TSTP Solution File: SCT088-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT088-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Unsatisfiable 1.51s 1.80s
% Output : Refutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT088-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 1 22:38:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.97/1.24 ============================== Prover9 ===============================
% 0.97/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.24 Process 25964 was started by sandbox on n023.cluster.edu,
% 0.97/1.24 Fri Jul 1 22:38:44 2022
% 0.97/1.24 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25811_n023.cluster.edu".
% 0.97/1.24 ============================== end of head ===========================
% 0.97/1.24
% 0.97/1.24 ============================== INPUT =================================
% 0.97/1.24
% 0.97/1.24 % Reading from file /tmp/Prover9_25811_n023.cluster.edu
% 0.97/1.24
% 0.97/1.24 set(prolog_style_variables).
% 0.97/1.24 set(auto2).
% 0.97/1.24 % set(auto2) -> set(auto).
% 0.97/1.24 % set(auto) -> set(auto_inference).
% 0.97/1.24 % set(auto) -> set(auto_setup).
% 0.97/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.24 % set(auto) -> set(auto_limits).
% 0.97/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.24 % set(auto) -> set(auto_denials).
% 0.97/1.24 % set(auto) -> set(auto_process).
% 0.97/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.24 % set(auto2) -> assign(stats, some).
% 0.97/1.24 % set(auto2) -> clear(echo_input).
% 0.97/1.24 % set(auto2) -> set(quiet).
% 0.97/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.24 % set(auto2) -> clear(print_given).
% 0.97/1.24 assign(lrs_ticks,-1).
% 0.97/1.24 assign(sos_limit,10000).
% 0.97/1.24 assign(order,kbo).
% 0.97/1.24 set(lex_order_vars).
% 0.97/1.24 clear(print_given).
% 0.97/1.24
% 0.97/1.24 % formulas(sos). % not echoed (674 formulas)
% 0.97/1.24
% 0.97/1.24 ============================== end of input ==========================
% 0.97/1.24
% 0.97/1.24 % From the command line: assign(max_seconds, 300).
% 0.97/1.24
% 0.97/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.24
% 0.97/1.24 % Formulas that are not ordinary clauses:
% 0.97/1.24
% 0.97/1.24 ============================== end of process non-clausal formulas ===
% 0.97/1.24
% 0.97/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.24
% 0.97/1.24 ============================== PREDICATE ELIMINATION =================
% 0.97/1.24 1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.97/1.24 2 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 0.97/1.24 3 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 0.97/1.24 4 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 0.97/1.24 5 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.97/1.24 6 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 0.97/1.24 7 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 0.97/1.24 8 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 0.97/1.24 9 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.97/1.24 10 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 0.97/1.24 11 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.97/1.24 12 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 0.97/1.24 13 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 0.97/1.24 14 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 0.97/1.24 15 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 0.97/1.24 16 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.97/1.24 17 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.97/1.24 18 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(D,C,A) | B = D | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 0.97/1.24 19 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 0.97/1.24 20 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 0.97/1.24 21 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 0.97/1.24 22 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 0.97/1.24 23 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 0.97/1.24 24 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 0.97/1.24 25 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 0.97/1.24 26 -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 | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(1,a,2,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,3,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,4,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(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),tc_nat). [resolve(1,a,5,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(1,a,6,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,7,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,8,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(1,a,9,a)].
% 0.97/1.24 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(1,a,10,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,11,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,12,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(1,a,13,a)].
% 0.97/1.24 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,16,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,17,a)].
% 0.97/1.24 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,18,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,19,a)].
% 0.97/1.24 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,20,a)].
% 0.97/1.24 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat),tc_nat). [resolve(1,a,21,a)].
% 0.97/1.24 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,22,a)].
% 0.97/1.24 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,23,a)].
% 0.97/1.24 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,24,a)].
% 0.97/1.24 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,25,a)].
% 0.97/1.24 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 | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,26,a)].
% 0.97/1.24 27 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(27,a,2,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,3,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(27,a,4,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(27,a,5,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(27,a,6,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,7,a)].
% 0.97/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,8,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(27,a,9,a)].
% 0.97/1.27 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(27,a,10,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(27,a,11,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,12,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(27,a,13,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(27,a,16,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(27,a,17,a)].
