TSTP Solution File: SWV692-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV692-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:27 EDT 2022
% Result : Timeout 300.01s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV692-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.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 : Wed Jun 15 08:30:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.18/1.57 ============================== Prover9 ===============================
% 1.18/1.57 Prover9 (32) version 2009-11A, November 2009.
% 1.18/1.57 Process 1106 was started by sandbox on n010.cluster.edu,
% 1.18/1.57 Wed Jun 15 08:30:10 2022
% 1.18/1.57 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_918_n010.cluster.edu".
% 1.18/1.57 ============================== end of head ===========================
% 1.18/1.57
% 1.18/1.57 ============================== INPUT =================================
% 1.18/1.57
% 1.18/1.57 % Reading from file /tmp/Prover9_918_n010.cluster.edu
% 1.18/1.57
% 1.18/1.57 set(prolog_style_variables).
% 1.18/1.57 set(auto2).
% 1.18/1.57 % set(auto2) -> set(auto).
% 1.18/1.57 % set(auto) -> set(auto_inference).
% 1.18/1.57 % set(auto) -> set(auto_setup).
% 1.18/1.57 % set(auto_setup) -> set(predicate_elim).
% 1.18/1.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.18/1.57 % set(auto) -> set(auto_limits).
% 1.18/1.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.18/1.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.18/1.57 % set(auto) -> set(auto_denials).
% 1.18/1.57 % set(auto) -> set(auto_process).
% 1.18/1.57 % set(auto2) -> assign(new_constants, 1).
% 1.18/1.57 % set(auto2) -> assign(fold_denial_max, 3).
% 1.18/1.57 % set(auto2) -> assign(max_weight, "200.000").
% 1.18/1.57 % set(auto2) -> assign(max_hours, 1).
% 1.18/1.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.18/1.57 % set(auto2) -> assign(max_seconds, 0).
% 1.18/1.57 % set(auto2) -> assign(max_minutes, 5).
% 1.18/1.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.18/1.57 % set(auto2) -> set(sort_initial_sos).
% 1.18/1.57 % set(auto2) -> assign(sos_limit, -1).
% 1.18/1.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.18/1.57 % set(auto2) -> assign(max_megs, 400).
% 1.18/1.57 % set(auto2) -> assign(stats, some).
% 1.18/1.57 % set(auto2) -> clear(echo_input).
% 1.18/1.57 % set(auto2) -> set(quiet).
% 1.18/1.57 % set(auto2) -> clear(print_initial_clauses).
% 1.18/1.57 % set(auto2) -> clear(print_given).
% 1.18/1.57 assign(lrs_ticks,-1).
% 1.18/1.57 assign(sos_limit,10000).
% 1.18/1.57 assign(order,kbo).
% 1.18/1.57 set(lex_order_vars).
% 1.18/1.57 clear(print_given).
% 1.18/1.57
% 1.18/1.57 % formulas(sos). % not echoed (985 formulas)
% 1.18/1.57
% 1.18/1.57 ============================== end of input ==========================
% 1.18/1.57
% 1.18/1.57 % From the command line: assign(max_seconds, 300).
% 1.18/1.57
% 1.18/1.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.18/1.57
% 1.18/1.57 % Formulas that are not ordinary clauses:
% 1.18/1.57
% 1.18/1.57 ============================== end of process non-clausal formulas ===
% 1.18/1.57
% 1.18/1.57 ============================== PROCESS INITIAL CLAUSES ===============
% 1.18/1.57
% 1.18/1.57 ============================== PREDICATE ELIMINATION =================
% 1.18/1.57 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.18/1.57 2 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.18/1.57 3 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.18/1.57 4 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.18/1.57 5 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.18/1.57 6 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.18/1.57 7 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.18/1.57 8 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.18/1.57 9 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.18/1.57 10 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.18/1.60 11 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.18/1.60 12 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.18/1.60 13 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.18/1.60 14 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.18/1.60 15 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.18/1.60 16 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.18/1.60 17 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.18/1.60 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(1,a,2,a)].
% 1.18/1.60 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(1,a,3,a)].
% 1.18/1.60 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(1,a,4,a)].
% 1.18/1.60 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(1,a,5,a)].
% 1.18/1.60 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(1,a,7,a)].
% 1.18/1.60 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(1,a,11,a)].
% 1.18/1.60 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(1,a,14,a)].
% 1.18/1.60 18 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.18/1.60 19 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 1.18/1.60 20 -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].
% 1.18/1.60 21 -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].
% 1.18/1.60 22 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.18/1.60 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(18,a,19,a)].
% 1.18/1.60 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(18,a,20,a)].
