TSTP Solution File: LCL781-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL781-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Sun Jul 17 13:50:07 EDT 2022
% Result : Timeout 300.06s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL781-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 03:59:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.81/1.13 ============================== Prover9 ===============================
% 0.81/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.13 Process 10582 was started by sandbox on n018.cluster.edu,
% 0.81/1.13 Sun Jul 3 03:59:20 2022
% 0.81/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10429_n018.cluster.edu".
% 0.81/1.13 ============================== end of head ===========================
% 0.81/1.13
% 0.81/1.13 ============================== INPUT =================================
% 0.81/1.13
% 0.81/1.13 % Reading from file /tmp/Prover9_10429_n018.cluster.edu
% 0.81/1.13
% 0.81/1.13 set(prolog_style_variables).
% 0.81/1.13 set(auto2).
% 0.81/1.13 % set(auto2) -> set(auto).
% 0.81/1.13 % set(auto) -> set(auto_inference).
% 0.81/1.13 % set(auto) -> set(auto_setup).
% 0.81/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.13 % set(auto) -> set(auto_limits).
% 0.81/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.13 % set(auto) -> set(auto_denials).
% 0.81/1.13 % set(auto) -> set(auto_process).
% 0.81/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.13 % set(auto2) -> assign(stats, some).
% 0.81/1.13 % set(auto2) -> clear(echo_input).
% 0.81/1.13 % set(auto2) -> set(quiet).
% 0.81/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.13 % set(auto2) -> clear(print_given).
% 0.81/1.13 assign(lrs_ticks,-1).
% 0.81/1.13 assign(sos_limit,10000).
% 0.81/1.13 assign(order,kbo).
% 0.81/1.13 set(lex_order_vars).
% 0.81/1.13 clear(print_given).
% 0.81/1.13
% 0.81/1.13 % formulas(sos). % not echoed (407 formulas)
% 0.81/1.13
% 0.81/1.13 ============================== end of input ==========================
% 0.81/1.13
% 0.81/1.13 % From the command line: assign(max_seconds, 300).
% 0.81/1.13
% 0.81/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.13
% 0.81/1.13 % Formulas that are not ordinary clauses:
% 0.81/1.13
% 0.81/1.13 ============================== end of process non-clausal formulas ===
% 0.81/1.13
% 0.81/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.13
% 0.81/1.13 ============================== PREDICATE ELIMINATION =================
% 0.81/1.13 1 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.81/1.13 2 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 0.81/1.13 3 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 0.81/1.13 4 -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].
% 0.81/1.13 5 -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].
% 0.81/1.13 6 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 0.81/1.13 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,2,a)].
% 0.81/1.13 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(1,a,3,a)].
% 0.81/1.14 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(1,a,4,a)].
% 0.81/1.14 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(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(1,a,5,a)].
% 0.81/1.14 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(1,a,6,a)].
% 0.81/1.14 7 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.81/1.14 8 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 0.81/1.14 9 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A) # label(cls_foldl__foldr1_0) # label(axiom). [assumption].
% 0.81/1.14 10 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A)) # label(cls_foldl__foldr1__lemma_0) # label(axiom). [assumption].
% 0.81/1.14 11 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.81/1.14 12 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.81/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(7,a,8,a)].
% 0.81/1.14 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat). [resolve(7,a,9,a)].
% 0.81/1.14 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat)). [resolve(7,a,10,a)].
% 0.81/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(7,a,11,a)].
% 0.81/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(7,a,12,a)].
% 0.81/1.14 13 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 0.81/1.14 14 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 0.81/1.14 15 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 0.81/1.14 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(13,a,14,a)].
% 0.81/1.14 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(13,a,15,a)].
% 0.81/1.14 16 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.81/1.14 17 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 0.81/1.14 18 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.81/1.14 19 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.81/1.14 20 -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].
% 0.81/1.14 21 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.81/1.14 22 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.81/1.14 23 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.81/1.14 24 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.81/1.14 25 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.81/1.14 26 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.81/1.14 27 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.81/1.14 28 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.81/1.14 29 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.81/1.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(16,a,18,a)].
% 0.81/1.15 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(16,a,20,a)].
% 0.81/1.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(16,a,21,a)].
% 0.81/1.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(16,a,23,a)].
% 0.81/1.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(16,a,24,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(16,a,25,a)].
% 0.86/1.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(16,a,26,a)].
% 0.86/1.17 30 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.86/1.17 31 -class_OrderedGroup_Oab__semigroup__add(A) | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A) # label(cls_foldr__conv__foldl_0) # label(axiom). [assumption].