% 0.97/1.27 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(C,B,tc_Int_Oint) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,18,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,19,a)].
% 0.97/1.27 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,20,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Int_Oint),tc_Int_Oint). [resolve(27,a,21,a)].
% 0.97/1.27 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(27,a,22,a)].
% 0.97/1.27 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(27,a,23,a)].
% 0.97/1.27 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,24,a)].
% 0.97/1.27 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(27,a,25,a)].
% 0.97/1.27 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Int_Oint) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(27,a,26,a)].
% 0.97/1.27 28 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.97/1.27 29 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),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].
% 0.97/1.27 30 -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].
% 0.97/1.27 31 -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].
% 0.97/1.27 32 -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].
% 0.97/1.27 33 -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].
% 0.97/1.27 34 -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].
% 0.97/1.27 35 -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].
% 0.97/1.27 36 -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].
% 0.97/1.27 37 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 0.97/1.27 38 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 0.97/1.27 39 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 0.97/1.27 40 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 0.97/1.27 41 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 0.97/1.27 42 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 0.97/1.27 43 -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(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 0.97/1.27 44 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.97/1.27 45 -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].
% 0.97/1.27 46 -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].
% 0.97/1.27 47 -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].
% 0.97/1.27 48 -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].
% 0.97/1.27 49 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 0.97/1.27 50 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 0.97/1.27 51 -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].
% 0.97/1.27 52 -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].
% 0.97/1.27 53 -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].
% 0.97/1.27 54 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 0.97/1.27 55 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 0.97/1.27 56 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 0.97/1.27 57 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 0.97/1.27 58 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 0.97/1.27 59 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 0.97/1.27 60 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 0.97/1.27 61 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 0.97/1.27 62 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 0.97/1.27 63 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 0.97/1.27 64 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 0.97/1.27 65 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 0.97/1.27 66 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 0.97/1.27 67 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 0.97/1.27 68 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,B,A) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 0.97/1.27 69 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.97/1.27 70 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(B,C,A),A) = c_Orderings_Oord__class_Omin(B,C,A) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 0.97/1.27 71 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 0.97/1.27 72 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 0.97/1.27 73 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 0.97/1.27 74 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 0.97/1.27 75 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(C,c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 0.97/1.27 76 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = c_Orderings_Oord__class_Omin(C,B,A) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 0.97/1.27 77 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) # label(cls_sorted_Osimps_I3_J_0) # label(axiom). [assumption].
% 0.97/1.27 78 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_sorted_Osimps_I3_J_2) # label(axiom). [assumption].
% 0.97/1.27 79 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,B,A),A) # label(cls_sorted__Cons_0) # label(axiom). [assumption].
% 0.97/1.27 80 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(D,c_List_Olist_OCons(B,C,A),A),A) # label(cls_sorted_Osimps_I3_J_1) # label(axiom). [assumption].
% 0.97/1.27 81 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Odrop(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__drop_0) # label(axiom). [assumption].
% 0.97/1.27 82 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Otake(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__take_0) # label(axiom). [assumption].
% 0.97/1.27 83 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) # label(cls_sorted__append_0) # label(axiom). [assumption].
% 0.97/1.27 84 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(C,B,A),A) # label(cls_sorted__append_1) # label(axiom). [assumption].
% 0.97/1.27 85 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oremdups(B,A),A) | -c_List_Olinorder__class_Osorted(B,A) # label(cls_sorted__remdups_0) # label(axiom). [assumption].
% 0.97/1.27 86 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oremove1(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__remove1_0) # label(axiom). [assumption].
% 0.97/1.27 87 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_ONil(A),A) # label(cls_sorted_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.97/1.27 88 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_ONil(A),A),A) # label(cls_sorted_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(28,a,29,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(28,a,30,a)].
% 0.97/1.27 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(28,a,31,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(28,a,33,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(28,a,37,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(28,a,38,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(28,a,39,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(28,a,40,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(28,a,43,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(28,a,44,a)].
% 0.97/1.27 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(28,a,45,a)].
