TSTP Solution File: SCT091-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT091-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 22:03:50 EDT 2022
% Result : Unsatisfiable 4.49s 4.79s
% Output : Refutation 4.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT091-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 09:22:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.07/1.44 ============================== Prover9 ===============================
% 1.07/1.44 Prover9 (32) version 2009-11A, November 2009.
% 1.07/1.44 Process 4668 was started by sandbox on n007.cluster.edu,
% 1.07/1.44 Sat Jul 2 09:22:56 2022
% 1.07/1.44 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4514_n007.cluster.edu".
% 1.07/1.44 ============================== end of head ===========================
% 1.07/1.44
% 1.07/1.44 ============================== INPUT =================================
% 1.07/1.44
% 1.07/1.44 % Reading from file /tmp/Prover9_4514_n007.cluster.edu
% 1.07/1.44
% 1.07/1.44 set(prolog_style_variables).
% 1.07/1.44 set(auto2).
% 1.07/1.44 % set(auto2) -> set(auto).
% 1.07/1.44 % set(auto) -> set(auto_inference).
% 1.07/1.44 % set(auto) -> set(auto_setup).
% 1.07/1.44 % set(auto_setup) -> set(predicate_elim).
% 1.07/1.44 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.07/1.44 % set(auto) -> set(auto_limits).
% 1.07/1.44 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.07/1.44 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.07/1.44 % set(auto) -> set(auto_denials).
% 1.07/1.44 % set(auto) -> set(auto_process).
% 1.07/1.44 % set(auto2) -> assign(new_constants, 1).
% 1.07/1.44 % set(auto2) -> assign(fold_denial_max, 3).
% 1.07/1.44 % set(auto2) -> assign(max_weight, "200.000").
% 1.07/1.44 % set(auto2) -> assign(max_hours, 1).
% 1.07/1.44 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.07/1.44 % set(auto2) -> assign(max_seconds, 0).
% 1.07/1.44 % set(auto2) -> assign(max_minutes, 5).
% 1.07/1.44 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.07/1.44 % set(auto2) -> set(sort_initial_sos).
% 1.07/1.44 % set(auto2) -> assign(sos_limit, -1).
% 1.07/1.44 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.07/1.44 % set(auto2) -> assign(max_megs, 400).
% 1.07/1.44 % set(auto2) -> assign(stats, some).
% 1.07/1.44 % set(auto2) -> clear(echo_input).
% 1.07/1.44 % set(auto2) -> set(quiet).
% 1.07/1.44 % set(auto2) -> clear(print_initial_clauses).
% 1.07/1.44 % set(auto2) -> clear(print_given).
% 1.07/1.44 assign(lrs_ticks,-1).
% 1.07/1.44 assign(sos_limit,10000).
% 1.07/1.44 assign(order,kbo).
% 1.07/1.44 set(lex_order_vars).
% 1.07/1.44 clear(print_given).
% 1.07/1.44
% 1.07/1.44 % formulas(sos). % not echoed (871 formulas)
% 1.07/1.44
% 1.07/1.44 ============================== end of input ==========================
% 1.07/1.44
% 1.07/1.44 % From the command line: assign(max_seconds, 300).
% 1.07/1.44
% 1.07/1.44 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.07/1.44
% 1.07/1.44 % Formulas that are not ordinary clauses:
% 1.07/1.44
% 1.07/1.44 ============================== end of process non-clausal formulas ===
% 1.07/1.44
% 1.07/1.44 ============================== PROCESS INITIAL CLAUSES ===============
% 1.07/1.44
% 1.07/1.44 ============================== PREDICATE ELIMINATION =================
% 1.07/1.44 1 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.07/1.44 2 -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].
% 1.07/1.44 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].
% 1.07/1.44 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(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].
% 1.07/1.44 5 -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].
% 1.07/1.44 6 -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].
% 1.07/1.44 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,2,a)].
% 1.07/1.44 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)].
% 1.07/1.56 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(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,4,a)].
% 1.07/1.56 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(1,a,5,a)].
% 1.07/1.56 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,6,a)].
% 1.07/1.56 7 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.07/1.56 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.07/1.56 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.07/1.56 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.07/1.56 11 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.07/1.56 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.07/1.56 13 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.07/1.56 14 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.07/1.56 15 -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].
% 1.07/1.56 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.07/1.56 17 -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].
% 1.07/1.56 18 -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].
% 1.07/1.56 19 -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].
% 1.07/1.56 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].
% 1.07/1.56 21 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Finite__Set_Osetprod(B,C,D,A) != c_HOL_Ozero__class_Ozero(A) | -c_Finite__Set_Ofinite(C,D) | hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(C,B,D,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_1) # label(axiom). [assumption].