% 1.18/1.60 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(18,a,21,a)].
% 1.18/1.60 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(18,a,22,a)].
% 1.18/1.63 23 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.18/1.63 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(23,a,19,a)].
% 1.18/1.63 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(23,a,20,a)].
% 1.18/1.63 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(23,a,21,a)].
% 1.18/1.63 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)). [resolve(23,a,22,a)].
% 1.18/1.63 24 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__semiring_Ogb__semiring__axioms_H_0) # label(axiom). [assumption].
% 1.18/1.63 25 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,B,V6,V7,V8) # label(cls_gb__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.18/1.63 26 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) | -c_Groebner__Basis_Ogb__semiring(E,F,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.18/1.63 27 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(F,B,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.18/1.63 28 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) = hAPP(hAPP(C,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,B),E)) | -c_Groebner__Basis_Ogb__semiring(C,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.18/1.63 29 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.18/1.63 30 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.18/1.63 31 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.18/1.63 32 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.18/1.63 33 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.18/1.63 34 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.18/1.63 35 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.18/1.63 36 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.18/1.63 37 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.18/1.63 38 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.18/1.63 39 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.18/1.63 40 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.18/1.63 41 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(A,F,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.18/1.63 42 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.18/1.63 43 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.18/1.63 44 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.18/1.63 45 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.18/1.63 46 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.18/1.63 47 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E))) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.18/1.63 48 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.18/1.63 49 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,V6) # label(cls_gb__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.18/1.63 50 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.18/1.63 51 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.18/1.63 52 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.18/1.63 53 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(B,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.18/1.63 54 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.18/1.63 55 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.18/1.63 56 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.18/1.63 57 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,V6) # label(cls_gb__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.18/1.63 58 hAPP(hAPP(A,B),hAPP(hAPP(C,D),B)) = hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.18/1.67 59 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.18/1.67 60 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D)) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.18/1.67 61 hAPP(hAPP(A,B),hAPP(c_Suc,C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.18/1.67 62 hAPP(hAPP(A,B),hAPP(c_Suc,C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.18/1.67 63 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C) = hAPP(hAPP(B,C),hAPP(c_Suc,D)) | -c_Groebner__Basis_Ogb__semiring(E,A,B,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.18/1.67 64 hAPP(hAPP(A,B),hAPP(hAPP(C,B),D)) = hAPP(hAPP(C,B),hAPP(c_Suc,D)) | -c_Groebner__Basis_Ogb__semiring(E,A,C,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.18/1.67 65 hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat)) = C | -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,V6) # label(cls_gb__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.18/1.67 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)). [resolve(24,b,25,b)].
% 1.18/1.67 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)). [resolve(24,b,26,b)].
% 1.18/1.67 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). [resolve(24,b,61,b)].
% 1.18/1.67 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)). [resolve(24,b,63,b)].
% 1.18/1.67 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)). [resolve(24,b,64,b)].
% 1.18/1.67 66 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_Groebner__Basis_Osemiringb(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__ringb_Osemiringb__axioms_H_0) # label(axiom). [assumption].
% 1.18/1.67 67 A != hAPP(hAPP(B,A),C) | -c_Groebner__Basis_Osemiringb(B,D,E,F,V6,V7) | C = F # label(cls_semiringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.18/1.67 68 hAPP(hAPP(A,B),C) != hAPP(hAPP(A,B),D) | -c_Groebner__Basis_Osemiringb(A,E,F,V6,V7,V8) | C = D # label(cls_semiringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.18/1.67 69 -c_Groebner__Basis_Osemiringb(A,B,C,D,E,F) | V6 = hAPP(hAPP(A,V6),D) # label(cls_semiringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.18/1.67 70 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(A,hAPP(hAPP(B,C),E)),hAPP(hAPP(B,C),D)) | -c_Groebner__Basis_Osemiringb(A,B,F,V6,V7,V8) # label(cls_semiringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.18/1.67 71 -c_Groebner__Basis_Osemiringb(A,B,C,D,E,F) | hAPP(hAPP(A,hAPP(hAPP(B,V6),V7)),hAPP(hAPP(B,V6),V8)) = hAPP(hAPP(A,hAPP(hAPP(B,V6),V8)),hAPP(hAPP(B,V6),V7)) # label(cls_semiringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.18/1.67 72 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) != hAPP(hAPP(A,B),hAPP(hAPP(C,D),F)) | E = F | D = V6 | -c_Groebner__Basis_Osemiringb(A,C,V7,V6,V8,V9) # label(cls_semiringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.47/1.72 73 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),F)) != hAPP(hAPP(A,hAPP(hAPP(B,C),F)),hAPP(hAPP(B,E),D)) | -c_Groebner__Basis_Osemiringb(A,B,V6,V7,V8,V9) | D = F | C = E # label(cls_semiringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.47/1.72 74 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),F)) != hAPP(hAPP(A,hAPP(hAPP(B,C),F)),hAPP(hAPP(B,E),D)) | D = F | C = E | -c_Groebner__Basis_Osemiringb(A,B,V6,V7,V8,V9) # label(cls_semiringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.47/1.72 75 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.47/1.72 76 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.47/1.72 77 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.47/1.72 78 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.47/1.72 79 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.47/1.72 80 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.47/1.72 81 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.47/1.72 82 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.47/1.72 83 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.47/1.72 84 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.47/1.72 85 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.47/1.72 86 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.47/1.72 87 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.47/1.72 88 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.47/1.72 89 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.47/1.72 90 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.47/1.72 91 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.47/1.72 92 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.47/1.72 93 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.47/1.72 94 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.47/1.72 95 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.47/1.72 96 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.47/1.72 97 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.47/1.72 98 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.47/1.72 99 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,D)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Suc,D)))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.47/1.72 100 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Suc,C)) | B = D | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.47/1.72 101 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.47/1.72 102 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.47/1.72 103 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.47/1.72 104 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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].