% 0.97/1.27 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(28,a,51,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(28,a,53,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(28,a,54,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(28,a,55,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(28,a,56,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(28,a,57,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),A,tc_nat). [resolve(28,a,62,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),B,tc_nat). [resolve(28,a,63,a)].
% 0.97/1.27 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(28,a,64,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(28,a,67,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,A,tc_nat) = A. [resolve(28,a,68,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(28,a,69,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(A,B,tc_nat). [resolve(28,a,70,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(28,a,71,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(28,a,72,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(28,a,73,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(28,a,74,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat). [resolve(28,a,75,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = c_Orderings_Oord__class_Omin(B,A,tc_nat). [resolve(28,a,76,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat). [resolve(28,a,77,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(28,a,78,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,A,tc_nat),tc_nat). [resolve(28,a,79,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Odrop(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(28,a,81,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Otake(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(28,a,82,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat). [resolve(28,a,83,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_nat),tc_nat). [resolve(28,a,84,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Oremdups(A,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat). [resolve(28,a,85,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(28,a,86,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(28,a,87,a)].
% 0.97/1.27 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat). [resolve(28,a,88,a)].
% 0.97/1.27 89 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(89,a,29,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(89,a,30,a)].
% 0.97/1.27 Derived: -c_lessequals(A,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(89,a,31,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(89,a,33,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(89,a,37,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(89,a,38,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,39,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,40,a)].
% 0.97/1.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(89,a,43,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(89,a,44,a)].
% 0.97/1.27 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(89,a,45,a)].
% 0.97/1.27 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(89,a,51,a)].
% 0.97/1.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(89,a,53,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,54,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,55,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(89,a,56,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(89,a,57,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),A,tc_Int_Oint). [resolve(89,a,62,a)].
% 0.97/1.27 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),B,tc_Int_Oint). [resolve(89,a,63,a)].
% 0.97/1.27 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(89,a,64,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(C,B,tc_Int_Oint) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(89,a,67,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,A,tc_Int_Oint) = A. [resolve(89,a,68,a)].
% 0.97/1.27 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(89,a,69,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint). [resolve(89,a,70,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(89,a,71,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) != A | c_lessequals(A,B,tc_Int_Oint). [resolve(89,a,72,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = B | -c_lessequals(B,A,tc_Int_Oint). [resolve(89,a,73,a)].
% 0.97/1.27 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,74,a)].
% 0.97/1.30 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,75,a)].
% 0.97/1.30 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = c_Orderings_Oord__class_Omin(B,A,tc_Int_Oint). [resolve(89,a,76,a)].
% 0.97/1.30 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(89,a,77,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(89,a,78,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,79,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Odrop(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(89,a,81,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Otake(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(89,a,82,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,83,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(89,a,84,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Oremdups(A,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(A,tc_Int_Oint). [resolve(89,a,85,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(89,a,86,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint). [resolve(89,a,87,a)].
% 0.97/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(89,a,88,a)].
% 0.97/1.30 90 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.30 91 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.97/1.30 92 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 0.97/1.30 93 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 0.97/1.30 94 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 0.97/1.30 95 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 0.97/1.30 96 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.97/1.30 97 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 0.97/1.30 98 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 0.97/1.30 99 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.97/1.30 100 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),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].
% 0.97/1.30 101 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 0.97/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(90,a,91,a)].
% 0.97/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(90,a,92,a)].
% 0.97/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(90,a,93,a)].
% 0.97/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(90,a,94,a)].
% 0.97/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(90,a,95,a)].
% 0.97/1.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(90,a,97,a)].
% 0.97/1.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(90,a,98,a)].
% 0.97/1.30 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(90,a,99,a)].
% 0.97/1.30 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),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(90,a,100,a)].
% 0.97/1.33 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(90,a,101,a)].
% 0.97/1.33 102 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(102,a,91,a)].
% 0.97/1.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(102,a,92,a)].
% 0.97/1.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(102,a,93,a)].
% 0.97/1.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(102,a,94,a)].
% 0.97/1.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(102,a,95,a)].
% 0.97/1.33 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(102,a,97,a)].
% 0.97/1.33 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(102,a,98,a)].
% 0.97/1.33 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(102,a,99,a)].
% 0.97/1.33 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(102,a,100,a)].
% 0.97/1.33 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(102,a,101,a)].
