TSTP Solution File: SCT086-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT086-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:03:49 EDT 2022
% Result : Timeout 300.06s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT086-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 21:56:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.97/1.33 ============================== Prover9 ===============================
% 0.97/1.33 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.33 Process 15196 was started by sandbox on n025.cluster.edu,
% 0.97/1.33 Fri Jul 1 21:56:40 2022
% 0.97/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15043_n025.cluster.edu".
% 0.97/1.33 ============================== end of head ===========================
% 0.97/1.33
% 0.97/1.33 ============================== INPUT =================================
% 0.97/1.33
% 0.97/1.33 % Reading from file /tmp/Prover9_15043_n025.cluster.edu
% 0.97/1.33
% 0.97/1.33 set(prolog_style_variables).
% 0.97/1.33 set(auto2).
% 0.97/1.33 % set(auto2) -> set(auto).
% 0.97/1.33 % set(auto) -> set(auto_inference).
% 0.97/1.33 % set(auto) -> set(auto_setup).
% 0.97/1.33 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.33 % set(auto) -> set(auto_limits).
% 0.97/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.33 % set(auto) -> set(auto_denials).
% 0.97/1.33 % set(auto) -> set(auto_process).
% 0.97/1.33 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.33 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.33 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.33 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.33 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.33 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.33 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.33 % set(auto2) -> assign(stats, some).
% 0.97/1.33 % set(auto2) -> clear(echo_input).
% 0.97/1.33 % set(auto2) -> set(quiet).
% 0.97/1.33 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.33 % set(auto2) -> clear(print_given).
% 0.97/1.33 assign(lrs_ticks,-1).
% 0.97/1.33 assign(sos_limit,10000).
% 0.97/1.33 assign(order,kbo).
% 0.97/1.33 set(lex_order_vars).
% 0.97/1.33 clear(print_given).
% 0.97/1.33
% 0.97/1.33 % formulas(sos). % not echoed (560 formulas)
% 0.97/1.33
% 0.97/1.33 ============================== end of input ==========================
% 0.97/1.33
% 0.97/1.33 % From the command line: assign(max_seconds, 300).
% 0.97/1.33
% 0.97/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.33
% 0.97/1.33 % Formulas that are not ordinary clauses:
% 0.97/1.33
% 0.97/1.33 ============================== end of process non-clausal formulas ===
% 0.97/1.33
% 0.97/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.33
% 0.97/1.33 ============================== PREDICATE ELIMINATION =================
% 0.97/1.33 1 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(C,B,A,A)),D)) | C = B | -hBOOL(hAPP(hAPP(c_in(A),B),E)) | -hBOOL(hAPP(hAPP(c_in(A),C),E)) | -c_Relation_Ototal__on(E,D,A) # label(cls_total__on__def_0) # label(axiom). [assumption].
% 0.97/1.33 2 c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,A) # label(cls_total__on__empty_0) # label(axiom). [assumption].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(C,B,A,A)),D)) | C = B | -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))) | -hBOOL(hAPP(hAPP(c_in(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))). [resolve(1,f,2,a)].
% 0.97/1.33 3 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 0.97/1.33 4 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 0.97/1.33 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(3,a,4,a)].
% 0.97/1.33 5 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.97/1.33 6 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 0.97/1.33 7 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,c_Suc(C),A)),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 0.97/1.33 8 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 0.97/1.33 9 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 0.97/1.33 10 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,c_Suc(D),A)),c_Power_Opower__class_Opower(C,c_Suc(D),A))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 0.97/1.33 11 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 0.97/1.33 12 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),D),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 0.97/1.33 13 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.97/1.33 14 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 0.97/1.33 15 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 0.97/1.33 16 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 0.97/1.33 17 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.97/1.33 18 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.97/1.33 19 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 0.97/1.33 20 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 0.97/1.33 21 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,D,A)),c_Power_Opower__class_Opower(C,D,A))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 0.97/1.33 22 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,c_Suc(C),A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 0.97/1.33 23 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.97/1.33 24 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 0.97/1.33 25 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 0.97/1.33 26 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 0.97/1.33 27 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 0.97/1.33 28 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 0.97/1.33 29 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 0.97/1.33 30 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 0.97/1.33 31 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 0.97/1.33 32 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(5,a,6,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(5,a,7,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(5,a,8,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(5,a,9,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat)),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat))). [resolve(5,a,10,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(5,a,11,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)). [resolve(5,a,12,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(5,a,13,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(5,a,14,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(5,a,15,a)].
% 0.97/1.33 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(5,a,16,a)].
% 0.97/1.33 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(5,a,17,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(5,a,18,a)].
% 0.97/1.33 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | B = C. [resolve(5,a,19,a)].
% 0.97/1.33 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(5,a,20,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat)),c_Power_Opower__class_Opower(B,C,tc_nat))). [resolve(5,a,21,a)].