% 1.47/1.72 105 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.47/1.72 106 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.47/1.72 107 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.47/1.72 108 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.47/1.72 109 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.47/1.72 110 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.47/1.72 111 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.47/1.72 112 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.47/1.72 113 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.47/1.72 114 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.47/1.72 115 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.47/1.72 116 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.47/1.72 117 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.47/1.72 118 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | B = D | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,76,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(75,a,77,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(75,a,79,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(75,a,80,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(75,a,81,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,82,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,83,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(75,a,84,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(75,a,85,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(75,a,86,a)].
% 1.47/1.72 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(75,a,87,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(75,a,88,a)].
% 1.47/1.72 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(75,a,89,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(75,a,90,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,91,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(75,a,92,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(75,a,93,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,94,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,95,a)].
% 1.47/1.72 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(75,a,96,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(75,a,97,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,C)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_Suc,C)))). [resolve(75,a,99,a)].
% 1.47/1.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_Suc,B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,100,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C))). [resolve(75,a,101,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,102,a)].
% 1.47/1.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C. [resolve(75,a,103,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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(75,a,104,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,105,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,106,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,107,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(75,a,108,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,109,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(75,a,110,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(75,a,113,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(75,a,114,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(75,a,115,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(75,a,116,a)].
% 1.47/1.72 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,117,a)].
% 1.47/1.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(75,a,118,a)].
% 1.47/1.75 119 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.47/1.75 120 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D))),B) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 1.47/1.75 121 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 1.47/1.75 122 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 1.47/1.75 123 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 1.47/1.75 124 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D)),tc_nat,A,tc_nat),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat))) # label(cls_lemma__realpow__diff__sumr_0) # label(axiom). [assumption].
% 1.47/1.75 125 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,A,tc_nat),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))) # label(cls_lemma__realpow__diff__sumr2_0) # label(axiom). [assumption].
% 1.47/1.75 126 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.47/1.75 127 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B),tc_nat,A,A),A,tc_fun(A,A),tc_nat),tc_nat,A,A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) # label(cls_lemma__termdiff1_0) # label(axiom). [assumption].
% 1.47/1.75 128 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.47/1.75 129 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.47/1.75 130 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.47/1.75 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(119,a,120,a)].
% 1.47/1.75 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(119,a,121,a)].
% 1.47/1.75 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(119,a,122,a)].
% 1.47/1.75 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C). [resolve(119,a,123,a)].
% 1.47/1.75 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(119,a,124,b)].
% 1.47/1.75 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(119,a,125,b)].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(119,a,126,a)].
% 1.47/1.76 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(119,a,127,b)].
% 1.47/1.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(119,a,128,a)].
% 1.47/1.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(119,a,129,a)].
% 1.47/1.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(119,a,130,a)].
% 1.47/1.76 131 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(131,a,120,a)].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)). [resolve(131,a,121,a)].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(131,a,122,a)].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C). [resolve(131,a,123,a)].
% 1.47/1.76 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(131,a,124,b)].
% 1.47/1.76 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(131,a,125,b)].
% 1.47/1.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(131,a,126,a)].
% 1.47/1.76 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(131,a,127,b)].
% 1.47/1.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(131,a,128,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(131,a,129,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(131,a,130,a)].