% 0.97/1.33 103 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.33 104 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.06/1.34 105 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.06/1.34 106 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),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].
% 1.06/1.34 107 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.06/1.34 108 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(103,a,104,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,105,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,106,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,107,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(103,a,108,a)].
% 1.06/1.34 109 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(109,a,104,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(109,a,105,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(109,a,106,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(109,a,107,a)].
% 1.06/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(109,a,108,a)].
% 1.06/1.34 110 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.06/1.34 111 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.06/1.34 112 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.06/1.36 113 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.06/1.36 114 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.06/1.36 115 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.06/1.36 116 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.06/1.36 117 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.06/1.36 118 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.06/1.36 119 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.06/1.36 120 -class_OrderedGroup_Olordered__ab__group__add(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_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.06/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(110,a,111,a)].
% 1.06/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(110,a,114,a)].
% 1.06/1.36 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(110,a,115,a)].
% 1.06/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(110,a,117,a)].
% 1.06/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(110,a,118,a)].
% 1.06/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(110,a,120,a)].
% 1.06/1.36 121 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.06/1.36 122 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.06/1.36 123 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.06/1.36 124 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.06/1.36 125 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.06/1.36 126 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.06/1.36 127 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.06/1.36 128 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.06/1.36 129 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.06/1.36 130 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.06/1.36 131 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.06/1.36 132 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.06/1.36 133 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.06/1.36 134 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 1.06/1.36 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(121,a,122,a)].
% 1.06/1.36 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(121,a,123,a)].
% 1.06/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(121,a,125,a)].
% 1.06/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(121,a,127,a)].
% 1.06/1.36 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(121,a,128,a)].
% 1.06/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(121,a,129,a)].
% 1.06/1.37 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(121,a,130,a)].
% 1.06/1.37 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(121,a,131,a)].
% 1.06/1.37 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(121,a,132,a)].
% 1.06/1.37 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(121,a,133,a)].
% 1.06/1.37 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(121,a,134,a)].
% 1.06/1.37 135 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.06/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(135,a,122,a)].
% 1.06/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(135,a,123,a)].
% 1.06/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(135,a,125,a)].
% 1.06/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(135,a,127,a)].
% 1.06/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(135,a,128,a)].
% 1.06/1.37 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(135,a,129,a)].
% 1.06/1.37 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(135,a,130,a)].
% 1.06/1.37 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(135,a,131,a)].
% 1.06/1.37 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(135,a,132,a)].
% 1.06/1.37 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(135,a,133,a)].
% 1.06/1.37 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(135,a,134,a)].
% 1.06/1.37 136 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.06/1.37 137 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 1.06/1.39 138 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 1.06/1.39 139 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.06/1.39 140 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.06/1.39 141 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.06/1.39 142 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.06/1.39 143 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.06/1.39 144 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.06/1.39 145 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 1.06/1.39 146 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 1.06/1.39 147 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.06/1.39 148 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 1.06/1.39 149 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 1.06/1.39 150 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_min__diff__distrib__left_0) # label(axiom). [assumption].
% 1.06/1.39 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(140,a,141,a)].
% 1.06/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(140,a,142,a)].
% 1.06/1.39 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(C,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(140,a,143,a)].
% 1.06/1.39 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,D,tc_Int_Oint). [resolve(140,a,144,a)].
% 1.06/1.39 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(140,a,145,a)].
% 1.12/1.42 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(140,a,146,a)].
% 1.12/1.42 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(140,a,147,a)].
% 1.12/1.42 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(140,a,148,a)].
% 1.12/1.42 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(140,a,149,a)].
% 1.12/1.42 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(140,a,150,a)].
% 1.12/1.42 151 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.12/1.42 152 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.12/1.42 153 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.12/1.42 154 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.12/1.42 155 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.12/1.42 156 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.12/1.42 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(151,a,152,a)].
% 1.12/1.42 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(151,a,153,a)].
% 1.12/1.42 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(151,a,154,a)].
% 1.12/1.42 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(151,a,155,a)].
% 1.12/1.42 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(151,a,156,a)].
