.000
% 5.35/5.61
% 5.35/5.61 Low Water (displace): id=12970, wt=13.000
% 5.35/5.61
% 5.35/5.61 ============================== PROOF =================================
% 5.35/5.61 % SZS status Unsatisfiable
% 5.35/5.61 % SZS output start Refutation
% 5.35/5.61
% 5.35/5.61 % Proof 1 at 3.96 (+ 0.08) seconds.
% 5.35/5.61 % Length of proof is 26.
% 5.35/5.61 % Level of proof is 7.
% 5.35/5.61 % Maximum clause weight is 18.000.
% 5.35/5.61 % Given clauses 1902.
% 5.35/5.61
% 5.35/5.61 574 c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) # label(cls_empty__subsetI_0) # label(axiom). [assumption].
% 5.35/5.61 588 c_lessequals(c_Set_Oinsert(A,B,C),c_Set_Oinsert(A,D,C),tc_fun(C,tc_bool)) | -c_lessequals(B,D,tc_fun(C,tc_bool)) # label(cls_insert__mono_0) # label(axiom). [assumption].
% 5.35/5.61 602 hBOOL(hAPP(hAPP(v_P,A),B)) | -c_lessequals(B,A,tc_fun(t_a,tc_bool)) # label(cls_assms_I1_J_0) # label(axiom). [assumption].
% 5.35/5.61 625 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 5.35/5.61 721 c_Collect(c_fequal(A,B),B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 5.35/5.61 722 c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = c_fequal(A,B). [copy(721),rewrite([625(2)]),flip(a)].
% 5.35/5.61 746 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = c_Set_Oinsert(A,B,C) # label(cls_insert__Diff__single_0) # label(axiom). [assumption].
% 5.35/5.61 747 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_fequal(A,C),tc_fun(C,tc_bool)),C) = c_Set_Oinsert(A,B,C). [copy(746),rewrite([722(4)])].
% 5.35/5.61 758 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = B | -hBOOL(c_in(A,B,C)) # label(cls_insert__Diff_0) # label(axiom). [assumption].
% 5.35/5.61 759 c_Set_Oinsert(A,B,C) = B | -hBOOL(c_in(A,B,C)). [copy(758),rewrite([722(4),747(5)])].
% 5.35/5.61 804 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 5.35/5.61 805 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,A,C)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 5.35/5.61 816 -hBOOL(c_in(A,B,C)) | hBOOL(c_in(hAPP(D,A),c_Set_Oimage(D,B,C,E),E)) # label(cls_rev__image__eqI_0) # label(axiom). [assumption].
% 5.35/5.61 818 v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 5.35/5.61 819 c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = v_G. [copy(818),flip(a)].
% 5.35/5.61 820 hBOOL(c_in(v_x,v_U,tc_Com_Opname)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 5.35/5.61 821 -hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 5.35/5.61 822 -hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a))). [copy(821),rewrite([819(6),722(12)])].
% 5.35/5.61 2221 c_lessequals(c_fequal(A,B),c_Set_Oinsert(A,C,B),tc_fun(B,tc_bool)). [resolve(588,b,574,a),rewrite([722(4)])].
% 5.35/5.61 4016 hBOOL(c_in(hAPP(A,v_x),c_Set_Oimage(A,v_U,tc_Com_Opname,B),B)). [resolve(820,a,816,a)].
% 5.35/5.61 13032 hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a)). [para(819(a,1),4016(a,1,2))].
% 5.35/5.61 13068 hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x))). [resolve(13032,a,805,b)].
% 5.35/5.61 13090 hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,A)). [resolve(13068,a,804,b)].
% 5.35/5.61 13109 c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,A) = v_G. [resolve(13090,a,759,b)].
% 5.35/5.61 13134 c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),A),v_G,tc_fun(A,tc_bool)). [para(13109(a,1),2221(a,2))].
% 5.35/5.61 13265 $F. [resolve(13134,a,602,b),unit_del(a,822)].
% 5.35/5.61
% 5.35/5.61 % SZS output end Refutation
% 5.35/5.61 ============================== end of proof ==========================
% 5.35/5.61
% 5.35/5.61 ============================== STATISTICS ============================
% 5.35/5.61
% 5.35/5.61 Given=1902. Generated=59264. Kept=12873. proofs=1.
% 5.35/5.61 Usable=1873. Sos=9999. Demods=1359. Limbo=4, Disabled=2049. Hints=0.
% 5.35/5.61 Megabytes=23.92.
% 5.35/5.61 User_CPU=3.96, System_CPU=0.08, Wall_clock=4.
% 5.35/5.61
% 5.35/5.61 ============================== end of statistics =====================
% 5.35/5.61
% 5.35/5.61 ============================== end of search =========================
% 5.35/5.61
% 5.35/5.61 THEOREM PROVED
% 5.35/5.61 % SZS status Unsatisfiable
% 5.35/5.61
% 5.35/5.61 Exiting with 1 proof.
% 5.35/5.61
% 5.35/5.61 Process 546 exit (max_proofs) Wed Jun 15 01:54:49 2022
% 5.35/5.61 Prover9 interrupted
%------------------------------------------------------------------------------