% 1.54/1.79 132 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.54/1.79 133 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 1.54/1.79 134 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(B,D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 1.54/1.79 135 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 1.54/1.79 136 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.54/1.79 137 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.54/1.79 138 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.54/1.79 139 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.54/1.79 140 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(D,E,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_setsum__add__nat__ivl_0) # label(axiom). [assumption].
% 1.54/1.79 141 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBB(B,c_Suc,tc_nat,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 1.54/1.79 142 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 1.54/1.79 143 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBB(B,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),D),tc_nat,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat)) # label(cls_setsum__shift__bounds__nat__ivl_0) # label(axiom). [assumption].
% 1.54/1.79 144 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBB(B,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),D),tc_nat,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat))) # label(cls_sumr__offset3_0) # label(axiom). [assumption].
% 1.54/1.79 145 -class_Power_Opower(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),C),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) # label(cls_lemma__realpow__rev__sumr_0) # label(axiom). [assumption].
% 1.54/1.79 146 -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].
% 1.54/1.79 147 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(C,A),D,tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),B,tc_fun(C,tc_bool),A),E)),F) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(B,A),c_COMBC(D,B,C,A),tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),C,tc_fun(B,tc_bool),A),F)),E) # label(cls_setsum__commute_0) # label(axiom). [assumption].
% 1.54/1.79 148 -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].
% 1.54/1.79 149 -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].
% 1.54/1.79 150 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),C,A,tc_fun(A,A),B),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.54/1.79 151 -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].
% 1.54/1.79 152 -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].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(132,a,133,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(132,a,134,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(132,a,135,a)].
% 1.54/1.79 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(132,a,136,b)].
% 1.54/1.79 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(132,a,137,b)].
% 1.54/1.79 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(132,a,138,b)].
% 1.54/1.79 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(132,a,139,b)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(132,a,140,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(132,a,141,a)].
% 1.54/1.79 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(132,a,142,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(132,a,143,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(132,a,144,a)].
% 1.54/1.79 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(132,a,145,b)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(132,a,146,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat),C,tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),A,tc_fun(B,tc_bool),tc_nat),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat),c_COMBC(C,A,B,tc_nat),tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),B,tc_fun(A,tc_bool),tc_nat),E)),D). [resolve(132,a,147,a)].
% 1.54/1.79 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(132,a,148,a)].
% 1.54/1.79 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(132,a,149,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_fun(tc_nat,tc_nat),A),C,A,tc_nat,tc_nat)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),C),D)). [resolve(132,a,150,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(132,a,151,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(132,a,152,a)].
% 1.54/1.79 153 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(153,a,133,a)].
% 1.54/1.79 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(153,a,134,a)].
% 1.54/1.80 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(153,a,135,a)].
% 1.54/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(153,a,136,b)].
% 1.54/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),C)). [resolve(153,a,137,b)].
% 1.54/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(153,a,138,b)].
% 1.54/1.80 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(153,a,139,b)].
% 1.54/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(153,a,140,a)].
% 1.54/1.80 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(153,a,141,a)].
% 1.54/1.80 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(153,a,142,a)].
% 1.54/1.80 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(153,a,143,a)].
% 1.54/1.80 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(153,a,144,a)].
% 1.54/1.86 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(153,a,145,b)].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A). [resolve(153,a,146,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),C,tc_fun(B,tc_Complex_Ocomplex),tc_fun(tc_fun(B,tc_bool),tc_Complex_Ocomplex),A),A,tc_fun(B,tc_bool),tc_Complex_Ocomplex),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBC(C,A,B,tc_Complex_Ocomplex),tc_fun(A,tc_Complex_Ocomplex),tc_fun(tc_fun(A,tc_bool),tc_Complex_Ocomplex),B),B,tc_fun(A,tc_bool),tc_Complex_Ocomplex),E)),D). [resolve(153,a,147,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(153,a,148,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(153,a,149,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(153,a,150,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(153,a,151,a)].
% 1.54/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(153,a,152,a)].
% 1.54/1.86 154 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.54/1.86 155 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.54/1.86 156 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.54/1.86 157 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.54/1.86 158 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.54/1.86 159 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.54/1.86 160 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.54/1.86 161 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.54/1.86 162 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.54/1.86 163 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.54/1.86 164 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.54/1.86 165 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.54/1.86 166 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.54/1.86 167 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.54/1.86 168 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.54/1.86 169 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.54/1.86 170 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(154,a,155,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(154,a,156,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(154,a,157,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(154,a,158,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(154,a,159,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(154,a,160,a)].