% 1.12/1.42 157 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.12/1.42 158 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 1.12/1.42 159 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 1.12/1.42 160 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 1.12/1.42 161 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 1.12/1.42 162 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 1.12/1.44 163 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,158,a)].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(157,a,159,a)].
% 1.12/1.44 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(157,a,161,a)].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(157,a,162,a)].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(157,a,163,a)].
% 1.12/1.44 164 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.12/1.44 165 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 1.12/1.44 166 -class_OrderedGroup_Oab__group__add(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_add__cancel__21_1) # label(axiom). [assumption].
% 1.12/1.44 167 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != c_HOL_Oplus__class_Oplus(C,E,A) | c_HOL_Oplus__class_Oplus(B,D,A) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 1.12/1.44 168 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 1.12/1.44 169 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 1.12/1.44 170 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 1.12/1.44 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(164,a,166,a)].
% 1.12/1.44 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) = D. [resolve(164,a,167,a)].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,C,tc_Int_Oint) | A = B. [resolve(164,a,168,a)].
% 1.12/1.44 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint) | B = C. [resolve(164,a,169,a)].
% 1.12/1.44 171 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.12/1.44 172 -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].
% 1.12/1.44 173 -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].
% 1.12/1.44 174 -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].
% 1.12/1.44 175 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.12/1.44 176 -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].
% 1.12/1.44 177 -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].
% 1.12/1.45 178 -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].
% 1.12/1.45 179 -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].
% 1.12/1.45 180 -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].
% 1.12/1.45 181 -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].
% 1.12/1.45 182 -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].
% 1.12/1.45 183 -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].
% 1.12/1.45 184 -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].
% 1.12/1.45 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(171,a,172,a)].
% 1.12/1.45 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(171,a,174,a)].
% 1.12/1.45 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(171,a,175,a)].
% 1.12/1.45 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(171,a,176,a)].
% 1.12/1.45 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(171,a,178,a)].
% 1.12/1.45 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(171,a,179,a)].
% 1.12/1.45 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(171,a,180,a)].
% 1.12/1.45 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(171,a,181,a)].
% 1.12/1.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(171,a,182,a)].
% 1.12/1.45 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(171,a,183,a)].
% 1.12/1.45 185 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.12/1.45 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,A,tc_Int_Oint). [resolve(185,a,172,a)].
% 1.12/1.45 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = A. [resolve(185,a,174,a)].
% 1.12/1.45 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(185,a,175,a)].
% 1.12/1.45 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(185,a,176,a)].
% 1.19/1.46 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(185,a,178,a)].
% 1.19/1.46 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(185,a,180,a)].
% 1.19/1.46 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(185,a,181,a)].
% 1.19/1.46 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(185,a,182,a)].
% 1.19/1.46 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(185,a,183,a)].
% 1.19/1.46 186 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.19/1.46 187 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 1.19/1.46 188 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 1.19/1.46 189 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,A),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 1.19/1.46 190 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 1.19/1.46 191 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 1.19/1.46 192 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 1.19/1.46 193 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 1.19/1.46 194 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 1.19/1.46 195 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 1.19/1.46 196 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 1.19/1.46 197 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 1.19/1.46 198 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 1.19/1.46 199 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(186,a,187,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(186,a,188,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_nat),B,tc_nat). [resolve(186,a,189,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(186,a,190,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(186,a,191,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(186,a,192,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(186,a,193,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(186,a,194,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(186,a,195,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(186,a,196,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(186,a,197,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat),C,tc_nat). [resolve(186,a,198,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(186,a,199,a)].
% 1.19/1.46 200 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(200,a,187,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(200,a,188,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(200,a,189,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(200,a,190,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(200,a,191,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(200,a,192,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(200,a,193,a)].
% 1.19/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(200,a,194,a)].
% 1.24/1.50 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(200,a,195,a)].
% 1.24/1.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(200,a,196,a)].
% 1.24/1.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(200,a,197,a)].
% 1.24/1.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(200,a,198,a)].
% 1.24/1.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(200,a,199,a)].
% 1.24/1.50 201 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.24/1.50 202 -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].
% 1.24/1.50 203 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.24/1.50 204 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.24/1.50 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(201,a,202,a)].
% 1.24/1.50 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(201,a,203,a)].