% 1.07/1.56 22 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Finite__Set_Osetprod(B,C,D,A) != c_HOL_Ozero__class_Ozero(A) | -c_Finite__Set_Ofinite(C,D) | hBOOL(hAPP(hAPP(c_in(D),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(C,B,D,A)),C)) # label(cls_setprod__zero__iff_0) # label(axiom). [assumption].
% 1.07/1.56 23 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero_0) # label(axiom). [assumption].
% 1.07/1.56 24 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_in(D),C),E)) | -c_Finite__Set_Ofinite(E,D) | c_Finite__Set_Osetprod(B,E,D,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_2) # label(axiom). [assumption].
% 1.07/1.56 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(7,a,8,a)].
% 1.07/1.56 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(7,a,9,a)].
% 1.07/1.56 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(7,a,10,a)].
% 1.07/1.56 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(7,a,11,a)].
% 1.07/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(7,a,13,a)].
% 1.07/1.56 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(7,a,15,a)].
% 1.07/1.56 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(7,a,16,a)].
% 1.07/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(7,a,17,a)].
% 1.07/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(7,a,18,a)].
% 1.07/1.56 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(7,a,20,a)].
% 1.07/1.56 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | c_Finite__Set_Osetprod(A,B,C,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_Finite__Set_Ofinite(B,C) | hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(B,A,C,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(7,a,21,b)].
% 1.07/1.56 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | c_Finite__Set_Osetprod(A,B,C,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_Finite__Set_Ofinite(B,C) | hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(B,A,C,tc_nat)),B)). [resolve(7,a,22,b)].
% 1.07/1.56 Derived: hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_in(C),B),D)) | -c_Finite__Set_Ofinite(D,C) | c_Finite__Set_Osetprod(A,D,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(7,a,23,a)].
% 1.07/1.62 25 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.07/1.62 26 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.07/1.62 27 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.07/1.62 28 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.07/1.62 29 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.07/1.62 30 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.07/1.62 31 -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].
% 1.07/1.62 32 -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].
% 1.07/1.62 33 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oinsert(C,D,E),E,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,D,E,A)) | hBOOL(hAPP(hAPP(c_in(E),C),D)) | -c_Finite__Set_Ofinite(D,E) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.07/1.62 34 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.07/1.62 35 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.07/1.62 36 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(D,c_Lattices_Olower__semilattice__class_Oinf(F,C,tc_fun(B,tc_bool)),B,A)),c_Finite__Set_Osetsum(E,c_Lattices_Olower__semilattice__class_Oinf(F,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(B,tc_bool)),C),tc_fun(B,tc_bool)),B,A)) | -c_Finite__Set_Ofinite(F,B) # label(cls_setsum__cases_0) # label(axiom). [assumption].
% 1.07/1.62 37 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -c_lessequals(B,D,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.07/1.62 38 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.07/1.62 39 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(c_Finite__Set_Osetsum(B,C,D,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__nonpos__1__1(C,B,D,A)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_setsum__nonpos_1) # label(axiom). [assumption].
% 1.07/1.62 40 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),C),D,C,A,A),E,C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,E,C,A)),c_Finite__Set_Osetsum(D,E,C,A)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.07/1.62 41 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 1.07/1.62 42 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(c_Finite__Set_Osetsum(B,C,D,A),c_HOL_Ozero__class_Ozero(A),A) | hBOOL(hAPP(hAPP(c_in(D),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__nonpos__1__1(C,B,D,A)),C)) # label(cls_setsum__nonpos_0) # label(axiom). [assumption].
% 1.07/1.62 43 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,tc_bool)),E,A) = c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(E),D,E,tc_fun(E,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),E),B,E,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),E,A,A),C,E,A) | -c_Finite__Set_Ofinite(C,E) # label(cls_setsum__restrict__set_0) # label(axiom). [assumption].
% 1.07/1.62 44 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fequal(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A) = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_H_1) # label(axiom). [assumption].
% 1.07/1.62 45 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fequal(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_H_0) # label(axiom). [assumption].
% 1.07/1.62 46 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 1.07/1.62 47 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 1.07/1.62 48 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fequal(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_0) # label(axiom). [assumption].