% 1.54/1.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(154,a,161,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(154,a,163,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(154,a,164,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(154,a,165,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(154,a,166,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(154,a,167,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(154,a,168,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(154,a,169,a)].
% 1.68/1.92 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(154,a,170,a)].
% 1.68/1.92 171 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.68/1.92 172 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.68/1.92 173 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.68/1.92 174 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.68/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(173,a,174,a)].
% 1.68/1.99 175 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.68/1.99 176 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.68/1.99 177 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.68/1.99 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(175,a,177,a)].
% 1.68/1.99 178 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.68/1.99 179 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiableI_0) # label(axiom). [assumption].
% 1.68/1.99 180 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiable__def_1) # label(axiom). [assumption].
% 1.68/1.99 181 -class_RealVector_Oreal__normed__field(A) | B = C | -c_Deriv_Oderiv(D,E,C,A) | -c_Deriv_Oderiv(D,E,B,A) # label(cls_DERIV__unique_0) # label(axiom). [assumption].
% 1.68/1.99 182 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBB(B,C,A,A,A),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) # label(cls_DERIV__chain2_0) # label(axiom). [assumption].
% 1.68/1.99 183 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBB(B,C,A,A,A),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) | -c_Deriv_Oderiv(C,D,F,A) # label(cls_DERIV__chain_H_0) # label(axiom). [assumption].
% 1.68/1.99 184 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),A) | -c_Deriv_Oderiv(C,D,E,A) # label(cls_DERIV__cmult_0) # label(axiom). [assumption].
% 1.68/1.99 185 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBB(B,C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,hAPP(C,D),A) # label(cls_differentiable__compose_0) # label(axiom). [assumption].
% 1.68/1.99 186 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,B,A) # label(cls_DERIV__cmult__Id_0) # label(axiom). [assumption].
% 1.68/1.99 187 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),A),A,tc_nat,A),hAPP(c_Suc,C)),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(B,D)),C))),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__power__Suc_0) # label(axiom). [assumption].
% 1.68/1.99 188 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),A),A,tc_nat,A),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(B,D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__power_0) # label(axiom). [assumption].
% 1.68/1.99 189 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),A),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__mult_0) # label(axiom). [assumption].
% 1.68/1.99 190 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__add_0) # label(axiom). [assumption].
% 1.68/1.99 191 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),A),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__sum_0) # label(axiom). [assumption].
% 1.68/1.99 192 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__diff_0) # label(axiom). [assumption].
% 1.68/1.99 193 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),A),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__diff_0) # label(axiom). [assumption].
% 1.68/1.99 194 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),A),A,A,A),C),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),C),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__cdivide_0) # label(axiom). [assumption].
% 1.68/1.99 195 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),tc_nat,A,A),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_divide_OLIMSEQ_0) # label(axiom). [assumption].
% 1.68/1.99 196 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),A),A,tc_nat,A),C),D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__power_0) # label(axiom). [assumption].
% 1.68/1.99 197 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(C,D))),A) | -c_Deriv_Oderiv(C,D,E,A) | -c_Deriv_Oderiv(B,D,F,A) # label(cls_DERIV__mult_H_0) # label(axiom). [assumption].
% 1.68/1.99 198 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D))),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__mult_0) # label(axiom). [assumption].
% 1.68/1.99 199 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),A),C,A,A,A),D,A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__divide_0) # label(axiom). [assumption].
% 1.68/1.99 200 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D)))),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(C,D)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__quotient_0) # label(axiom). [assumption].
% 1.68/1.99 201 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E),A) | E = c_HOL_Ozero__class_Ozero(A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__divide_0) # label(axiom). [assumption].
% 1.68/1.99 202 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),A),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(C,D)),hAPP(C,D))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__divide_0) # label(axiom). [assumption].
% 1.68/1.99 203 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),B,A,A),E)),D) # label(cls_divide_Osetsum_0) # label(axiom). [assumption].
% 1.68/1.99 204 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 1.68/1.99 205 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 1.68/1.99 206 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(178,a,179,a)].
% 1.68/1.99 Derived: A = B | -c_Deriv_Oderiv(C,D,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(C,D,A,tc_Complex_Ocomplex). [resolve(178,a,181,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBB(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,hAPP(B,C),D,tc_Complex_Ocomplex). [resolve(178,a,182,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex). [resolve(178,a,184,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(c_COMBB(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_Complex_Ocomplex). [resolve(178,a,185,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,A,tc_Complex_Ocomplex). [resolve(178,a,186,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),hAPP(c_Suc,B)),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(A,C)),B))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,187,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(A,C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,188,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(178,a,189,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,190,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(178,a,191,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,192,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(178,a,193,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),B),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,194,a)].