% 0.86/1.17 32 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 0.86/1.17 Derived: c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,A,tc_nat,tc_nat). [resolve(30,a,31,a)].
% 0.86/1.17 33 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.86/1.17 34 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 0.86/1.17 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(33,a,34,a)].
% 0.86/1.17 35 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.86/1.17 36 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 0.86/1.17 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(35,a,36,a)].
% 0.86/1.17 37 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.86/1.17 38 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.86/1.17 39 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.86/1.17 40 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.86/1.17 41 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 0.86/1.17 42 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 0.86/1.17 43 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.86/1.17 44 -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].
% 0.86/1.17 45 -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].
% 0.86/1.17 46 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.86/1.17 47 -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].
% 0.86/1.17 48 -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].
% 0.86/1.17 49 -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].
% 0.86/1.17 50 -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].
% 0.86/1.17 51 -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].
% 0.86/1.17 52 -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].
% 0.86/1.17 53 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 0.86/1.17 54 -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].
% 0.86/1.17 55 -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].
% 0.86/1.17 56 -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].
% 0.86/1.17 57 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 0.86/1.17 58 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 0.86/1.17 59 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 0.86/1.17 60 -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].
% 0.86/1.17 61 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.86/1.17 62 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 0.86/1.17 63 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 0.86/1.17 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(43,a,44,a)].
% 0.86/1.17 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(43,a,45,a)].
% 0.86/1.17 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(43,a,46,a)].
% 0.86/1.17 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(43,a,47,a)].
% 0.86/1.17 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(43,a,48,a)].
% 0.86/1.17 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(43,a,49,a)].
% 0.86/1.17 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(43,a,52,a)].
% 0.86/1.17 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(43,a,53,a)].
% 0.86/1.17 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(43,a,54,a)].
% 0.86/1.17 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(43,a,55,a)].
% 0.86/1.17 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(43,a,56,a)].
% 0.86/1.17 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),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(43,a,57,a)].
% 0.86/1.17 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(43,a,58,a)].
% 0.86/1.17 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(43,a,59,a)].
% 0.86/1.18 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(43,a,60,a)].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(43,a,61,a)].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(43,a,62,a)].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(43,a,63,a)].
% 0.86/1.18 64 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.86/1.18 65 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 0.86/1.18 66 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.86/1.18 67 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(64,a,65,a)].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(64,a,66,a)].
% 0.86/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(64,a,67,a)].
% 0.86/1.18 68 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.86/1.18 69 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 0.86/1.18 70 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 0.86/1.18 71 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 0.86/1.18 72 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 0.86/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(68,a,70,a)].
% 0.86/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(68,a,72,a)].
% 0.86/1.20 73 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.86/1.20 74 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 0.86/1.20 75 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 0.86/1.20 76 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A) # label(cls_of__nat__power_0) # label(axiom). [assumption].
% 0.86/1.20 77 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 0.86/1.20 78 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 0.86/1.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(73,a,74,a)].
% 0.86/1.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(73,a,75,a)].
% 0.86/1.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),B,tc_nat). [resolve(73,a,76,a)].
% 0.86/1.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(73,a,77,a)].
% 0.86/1.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(73,a,78,a)].
% 0.86/1.20 79 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.86/1.20 80 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.86/1.20 81 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.86/1.20 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(79,a,80,a)].
% 0.86/1.20 82 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 0.86/1.20 83 -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].
% 0.86/1.22 84 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 0.86/1.22 85 -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].
% 0.86/1.22 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(82,a,83,a)].
% 0.86/1.22 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(82,a,84,a)].
% 0.86/1.22 86 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.86/1.22 87 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 0.86/1.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(86,a,87,a)].
% 0.86/1.22 88 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.86/1.22 89 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 0.86/1.22 90 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.86/1.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(88,a,90,a)].
% 0.86/1.22 91 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.86/1.22 92 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.86/1.22 93 -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].
% 0.86/1.22 94 -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].
% 0.86/1.22 95 -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].
% 0.86/1.22 96 -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].
% 0.86/1.22 97 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.86/1.22 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(91,a,92,a)].
% 0.86/1.22 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(91,a,93,a)].
% 0.86/1.22 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(91,a,97,a)].
% 0.86/1.22 98 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.86/1.22 99 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.86/1.22 Derived: A = A. [resolve(98,b,99,a)].
% 0.86/1.22
% 0.86/1.22 ============================== end predicate elimination =============
% 0.86/1.22
% 0.86/1.22 Auto_denials: (non-Horn, no changes).
% 0.86/1.22
% 0.86/1.22 Term ordering decisions:
% 0.86/1.22 Function symbol KB weights: tc_nat=1. tCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------