% 1.07/1.62 49 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fequal(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A) = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_1) # label(axiom). [assumption].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(A,c_Set_Oinsert(B,C,D),D,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,C,D,tc_nat)) | hBOOL(hAPP(hAPP(c_in(D),B),C)) | -c_Finite__Set_Ofinite(C,D). [resolve(27,a,33,a)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(27,a,34,b)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(27,a,35,b)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_in(A),B,A,tc_fun(A,tc_bool),tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),D,A,tc_nat,tc_nat),E,A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(C,c_Lattices_Olower__semilattice__class_Oinf(E,B,tc_fun(A,tc_bool)),A,tc_nat)),c_Finite__Set_Osetsum(D,c_Lattices_Olower__semilattice__class_Oinf(E,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),tc_fun(A,tc_bool)),A,tc_nat)) | -c_Finite__Set_Ofinite(E,A). [resolve(27,a,36,a)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -c_lessequals(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(27,a,37,b)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(27,a,38,b)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) | c_lessequals(c_Finite__Set_Osetsum(A,B,C,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__nonpos__1__1(B,A,C,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(27,a,39,b)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),B),C,B,tc_nat,tc_nat),D,B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,D,B,tc_nat)),c_Finite__Set_Osetsum(C,D,B,tc_nat)). [resolve(27,a,40,a)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(27,a,41,a)].
% 1.07/1.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) | c_lessequals(c_Finite__Set_Osetsum(A,B,C,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__nonpos__1__1(B,A,C,tc_nat)),B)). [resolve(27,a,42,b)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),D,tc_nat) = c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_in(D),C,D,tc_fun(D,tc_bool),tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),D),A,D,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat,tc_nat),B,D,tc_nat) | -c_Finite__Set_Ofinite(B,D). [resolve(27,a,43,a)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),hAPP(c_fequal(A),B),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(27,a,44,a)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),hAPP(c_fequal(A),B),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(27,a,45,a)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(27,a,46,a)].
% 1.07/1.62 Derived: c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_fequal(A),B,A,A,tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(27,a,48,a)].
% 1.55/1.79 Derived: c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_fequal(A),B,A,A,tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(27,a,49,a)].
% 1.55/1.79 50 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.55/1.79 51 -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].
% 1.55/1.79 52 -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].
% 1.55/1.79 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(50,a,52,a)].
% 1.55/1.79 53 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.55/1.79 54 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 1.55/1.79 55 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 1.55/1.79 56 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.55/1.79 57 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.55/1.79 58 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.55/1.79 59 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.55/1.79 60 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.55/1.79 61 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.55/1.79 62 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.55/1.79 63 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.55/1.79 64 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.55/1.79 65 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.55/1.79 66 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.55/1.79 67 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.58/1.84 68 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.58/1.84 69 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.58/1.84 70 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.58/1.84 71 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.58/1.84 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(53,a,54,a)].
% 1.58/1.84 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(53,a,55,a)].
% 1.58/1.84 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(A,B,tc_nat). [resolve(53,a,56,a)].
% 1.58/1.84 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | c_lessequals(B,A,tc_nat). [resolve(53,a,58,a)].
% 1.58/1.84 Derived: -c_lessequals(A,A,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(53,a,59,a)].
% 1.58/1.84 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(B,A,tc_nat). [resolve(53,a,61,a)].
% 1.58/1.84 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(53,a,65,a)].
% 1.58/1.84 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(53,a,66,a)].
% 1.58/1.84 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(53,a,67,a)].
% 1.58/1.84 72 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.58/1.84 73 -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].
% 1.58/1.84 74 -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].
% 1.58/1.84 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(72,a,74,a)].
% 1.58/1.84 75 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.58/1.84 76 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.58/1.84 77 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.58/1.84 78 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.58/1.84 79 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.58/1.84 80 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.58/1.84 81 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.58/1.84 82 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.58/1.84 83 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.58/1.84 84 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.58/1.84 85 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.58/1.84 86 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.58/1.84 87 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.58/1.84 88 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.58/1.84 89 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.58/1.84 90 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.58/1.84 91 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.58/1.84 92 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.58/1.84 93 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.58/1.84 94 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.58/1.84 95 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.58/1.84 96 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(75,a,76,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(75,a,77,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(75,a,78,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(75,a,79,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(75,a,80,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(75,a,81,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(75,a,82,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(75,a,83,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(75,a,84,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(75,a,85,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(75,a,88,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(75,a,91,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(75,a,92,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(75,a,93,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(75,a,94,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(75,a,95,a)].
% 1.58/1.84 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(75,a,96,a)].
% 1.58/1.84 97 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(97,a,76,a)].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(97,a,77,a)].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(97,a,78,a)].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(97,a,79,a)].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(97,a,80,a)].
% 1.58/1.84 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(97,a,81,a)].
% 1.58/1.84 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(97,a,82,a)].
% 1.58/1.84 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(97,a,83,a)].
% 1.58/1.84 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(97,a,84,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(97,a,85,a)].