% 1.68/1.99 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,195,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(178,a,196,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(B,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,E,tc_Complex_Ocomplex). [resolve(178,a,197,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,198,a)].
% 1.68/1.99 Derived: c_Deriv_Odifferentiable(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(178,a,199,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,200,a)].
% 1.68/1.99 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,201,a)].
% 1.68/1.99 Derived: c_Deriv_Oderiv(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(B,C))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(178,a,202,a)].
% 1.68/1.99 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D)),C). [resolve(178,a,203,a)].
% 1.78/2.06 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(178,a,204,a)].
% 1.78/2.06 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(178,a,205,a)].
% 1.78/2.06 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(178,a,206,a)].
% 1.78/2.06 207 class_RealVector_Ometric__space(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Ometric__space) # label(axiom). [assumption].
% 1.78/2.06 208 -class_RealVector_Ometric__space(A) | B = C | -c_SEQ_OLIMSEQ(D,C,A) | -c_SEQ_OLIMSEQ(D,B,A) # label(cls_LIMSEQ__unique_0) # label(axiom). [assumption].
% 1.78/2.06 209 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Suc_0) # label(axiom). [assumption].
% 1.78/2.06 210 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_LIMSEQ__Suc__iff_0) # label(axiom). [assumption].
% 1.78/2.06 211 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_COMBB(B,hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,A,tc_nat),D,A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__linear_0) # label(axiom). [assumption].
% 1.78/2.06 212 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_COMBB(B,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,A,tc_nat),D,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__ignore__initial__segment_0) # label(axiom). [assumption].
% 1.78/2.06 213 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(B,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),D),tc_nat,A,tc_nat),C,A) # label(cls_LIMSEQ__offset_0) # label(axiom). [assumption].
% 1.78/2.06 Derived: A = B | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,A,tc_Complex_Ocomplex). [resolve(207,a,208,a)].
% 1.78/2.06 Derived: c_SEQ_OLIMSEQ(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(207,a,209,a)].
% 1.78/2.06 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(207,a,210,a)].
% 1.78/2.06 Derived: c_SEQ_OLIMSEQ(c_COMBB(A,hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),B),tc_nat,tc_Complex_Ocomplex,tc_nat),C,tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(207,a,211,a)].
% 1.78/2.06 Derived: c_SEQ_OLIMSEQ(c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),B),tc_nat,tc_Complex_Ocomplex,tc_nat),C,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(207,a,212,a)].
% 1.78/2.06 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(207,a,213,a)].
% 1.78/2.06 214 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.78/2.06 215 -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].
% 1.78/2.06 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(214,a,215,a)].
% 1.86/2.10 216 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.86/2.10 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B. [resolve(216,a,215,a)].
% 1.86/2.10 217 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.86/2.10 218 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.86/2.10 219 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.86/2.10 220 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.86/2.10 221 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.86/2.10 222 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.86/2.10 223 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.86/2.10 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(217,a,218,a)].
% 1.86/2.10 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(217,a,219,a)].
% 1.86/2.10 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(217,a,220,a)].
% 1.86/2.10 224 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.86/2.10 225 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 1.86/2.10 226 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(224,a,225,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(224,a,226,a)].
% 1.86/2.12 227 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.86/2.12 228 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.86/2.12 229 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(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].
% 1.86/2.12 230 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.86/2.12 231 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.86/2.12 232 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.86/2.12 233 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.86/2.12 234 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.86/2.12 235 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.86/2.12 236 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.86/2.12 237 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.86/2.12 238 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(227,a,228,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(227,a,230,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(227,a,231,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(227,a,232,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(227,a,234,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(227,a,235,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(227,a,236,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(227,a,237,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(227,a,238,a)].
% 1.94/2.18 239 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.94/2.18 240 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_Suc,B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.94/2.18 241 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),B,A,A),E)),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.94/2.18 242 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),D,A,A,C)),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.94/2.18 243 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.94/2.18 244 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.94/2.18 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(239,a,240,a)].
% 1.94/2.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),B,tc_nat,tc_fun(tc_nat,tc_nat),A),A,tc_nat,tc_nat),D)),C). [resolve(239,a,241,a)].
% 1.94/2.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C,tc_nat,tc_nat,B)),D). [resolve(239,a,242,a)].
% 1.94/2.18 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(239,a,243,a)].
% 1.94/2.18 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(239,a,244,a)].
% 1.94/2.18 245 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.94/2.18 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(245,a,240,a)].
% 1.94/2.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D)),C). [resolve(245,a,241,a)].