% 0.97/1.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(5,a,22,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))). [resolve(5,a,23,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(5,a,24,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(5,a,25,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(5,a,28,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(5,a,29,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(5,a,30,a)].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))). [resolve(5,a,32,a)].
% 0.97/1.35 33 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Relation_Orefl__on(D,C,A) # label(cls_refl__onD_0) # label(axiom). [assumption].
% 0.97/1.35 34 c_Relation_Orefl__on(A,c_Relation_OId__on(A,B),B) # label(cls_refl__on__Id__on_0) # label(axiom). [assumption].
% 0.97/1.35 35 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Equiv__Relations_Oequiv(D,C,A). [resolve(33,c,35,a)].
% 0.97/1.35 36 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E)) | -c_Relation_Orefl__on(C,E,A) # label(cls_refl__onD1_0) # label(axiom). [assumption].
% 0.97/1.35 37 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E)) | -c_Relation_Orefl__on(C,E,A) # label(cls_refl__onD2_0) # label(axiom). [assumption].
% 0.97/1.35 Derived: hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),c_Relation_OId__on(C,A))). [resolve(37,c,34,a)].
% 0.97/1.35 38 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Relation_Orefl__on(D,C,A) # label(cls_refl__on__def_1) # label(axiom). [assumption].
% 0.97/1.35 39 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.97/1.35 40 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 0.97/1.35 41 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 0.97/1.35 42 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 0.97/1.35 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(39,a,40,a)].
% 0.97/1.35 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(39,a,41,a)].
% 0.97/1.35 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(39,a,42,a)].
% 0.97/1.35 43 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.35 44 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 0.97/1.35 45 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 0.97/1.35 46 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 0.97/1.35 47 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 0.97/1.35 48 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.97/1.35 49 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.97/1.35 50 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.97/1.35 51 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 0.97/1.35 52 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 0.97/1.35 53 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 0.97/1.36 54 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(43,a,44,a)].
% 0.97/1.36 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(43,a,45,a)].
% 0.97/1.36 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(43,a,46,a)].
% 0.97/1.36 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(43,a,47,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(43,a,48,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(43,a,49,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(43,a,51,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(43,a,52,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(43,a,53,a)].
% 0.97/1.36 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(43,a,54,a)].
% 0.97/1.36 55 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.97/1.36 56 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 0.97/1.36 57 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 0.97/1.36 58 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 0.97/1.36 59 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 0.97/1.36 60 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 0.97/1.36 61 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(D,B,A)),c_HOL_Oplus__class_Oplus(D,C,A))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 0.97/1.36 62 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,D,A)),c_HOL_Oplus__class_Oplus(C,D,A))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 0.97/1.36 63 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 0.97/1.36 64 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(D,B,A)),c_HOL_Oplus__class_Oplus(D,C,A))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 0.97/1.36 65 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 0.97/1.36 66 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,D,A)),c_HOL_Oplus__class_Oplus(C,D,A))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 0.97/1.36 67 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 0.97/1.36 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(55,a,56,a)].
% 0.97/1.36 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)). [resolve(55,a,57,a)].
% 0.97/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(55,a,58,a)].
% 0.97/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(55,a,59,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(55,a,60,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(C,A,tc_nat)),c_HOL_Oplus__class_Oplus(C,B,tc_nat))). [resolve(55,a,61,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat)),c_HOL_Oplus__class_Oplus(B,C,tc_nat))). [resolve(55,a,62,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(55,a,63,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(C,A,tc_nat)),c_HOL_Oplus__class_Oplus(C,B,tc_nat))). [resolve(55,a,64,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(55,a,65,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat)),c_HOL_Oplus__class_Oplus(B,C,tc_nat))). [resolve(55,a,66,a)].
% 0.97/1.37 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(55,a,67,a)].
% 0.97/1.37 68 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.97/1.37 69 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.97/1.37 70 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.97/1.37 71 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.97/1.37 72 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 0.97/1.37 73 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.97/1.37 74 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.97/1.37 75 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.97/1.37 76 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.97/1.39 77 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.97/1.39 78 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.97/1.39 79 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.97/1.39 80 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(68,a,69,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(68,a,70,a)].
% 0.97/1.39 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(68,a,72,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(68,a,73,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(68,a,75,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(68,a,77,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). [resolve(68,a,78,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(68,a,79,a)].
% 0.97/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,D,tc_nat),tc_nat). [resolve(68,a,80,a)].
% 0.97/1.39 81 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.97/1.39 82 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.97/1.39 83 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.97/1.39 84 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 0.97/1.39 85 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 0.97/1.39 86 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 0.97/1.39 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(84,a,85,a)].
% 0.97/1.39 87 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.97/1.39 88 -class_Orderings_Olinorder(A) | c_Orderings_Olinorder(c_COMBC(c_lessequals(A),A,A,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(A),A,A,tc_bool),A) # label(cls_dual__linorder_0) # label(axiom). [assumption].