% 1.58/1.88 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(97,a,88,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(97,a,91,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(97,a,92,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(97,a,93,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(97,a,94,a)].
% 1.58/1.88 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(97,a,95,a)].
% 1.58/1.88 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(97,a,96,a)].
% 1.58/1.88 98 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(98,a,76,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(98,a,77,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(98,a,78,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(98,a,79,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(98,a,80,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(98,a,81,a)].
% 1.58/1.88 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(98,a,82,a)].
% 1.58/1.88 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(98,a,83,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(98,a,84,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(98,a,85,a)].
% 1.58/1.88 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(98,a,88,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(98,a,91,a)].
% 1.58/1.88 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(98,a,92,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(98,a,93,a)].
% 1.58/1.88 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(98,a,94,a)].
% 1.58/1.88 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(98,a,95,a)].
% 1.58/1.88 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(98,a,96,a)].
% 1.58/1.88 99 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.58/1.91 100 -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].
% 1.58/1.91 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(99,a,100,a)].
% 1.58/1.91 101 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.58/1.91 102 -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].
% 1.58/1.91 103 -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].
% 1.58/1.91 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(101,a,103,a)].
% 1.58/1.91 104 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.58/1.91 105 -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 | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -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].
% 1.58/1.91 106 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.58/1.91 107 -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].
% 1.58/1.91 108 -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].
% 1.58/1.91 109 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,D,A)),c_Power_Opower__class_Opower(C,D,A))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.58/1.91 110 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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)))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.58/1.91 111 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.58/1.91 112 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.58/1.91 113 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(D,B,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.58/1.91 114 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.58/1.91 115 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | -c_lessequals(C,D,tc_nat) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.58/1.91 116 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Finite__Set_Osetprod(B,C,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__nonneg__1__1(C,B,D,A)),A) # label(cls_setprod__nonneg_1) # label(axiom). [assumption].
% 1.58/1.91 117 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Finite__Set_Osetprod(B,C,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(C,B,D,A)))) # label(cls_setprod__pos_1) # label(axiom). [assumption].
% 1.58/1.91 118 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.58/1.91 119 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.58/1.91 120 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.58/1.91 121 -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].
% 1.58/1.91 122 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.58/1.91 123 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.58/1.91 124 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.58/1.91 125 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Finite__Set_Osetprod(B,C,D,A),A) | hBOOL(hAPP(hAPP(c_in(D),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__nonneg__1__1(C,B,D,A)),C)) # label(cls_setprod__nonneg_0) # label(axiom). [assumption].
% 1.58/1.91 126 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,tc_nat) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.58/1.91 127 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Finite__Set_Osetprod(B,C,D,A))) | hBOOL(hAPP(hAPP(c_in(D),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(C,B,D,A)),C)) # label(cls_setprod__pos_0) # label(axiom). [assumption].
% 1.58/1.91 128 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.58/1.91 129 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.58/1.91 130 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(C,D,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.58/1.91 131 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.58/1.91 132 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.58/1.91 133 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.58/1.91 134 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.58/1.91 135 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.58/1.91 136 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.58/1.91 137 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.58/1.91 138 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.58/1.91 139 -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].
% 1.58/1.91 140 -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].
% 1.58/1.91 141 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.58/1.91 142 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.58/1.91 143 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.58/1.91 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -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(104,a,105,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(104,a,106,a)].
% 1.58/1.91 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(104,a,107,a)].
% 1.58/1.91 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(104,a,108,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat)),c_Power_Opower__class_Opower(B,C,tc_nat))). [resolve(104,a,109,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),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)))). [resolve(104,a,110,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(104,a,111,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(104,a,112,a)].
% 1.58/1.91 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(104,a,115,a)].
% 1.58/1.91 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Osetprod(A,B,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__nonneg__1__1(B,A,C,tc_nat)),tc_nat). [resolve(104,a,116,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(A,B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(B,A,C,tc_nat)))). [resolve(104,a,117,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(104,a,118,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(104,a,119,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(104,a,120,a)].
% 1.58/1.91 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(104,a,121,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(104,a,122,a)].
% 1.58/1.91 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | B = C. [resolve(104,a,123,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(104,a,124,a)].
% 1.58/1.91 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Osetprod(A,B,C,tc_nat),tc_nat) | hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__nonneg__1__1(B,A,C,tc_nat)),B)). [resolve(104,a,125,a)].
% 1.58/1.91 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(104,a,126,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(A,B,C,tc_nat))) | hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(B,A,C,tc_nat)),B)). [resolve(104,a,127,a)].
% 1.58/1.91 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(104,a,128,a)].
% 1.58/1.91 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(104,a,130,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(104,a,131,a)].