% 1.94/2.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,B)),D). [resolve(245,a,242,a)].
% 1.94/2.18 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(245,a,243,a)].
% 1.94/2.20 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(245,a,244,a)].
% 1.94/2.20 246 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.94/2.20 247 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom). [assumption].
% 1.94/2.20 248 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__mult_0) # label(axiom). [assumption].
% 1.94/2.20 249 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),tc_nat,A,A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_mult__left_OLIMSEQ_0) # label(axiom). [assumption].
% 1.94/2.20 250 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),tc_nat),tc_nat,tc_nat,A),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__pow_0) # label(axiom). [assumption].
% 1.94/2.20 251 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),B,A,A),E)),D) # label(cls_mult__left_Osetsum_0) # label(axiom). [assumption].
% 1.94/2.20 252 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 1.94/2.20 253 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 1.94/2.20 254 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 1.94/2.20 255 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 1.94/2.20 256 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),D,A,A,C)),E) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 1.94/2.20 257 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.94/2.20 258 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.94/2.20 259 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.94/2.20 260 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.94/2.20 261 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 1.94/2.20 262 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 1.94/2.20 263 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 1.94/2.20 264 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 1.94/2.20 265 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 1.94/2.20 Derived: c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(246,a,247,a)].
% 1.94/2.20 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(246,a,248,a)].
% 1.94/2.20 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(246,a,249,a)].
% 1.94/2.20 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_nat,tc_Complex_Ocomplex),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(246,a,250,a)].
% 1.94/2.20 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(246,a,252,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(246,a,254,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(246,a,257,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(246,a,259,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))). [resolve(246,a,261,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(246,a,262,a)].
% 1.94/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(246,a,264,a)].
% 1.94/2.24 266 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.94/2.24 267 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.94/2.24 268 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.94/2.24 269 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.94/2.24 270 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.94/2.24 271 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.94/2.28 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(266,a,267,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(266,a,268,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(266,a,269,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(266,a,270,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(266,a,271,a)].
% 1.94/2.28 272 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.94/2.28 273 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.94/2.28 274 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.94/2.28 275 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.94/2.28 276 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.94/2.28 277 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.94/2.28 278 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.94/2.28 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(275,a,276,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(275,a,277,a)].
% 1.94/2.28 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(275,a,278,a)].
% 1.94/2.28 279 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.94/2.28 280 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.94/2.28 281 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.94/2.28 282 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.94/2.28 283 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.94/2.28 284 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.94/2.28 285 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.94/2.28 286 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.94/2.28 287 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.94/2.28 288 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.94/2.28 289 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.94/2.28 290 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.94/2.28 291 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.94/2.28 292 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.94/2.28 293 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.94/2.28 294 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.94/2.28 295 -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].
% 1.94/2.28 296 -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].
% 1.94/2.28 297 -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].
% 1.94/2.28 298 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.94/2.28 299 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.94/2.28 300 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.94/2.28 301 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.94/2.28 302 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.94/2.28 303 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.94/2.28 304 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.94/2.28 305 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.94/2.28 306 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.94/2.28 307 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.94/2.28 308 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.94/2.28 309 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.94/2.28 310 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.94/2.28 311 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.94/2.28 312 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.94/2.28 313 -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].
% 1.94/2.28 314 -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].
% 1.94/2.28 315 -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].
% 1.94/2.28 316 -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].
% 1.94/2.28 317 -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].
% 1.94/2.28 318 -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].
% 1.94/2.28 319 -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].
% 1.94/2.28 320 -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].
% 1.94/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(279,a,280,a)].
% 1.94/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(279,a,282,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)). [resolve(279,a,283,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)). [resolve(279,a,284,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(279,a,285,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(279,a,286,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(279,a,287,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(279,a,288,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(279,a,289,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(279,a,290,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(279,a,292,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(279,a,293,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(279,a,294,a)].
% 2.04/2.28 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(279,a,295,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(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))),A). [resolve(279,a,298,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(279,a,299,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(279,a,300,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(279,a,302,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(279,a,303,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(279,a,304,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(279,a,307,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(279,a,311,a)].
% 2.04/2.28 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(279,a,313,a)].
% 2.04/2.28 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(279,a,315,a)].
% 2.04/2.28 321 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(321,a,280,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(321,a,282,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)). [resolve(321,a,283,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)). [resolve(321,a,284,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(321,a,285,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(321,a,286,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(321,a,287,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(321,a,288,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(321,a,289,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(321,a,290,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(321,a,294,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(321,a,295,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(321,a,298,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B). [resolve(321,a,302,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(321,a,303,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(321,a,304,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(321,a,307,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A). [resolve(321,a,311,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C). [resolve(321,a,313,a)].