% 0.97/1.39 89 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.97/1.39 90 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.97/1.39 91 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.97/1.39 92 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.97/1.39 93 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.97/1.39 94 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.97/1.39 95 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.97/1.39 96 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.97/1.39 97 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.97/1.39 98 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.97/1.39 99 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.97/1.39 100 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.97/1.39 101 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.97/1.39 102 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.97/1.39 103 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.97/1.39 104 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.97/1.39 Derived: c_Orderings_Olinorder(c_COMBC(c_lessequals(tc_nat),tc_nat,tc_nat,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(tc_nat),tc_nat,tc_nat,tc_bool),tc_nat). [resolve(87,a,88,a)].
% 0.97/1.39 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(87,a,89,a)].
% 0.97/1.39 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(87,a,91,a)].
% 0.97/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(87,a,92,a)].
% 0.97/1.39 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(87,a,93,a)].
% 0.97/1.39 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(87,a,98,a)].
% 0.97/1.39 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(87,a,101,a)].
% 0.97/1.40 105 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.40 106 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.97/1.40 107 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.97/1.40 108 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 0.97/1.40 109 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 0.97/1.40 110 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 0.97/1.40 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(105,a,108,a)].
% 0.97/1.40 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(105,a,109,a)].
% 0.97/1.40 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(105,a,110,a)].
% 0.97/1.40 111 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.40 112 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 0.97/1.40 113 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 0.97/1.40 114 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 0.97/1.40 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(111,a,114,a)].
% 0.97/1.40 115 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.40 116 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.50/2.79 117 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.50/2.79 118 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.50/2.79 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(117,a,118,a)].
% 2.50/2.79 119 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.50/2.79 120 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.50/2.79 121 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.50/2.79 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(119,a,121,a)].
% 2.50/2.79 122 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.50/2.79 123 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.50/2.79 Derived: A = A. [resolve(122,b,123,a)].
% 2.50/2.79
% 2.50/2.79 ============================== end predicate elimination =============
% 2.50/2.79
% 2.50/2.79 Auto_denials: (non-Horn, no changes).
% 2.50/2.79
% 2.50/2.79 Term ordering decisions:
% 2.50/2.79 Function symbol KB weights: tc_nat=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_bool=1. tc_Arrow__Order__Mirabelle_Oindi=1. v_h____=1. v_Lab____=1. v_Lba____=1. v_F=1. v_a____=1. v_b____=1. v_n=1. c_Arrow__Order__Mirabelle_OProf=1. hAPP=1. tc_fun=1. tc_prod=1. c_HOL_Ouminus__class_Ouminus=1. c_Relation_OId__on=1. c_Finite__Set_Ocard=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Wellfounded_Oacc=1. c_Wellfounded_Omeasure=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_in=1. c_HOL_Ozero__class_Ozero=1. c_Suc=1. c_HOL_Oone__class_Oone=1. c_Orderings_Otop__class_Otop=1. c_Orderings_Obot__class_Obot=1. c_HOL_OIf=1. c_HOL_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Wellfounded_Omlex__prod=1. c_COMBC=1. c_Pair=1. c_Set_Ovimage=1. c_Product__Type_OSigma=1. c_Relation_OImage=1. c_COMBB=1. v_sko__CHAINED__1=1. v_sko__local__Xthat__1=1.
% 2.50/2.79
% 2.50/2.79 ============================== end of process initial clauses ========
% 2.50/2.79
% 2.50/2.79 ============================== CLAUSES FOR SEARCH ====================
% 2.50/2.79
% 2.50/2.79 ============================== end of clauses for search =============
% 2.50/2.79
% 2.50/2.79 ============================== SEARCH ================================
% 2.50/2.79
% 2.50/2.79 % Starting search at 0.21 seconds.
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=157.000, iters=3398
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=145.000, iters=3333
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=141.000, iters=3400
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=124.000, iters=3390
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=122.000, iters=3363
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=121.000, iters=3345
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=117.000, iters=3349
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=110.000, iters=3430
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=108.000, iters=3357
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=107.000, iters=3561
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=105.000, iters=3439
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=104.000, iters=3397
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=102.000, iters=3411
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=100.000, iters=3337
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=99.000, iters=3377
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=94.000, iters=3339
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=93.000, iters=3451
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=91.000, iters=3353
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=90.000, iters=3438
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=88.000, iters=3375
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=86.000, iters=3336
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=83.000, iters=3488
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=81.000, iters=3444
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=78.000, iters=3418
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=74.000, iters=3429
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=70.000, iters=3382
% 2.50/2.79
% 2.50/2.79 Low Water (keep): wt=69.000, iters=3390
% 2.50/2.79
% 2.50/2.79 Low Water (keeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------