% 1.58/1.91 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(104,a,132,a)].
% 1.58/1.91 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(104,a,133,a)].
% 1.58/1.91 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(104,a,135,a)].
% 1.58/1.91 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(104,a,136,a)].
% 1.58/1.91 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(104,a,137,a)].
% 1.58/1.91 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(104,a,138,a)].
% 1.58/1.91 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(104,a,139,a)].
% 1.68/1.97 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(104,a,140,a)].
% 1.68/1.97 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(104,a,141,a)].
% 1.68/1.97 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(104,a,142,a)].
% 1.68/1.97 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(104,a,143,a)].
% 1.68/1.97 144 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.68/1.97 145 -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].
% 1.68/1.97 146 -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].
% 1.68/1.97 147 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.68/1.97 148 -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].
% 1.68/1.97 149 -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].
% 1.68/1.97 150 -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].
% 1.68/1.97 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(147,a,148,a)].
% 1.68/1.97 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(147,a,149,a)].
% 1.68/1.97 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(147,a,150,a)].
% 1.68/1.97 151 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oequiv(c_Relation_ODomain(A,B,B),A,B) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 1.68/1.97 152 hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_OImage(C,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A))) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Equiv__Relations_Oequiv(D,C,A) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 1.68/1.97 153 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | -hBOOL(hAPP(hAPP(c_in(A),E),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),c_Relation_OImage(D,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A,A),tc_fun(A,tc_bool)))) | -c_Equiv__Relations_Oequiv(F,D,A) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 1.68/1.97 154 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 1.68/1.97 155 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 1.68/1.97 156 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 1.68/1.97 157 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(hAPP(hAPP(c_in(C),D),E)) | -hBOOL(hAPP(hAPP(c_in(C),B),E)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 1.68/1.97 158 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 1.68/1.97 159 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(B,D,C,C)),A)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 1.68/1.97 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B))) | -hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_ODomain(A,B,B))). [resolve(151,b,152,c)].
% 1.68/1.97 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),E),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)))). [resolve(151,b,153,c)].
% 1.68/1.97 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,B,B))). [resolve(151,b,154,d)].
% 1.68/1.97 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)) | -hBOOL(hAPP(hAPP(c_in(B),D),c_Relation_ODomain(A,B,B))) | -hBOOL(hAPP(hAPP(c_in(B),C),c_Relation_ODomain(A,B,B))). [resolve(151,b,156,e)].
% 1.68/1.97 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(hAPP(hAPP(c_in(tc_prod(B,B)),c_Pair(C,D,B,B)),A)). [resolve(151,b,158,c)].
% 1.68/1.97 160 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) = A | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 1.68/1.97 161 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 1.68/1.97 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(161,b,151,b)].
% 1.68/1.98 162 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 1.68/1.98 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(162,b,151,b)].
% 1.68/1.98 163 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 1.68/1.98 Derived: hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ODomain(C,A,A))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),C)) | c_Relation_Orel__comp(c_Relation_Oconverse(C,A,A),C,A,A,A) != C. [resolve(163,c,151,b)].
% 1.68/1.98 164 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 1.68/1.98 165 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.68/1.98 166 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 1.68/1.98 167 -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) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.68/1.98 168 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.68/1.98 169 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.68/1.98 170 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.68/1.98 171 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.68/1.98 172 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 1.68/1.98 173 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 1.68/1.98 174 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 1.76/1.99 175 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.76/1.99 176 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.76/1.99 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(165,a,166,a)].
% 1.76/1.99 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(165,a,168,a)].
% 1.76/1.99 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(165,a,169,a)].
% 1.76/1.99 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(165,a,170,a)].
% 1.76/1.99 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(165,a,171,a)].
% 1.76/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(165,a,172,a)].
% 1.76/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(165,a,173,a)].
% 1.76/1.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(165,a,174,a)].
% 1.76/1.99 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(165,a,175,a)].
% 1.76/1.99 177 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.76/1.99 178 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.76/2.00 179 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.76/2.00 180 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.76/2.00 181 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -c_lessequals(C,E,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.76/2.00 182 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.76/2.00 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(177,a,178,a)].
% 1.76/2.00 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(177,a,179,a)].
% 1.76/2.00 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(177,a,180,a)].
% 1.76/2.00 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -c_lessequals(B,D,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(177,a,181,a)].
% 1.76/2.00 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -c_lessequals(A,C,tc_nat). [resolve(177,a,182,a)].
% 1.76/2.00 183 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.76/2.00 184 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Oone__class_Oone(A) # label(cls_setprod__empty_0) # label(axiom). [assumption].