% 1.24/1.50 205 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.24/1.50 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(A),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(205,a,202,a)].
% 1.24/1.50 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(205,a,203,a)].
% 1.24/1.50 206 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.24/1.50 207 -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].
% 1.24/1.50 208 -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].
% 1.24/1.50 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(206,a,208,a)].
% 1.24/1.50 209 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.24/1.50 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(209,a,208,a)].
% 1.24/1.50 210 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 1.24/1.50 211 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(F,D,A),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 1.24/1.53 212 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 1.24/1.53 213 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 1.24/1.53 214 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 1.24/1.53 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(210,a,211,a)].
% 1.24/1.53 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(210,a,212,a)].
% 1.24/1.53 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(210,a,213,a)].
% 1.24/1.53 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(210,a,214,a)].
% 1.24/1.53 215 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.24/1.53 216 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.24/1.53 217 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.24/1.53 218 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.24/1.53 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(215,a,218,a)].
% 1.24/1.53 219 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.24/1.53 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(219,a,218,a)].
% 1.24/1.53 220 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.24/1.53 221 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 1.27/1.56 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(220,a,221,a)].
% 1.27/1.56 222 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.27/1.56 223 -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].
% 1.27/1.56 224 -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_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.27/1.56 225 -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(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.27/1.56 226 -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].
% 1.27/1.56 227 -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].
% 1.27/1.56 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(222,a,223,a)].
% 1.27/1.56 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,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(222,a,224,a)].
% 1.27/1.56 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(222,a,226,a)].
% 1.27/1.56 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(222,a,227,a)].
% 1.27/1.56 228 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.27/1.56 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(228,a,224,a)].
% 1.27/1.56 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(228,a,226,a)].
% 1.27/1.56 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(228,a,227,a)].
% 1.27/1.56 229 class_Int_Onumber(tc_nat) # label(clsarity_nat__Int_Onumber) # label(axiom). [assumption].
% 1.27/1.56 230 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(C,A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_min__number__of_1) # label(axiom). [assumption].
% 1.27/1.56 231 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_min__number__of_0) # label(axiom). [assumption].
% 1.27/1.56 Derived: -class_HOL_Oord(tc_nat) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(B,tc_nat) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(229,a,230,a)].
% 1.36/1.64 232 class_Int_Onumber(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Onumber) # label(axiom). [assumption].
% 1.36/1.64 Derived: -class_HOL_Oord(tc_Int_Oint) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(232,a,230,a)].
% 1.36/1.64 233 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 234 -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].
% 1.36/1.64 235 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 236 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 1.36/1.64 237 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 1.36/1.64 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(236,a,237,a)].
% 1.36/1.64 238 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 239 -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].
% 1.36/1.64 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(238,a,239,a)].
% 1.36/1.64 240 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(240,a,239,a)].
% 1.36/1.64 241 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 242 -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].
% 1.36/1.64 243 -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].
% 1.36/1.64 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(241,a,243,a)].
% 1.36/1.64 244 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.36/1.64 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(244,a,243,a)].
% 1.36/1.64 245 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.36/1.64 246 -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].
% 1.36/1.64 247 -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].
% 1.36/1.64 248 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.36/1.64
% 1.36/1.64 ============================== end predicate elimination =============
% 1.51/1.80
% 1.51/1.80 Auto_denials: (non-Horn, no changes).