% 1.76/2.00 185 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fequal(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A) = c_Power_Opower__class_Opower(E,c_Finite__Set_Ocard(F,B),A) | hBOOL(hAPP(hAPP(c_in(B),C),F)) | -c_Finite__Set_Ofinite(F,B) # label(cls_setprod__gen__delta_1) # label(axiom). [assumption].
% 1.76/2.00 186 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fequal(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Oone__class_Oone(A),B,A,A),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_H_0) # label(axiom). [assumption].
% 1.76/2.00 187 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fequal(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Oone__class_Oone(A),B,A,A),E,B,A) = c_HOL_Oone__class_Oone(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_H_1) # label(axiom). [assumption].
% 1.87/2.11 188 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,C,D,A) = c_HOL_Oone__class_Oone(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setprod__def_1) # label(axiom). [assumption].
% 1.87/2.11 189 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(B,C,D,A) = c_HOL_Oone__class_Oone(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setprod__infinite_0) # label(axiom). [assumption].
% 1.87/2.11 190 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fequal(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Oone__class_Oone(A),B,A,A),E,B,A) = c_HOL_Oone__class_Oone(A) | hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_1) # label(axiom). [assumption].
% 1.87/2.11 191 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fequal(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Oone__class_Oone(A),B,A,A),E,B,A) = hAPP(D,C) | -hBOOL(hAPP(hAPP(c_in(B),C),E)) | -c_Finite__Set_Ofinite(E,B) # label(cls_setprod__delta_0) # label(axiom). [assumption].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(183,a,184,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_fequal(A),B,A,A,tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),D,A,tc_nat,tc_nat),E,A,tc_nat) = c_Power_Opower__class_Opower(D,c_Finite__Set_Ocard(E,A),tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),E)) | -c_Finite__Set_Ofinite(E,A). [resolve(183,a,185,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),hAPP(c_fequal(A),B),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Oone__class_Oone(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(183,a,186,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),hAPP(c_fequal(A),B),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Oone__class_Oone(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(183,a,187,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(A,B,C,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(183,a,188,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_fequal(A),B,A,A,tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Oone__class_Oone(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(183,a,190,a)].
% 1.87/2.12 Derived: c_Finite__Set_Osetprod(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(tc_nat),c_COMBC(c_fequal(A),B,A,A,tc_bool),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),C,A,tc_nat,tc_fun(tc_nat,tc_nat)),c_HOL_Oone__class_Oone(tc_nat),A,tc_nat,tc_nat),D,A,tc_nat) = hAPP(C,B) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A). [resolve(183,a,191,a)].
% 1.87/2.12 192 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.87/2.12 193 -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].
% 1.87/2.12 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(192,a,193,a)].
% 1.87/2.12
% 1.87/2.12 ============================== end predicate elimination =============
% 1.87/2.12
% 1.87/2.12 Auto_denials: (non-Horn, no changes).
% 1.87/2.12
% 1.87/2.12 Term ordering decisions:
% 1.87/2.12 Function symbol KB weights: tc_nat=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_bool=1. tc_Arrow__Order__Mirabelle_Oindi=1. v_c____=1. v_P____=1. t_a=1. v_d____=1. v_e____=1. v_h____=1. v_n____=1. c_Arrow__Order__Mirabelle_OProf=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Arrow__Order__Mirabelle_Oabove=1. v_Lab____=1. v_Lba____=1. v_a____=1. v_b____=1. hAPP=1. tc_fun=1. tc_prod=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Finite__Set_Ocard=1. c_Relation_OId__on=1. c_Wellfounded_Omeasure=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. v_sko__Arrow__Order__Mirabelle__Xthird__alt__1=1. c_in=1. c_HOL_Oord__class_Oless=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_Orderings_Obot__class_Obot=1. c_HOL_Oone__class_Oone=1. c_Orderings_Otop__class_Otop=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_OIf=1. c_Relation_OId=1. c_fequal=1. v_F=1. c_HOL_Oabs__class_Oabs=1. c_List_Olist_ONil=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_Relation_Oconverse=1. c_Power_Opower__class_Opower=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_List_Olist_OCons=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1=1. c_Wellfounded_Omlex__prod=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1=1. c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Relation_OImage=1. c_Set_Ovimage=1. c_Finite__Set_Osetsum=1. c_Finite__Set_Osetprod=1. v_sko__CHAINED__1=1. c_Relation_Oinv__image=1. c_Product__Type_OSigma=1. c_ATP__Linkup_Osko__Finite__Set__Xsetprod__nonneg__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xsetsum__nonpos__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1=1. c_ATP__Linkup_Osko__Relation__XDomainE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_COMBC=1. c_COMBB=1. c_Relation_Orel__comp=1. c_COMBS=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1.
% 3.07/3.38
% 3.07/3.38 ============================== end of process initial clauses ========
% 3.07/3.38
% 3.07/3.38 ============================== CLAUSES FOR SEARCH ====================
% 3.07/3.38
% 3.07/3.38 ============================== end of clauses for search =============
% 3.07/3.38
% 3.07/3.38 ============================== SEARCH ================================
% 3.07/3.38
% 3.07/3.38 % Starting search at 0.81 seconds.
% 3.07/3.38
% 3.07/3.38 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 77 (0.00 of 1.26 sec).
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=137.000, iters=3629
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=100.000, iters=3431
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=98.000, iters=3402
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=95.000, iters=3422
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=80.000, iters=3442
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=78.000, iters=3394
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=75.000, iters=3453
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=65.000, iters=3400
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=63.000, iters=3352
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=57.000, iters=3802
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=56.000, iters=3767
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=49.000, iters=3503
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=43.000, iters=3368
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=41.000, iters=3415
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=39.000, iters=3370
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=38.000, iters=3382
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=37.000, iters=3341
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=34.000, iters=3335
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=33.000, iters=3335
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=32.000, iters=3359
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=30.000, iters=3334
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=29.000, iters=3351
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=26.000, iters=3835
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=24.000, iters=3520
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=22.000, iters=3389
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=21.000, iters=3510
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=20.000, iters=3377
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=16.000, iters=3354
% 3.07/3.38
% 3.07/3.38 Low Water (keep): wt=14.000, iters=3340
% 3.07/3.38
% 3.07/3.38 Low Water (displace): id=2838, wt=192.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3967, wt=189.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2227, wt=187.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2158, wt=186.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=1631, wt=185.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3956, wt=184.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2136, wt=181.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3474, wt=179.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3965, wt=176.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3954, wt=174.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3950, wt=172.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3960, wt=166.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2803, wt=158.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2831, wt=153.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3479, wt=147.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3937, wt=145.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2842, wt=142.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3210, wt=137.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2858, wt=132.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3471, wt=129.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2846, wt=128.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2064, wt=127.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3353, wt=125.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2850, wt=124.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3676, wt=122.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3341, wt=121.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=1872, wt=120.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3467, wt=119.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2862, wt=118.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3951, wt=117.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3504, wt=115.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3356, wt=114.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3469, wt=113.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2875, wt=112.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3948, wt=111.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3963, wt=110.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=2854, wt=109.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3953, wt=108.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3365, wt=107.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3704, wt=106.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3466, wt=105.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3726, wt=104.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3634, wt=103.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3651, wt=102.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3506, wt=101.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3944, wt=100.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3608, wt=99.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3519, wt=98.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3972, wt=97.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=10205, wt=95.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=3938, wt=85.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11827, wt=71.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11825, wt=65.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11837, wt=63.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12011, wt=62.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11197, wt=60.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11818, wt=59.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=6039, wt=58.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11839, wt=57.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12018, wt=56.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11274, wt=55.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11203, wt=54.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11979, wt=53.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12291, wt=52.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=11833, wt=51.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=6951, wt=50.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12446, wt=49.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12295, wt=48.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12442, wt=47.000
% 4.49/4.79
% 4.49/4.79 Low Water (displace): id=12579, wt=12.000
% 4.49/4.79
% 4.49/4.79 ============================== PROOF =================================
% 4.49/4.79 % SZS status Unsatisfiable
% 4.49/4.79 % SZS output start Refutation
% 4.49/4.79
% 4.49/4.79 % Proof 1 at 3.43 (+ 0.06) seconds.
% 4.49/4.79 % Length of proof is 43.
% 4.49/4.79 % Level of proof is 16.
% 4.49/4.79 % Maximum clause weight is 36.000.
% 4.49/4.79 % Given clauses 2755.
% 4.49/4.79
% 4.49/4.79 1 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 4.49/4.79 5 -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].
% 4.49/4.79 53 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 4.49/4.79 61 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 4.49/4.79 81 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 4.49/4.79 84 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 4.49/4.79 94 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 4.49/4.79 97 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 4.49/4.79 104 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 4.49/4.79 141 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 4.49/4.79 218 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # label(cls_nat__add__commute_0) # label(axiom). [assumption].
% 4.49/4.79 253 c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat) # label(cls_le__add2_0) # label(axiom). [assumption].
% 4.49/4.79 281 A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_natgb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 4.49/4.79 282 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [copy(281),flip(a)].
% 4.49/4.79 283 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A # label(cls_plus__nat_Oadd__0_0) # label(axiom). [assumption].