% 1.51/1.80
% 1.51/1.80 Term ordering decisions:
% 1.51/1.80 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_bool=1. v_c____=1. v_d____=1. v_sko__Arrow__Order__Mirabelle__Xalt3__1=1. v_sko__Arrow__Order__Mirabelle__Xalt3__2=1. v_sko__Arrow__Order__Mirabelle__Xalt3__3=1. c_Nat_Osize__class_Osize=1. c_List_Orev=1. c_Int_Onumber__class_Onumber__of=1. c_List_Obutlast=1. c_List_Otl=1. c_List_Olast=1. c_List_Oremdups=1. c_List_Ohd=1. c_List_Orotate1=1. tc_fun=1. c_List_Osko__List__Xlist__Xexhaust__1__1=1. c_List_Osko__List__Xlist__Xexhaust__1__2=1. c_List_Osko__List__Xlist__Xnchotomy__1__1=1. c_List_Osko__List__Xlist__Xnchotomy__1__2=1. c_List_Osko__List__Xneq__Nil__conv__1__1=1. c_List_Osko__List__Xneq__Nil__conv__1__2=1. v_sko__Arrow__Order__Mirabelle__Xthird__alt__1=1. v_sko__CHAINED__1=1. c_HOL_Ozero__class_Ozero=1. c_List_Olist_ONil=1. c_Suc=1. tc_List_Olist=1. c_HOL_Oone__class_Oone=1. c_HOL_Oplus__class_Oplus=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_HOL_Ominus__class_Ominus=1. c_Divides_Odiv__class_Omod=1. c_Orderings_Oord__class_Omin=1. c_Power_Opower__class_Opower=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_List_Orotate=1. c_List_OremoveAll=1. c_List_Oremove1=1. c_List_Osplice=1. c_List_Olist__inter=1. c_List_Olist__update=1. c_List_Osko__List__XCons__eq__append__conv__1__1=1. c_List_Osko__List__Xappend__eq__Cons__conv__1__1=1.
% 1.51/1.80
% 1.51/1.80 ============================== end of process initial clauses ========
% 1.51/1.80
% 1.51/1.80 ============================== CLAUSES FOR SEARCH ====================
% 1.51/1.80
% 1.51/1.80 ============================== end of clauses for search =============
% 1.51/1.80
% 1.51/1.80 ============================== SEARCH ================================
% 1.51/1.80
% 1.51/1.80 % Starting search at 0.54 seconds.
% 1.51/1.80
% 1.51/1.80 ============================== PROOF =================================
% 1.51/1.80 % SZS status Unsatisfiable
% 1.51/1.80 % SZS output start Refutation
% 1.51/1.80
% 1.51/1.80 % Proof 1 at 0.64 (+ 0.01) seconds.
% 1.51/1.80 % Length of proof is 7.
% 1.51/1.80 % Level of proof is 2.
% 1.51/1.80 % Maximum clause weight is 18.000.
% 1.51/1.80 % Given clauses 218.
% 1.51/1.80
% 1.51/1.80 749 c_List_Odistinct(c_List_Olist_OCons(A,c_List_Olist_OCons(B,c_List_Olist_OCons(v_sko__CHAINED__1(A,B),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) | A = B # label(cls_CHAINED_0) # label(axiom). [assumption].
% 1.51/1.80 750 v_c____ != v_d____ # label(cls_CHAINED_0_02) # label(axiom). [assumption].
% 1.51/1.80 751 v_d____ != v_c____. [copy(750),flip(a)].
% 1.51/1.80 752 -v_thesis____ # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.51/1.80 753 v_thesis____ | -c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Olist_OCons(A,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.51/1.80 754 -c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Olist_OCons(A,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt). [copy(753),unit_del(a,752)].
% 1.51/1.80 2371 $F. [resolve(754,a,749,a),flip(a),unit_del(a,751)].
% 1.51/1.80
% 1.51/1.80 % SZS output end Refutation
% 1.51/1.80 ============================== end of proof ==========================
% 1.51/1.80
% 1.51/1.80 ============================== STATISTICS ============================
% 1.51/1.80
% 1.51/1.80 Given=218. Generated=3231. Kept=1852. proofs=1.
% 1.51/1.80 Usable=218. Sos=1399. Demods=365. Limbo=0, Disabled=1191. Hints=0.
% 1.51/1.80 Megabytes=4.72.
% 1.51/1.80 User_CPU=0.64, System_CPU=0.01, Wall_clock=1.
% 1.51/1.80
% 1.51/1.80 ============================== end of statistics =====================
% 1.51/1.80
% 1.51/1.80 ============================== end of search =========================
% 1.51/1.80
% 1.51/1.80 THEOREM PROVED
% 1.51/1.80 % SZS status Unsatisfiable
% 1.51/1.80
% 1.51/1.80 Exiting with 1 proof.
% 1.51/1.80
% 1.51/1.80 Process 25964 exit (max_proofs) Fri Jul 1 22:38:45 2022
% 1.51/1.80 Prover9 interrupted
%------------------------------------------------------------------------------