% 4.49/4.79 351 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) # label(cls_add__less__mono1_0) # label(axiom). [assumption].
% 4.49/4.79 592 hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 4.49/4.79 594 hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 4.49/4.79 652 c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(1,a,5,a)].
% 4.49/4.79 653 c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [copy(652),flip(a)].
% 4.49/4.79 694 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(B,A,tc_nat). [resolve(53,a,61,a)].
% 4.49/4.79 719 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(97,a,81,a)].
% 4.49/4.79 722 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(97,a,84,a)].
% 4.49/4.79 728 c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(97,a,94,a)].
% 4.49/4.79 779 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(104,a,141,a)].
% 4.49/4.79 856 c_HOL_Oone__class_Oone(tc_nat) = c_0. [new_symbol(653)].
% 4.49/4.79 875 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_0)). [back_rewrite(779),rewrite([856(7)])].
% 4.49/4.79 3090 c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat). [resolve(722,b,253,a)].
% 4.49/4.79 3828 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_0),A))). [resolve(875,a,351,b),rewrite([283(8)])].
% 4.49/4.79 14564 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [resolve(3090,a,694,b)].
% 4.49/4.79 14568 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C,D),E)),c_Lattices_Olower__semilattice__class_Oinf(F,hAPP(A,E),tc_nat))). [para(594(a,2),14564(a,1,1,2)),rewrite([719(10)])].
% 4.49/4.79 14648 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(B,A))),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(B,A),tc_nat))). [para(594(a,1),14568(a,1,1,2))].
% 4.49/4.79 14679 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))). [para(283(a,1),14648(a,1,1,2))].
% 4.49/4.79 14702 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(A,hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))). [para(592(a,1),14679(a,1,1,2)),rewrite([592(11)])].
% 4.49/4.79 14765 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,B)),c_Lattices_Olower__semilattice__class_Oinf(C,hAPP(A,B),tc_nat))). [para(218(a,1),14702(a,1,1,2,2)),rewrite([283(8),282(10)])].
% 4.49/4.79 14774 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(A,B),hAPP(C,B))),c_Lattices_Olower__semilattice__class_Oinf(D,hAPP(c_COMBS(A,C,E,F,V6),B),tc_nat))). [para(594(a,1),14765(a,1,1,2))].
% 4.49/4.79 15499 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(A,B),hAPP(C,B))),hAPP(c_COMBS(A,C,D,E,F),B))). [para(728(a,1),14774(a,1,2))].
% 4.49/4.79 15543 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(A,B,C,D,E),F)),hAPP(c_COMBS(A,B,V6,V7,V8),F))). [para(594(a,2),15499(a,1,1,2))].
% 4.49/4.79 15564 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(A,B,C,D,E),F)),hAPP(hAPP(A,F),hAPP(B,F)))). [para(594(a,1),15543(a,1,2))].
% 4.49/4.79 15574 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C,D),E)),hAPP(E,hAPP(A,E)))). [para(283(a,1),15564(a,1,2,1))].
% 4.49/4.79 15672 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D)),hAPP(D,D))). [para(283(a,1),15574(a,1,2,2))].
% 4.49/4.79 16400 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),c_COMBB(D,E,F,V6,V7))),hAPP(D,hAPP(E,c_COMBB(D,E,F,V6,V7))))). [para(592(a,1),15672(a,1,2))].
% 4.49/4.79 16401 $F. [resolve(16400,a,3828,a)].
% 4.49/4.79
% 4.49/4.79 % SZS output end Refutation
% 4.49/4.79 ============================== end of proof ==========================
% 4.49/4.79
% 4.49/4.79 ============================== STATISTICS ============================
% 4.49/4.79
% 4.49/4.79 Given=2755. Generated=100196. Kept=16131. proofs=1.
% 4.49/4.79 Usable=2743. Sos=9999. Demods=319. Limbo=3, Disabled=4422. Hints=0.
% 4.49/4.79 Megabytes=33.84.
% 4.49/4.79 User_CPU=3.43, System_CPU=0.06, Wall_clock=3.
% 4.49/4.79
% 4.49/4.79 ============================== end of statistics =====================
% 4.49/4.79
% 4.49/4.79 ============================== end of search =========================
% 4.49/4.79
% 4.49/4.79 THEOREM PROVED
% 4.49/4.79 % SZS status Unsatisfiable
% 4.49/4.79
% 4.49/4.79 Exiting with 1 proof.
% 4.49/4.79
% 4.49/4.79 Process 4668 exit (max_proofs) Sat Jul 2 09:22:59 2022
% 4.49/4.79 Prover9 interrupted
%------------------------------------------------------------------------------