% 2.04/2.28 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(321,a,315,a)].
% 2.04/2.28 322 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)). [resolve(24,b,25,b)].
% 2.04/2.28 323 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)). [resolve(24,b,26,b)].
% 2.04/2.28 324 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). [resolve(24,b,61,b)].
% 2.04/2.29 325 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)). [resolve(24,b,63,b)].
% 2.04/2.29 326 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)). [resolve(24,b,64,b)].
% 2.04/2.29 327 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 2.04/2.29 328 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),E))),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 2.04/2.29 329 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom). [assumption].
% 2.04/2.29 330 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_0) # label(axiom). [assumption].
% 2.04/2.29 331 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),C)) | hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_1) # label(axiom). [assumption].
% 2.04/2.29 332 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 2.04/2.29 333 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 2.04/2.29 334 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 2.04/2.29 335 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))),D) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 2.04/2.29 336 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 2.04/2.29 337 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 2.04/2.29 338 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),B,A,A),E)),D) # label(cls_setsum__divide__distrib_0) # label(axiom). [assumption].
% 2.04/2.29 339 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 2.04/2.29 340 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 2.04/2.29 341 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 2.04/2.29 342 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 2.04/2.29 343 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 2.04/2.29 344 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 2.04/2.29 345 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 2.04/2.29 346 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 2.04/2.29 347 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 2.04/2.29 348 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 2.04/2.29 349 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__divide_0) # label(axiom). [assumption].
% 2.04/2.29 350 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 2.04/2.29 351 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 2.04/2.29 352 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 2.04/2.29 353 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 2.04/2.29 354 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 2.04/2.29 355 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 2.04/2.29 356 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 2.04/2.29 357 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 2.04/2.29 358 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 2.04/2.29 359 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 2.04/2.29 360 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 2.04/2.29 361 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 2.04/2.29 362 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 2.04/2.30 363 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 2.04/2.30 364 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 2.04/2.30 365 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_Power_Opower__class_Opower(A),B)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Oone__class_Oone(A))) | B = c_HOL_Oone__class_Oone(A) # label(cls_geometric__sum_0) # label(axiom). [assumption].
% 2.04/2.30 366 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 2.04/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),D))),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,328,a)].
% 2.04/2.30 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,329,a)].
% 2.04/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,330,a)].
% 2.04/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),B)) | hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,331,a)].
% 2.04/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(327,a,332,a)].
% 2.04/2.30 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,333,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,334,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),C) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,335,a)].
% 2.06/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(327,a,336,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A). [resolve(327,a,339,a)].
% 2.06/2.30 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,340,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,341,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,342,a)].
% 2.06/2.30 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,343,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(327,a,344,a)].
% 2.06/2.30 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B). [resolve(327,a,345,a)].
% 2.06/2.30 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B). [resolve(327,a,346,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,347,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(327,a,348,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(327,a,349,a)].
% 2.06/2.30 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A). [resolve(327,a,350,a)].
% 2.06/2.30 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A) = B. [resolve(327,a,351,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),B). [resolve(327,a,355,a)].
% 2.06/2.30 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(327,a,356,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,360,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,362,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(327,a,363,a)].
% 2.06/2.30 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(327,a,364,a)].
% 2.06/2.31 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(327,a,365,a)].
% 2.06/2.31 367 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.06/2.31 368 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add_0) # label(axiom). [assumption].
% 2.06/2.31 369 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),tc_nat,A,A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add__const_0) # label(axiom). [assumption].
% 2.06/2.31 370 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff_0) # label(axiom). [assumption].
% 2.06/2.31 371 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),tc_nat,A,A),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff__const_0) # label(axiom). [assumption].
% 2.06/2.31 372 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),D,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero_0) # label(axiom). [assumption].
% 2.06/2.31 373 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),D,A,tc_fun(A,A),tc_nat),B,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero2_0) # label(axiom). [assumption].
% 2.06/2.31 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(367,a,368,a)].
% 2.06/2.31 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(367,a,369,a)].
% 2.06/2.31 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(367,a,370,a)].
% 2.06/2.31 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(367,a,371,a)].
% 2.08/2.32 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),C,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(367,a,372,a)].
% 2.08/2.32 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(367,a,373,a)].
% 2.08/2.32 374 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.08/2.32 375 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(E,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) # label(cls_setsum__diff__nat__ivl_0) # label(axiom). [assumption].
% 2.08/2.32 376 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBB(B,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),C),tc_nat,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))) # label(cls_sumr__offset_0) # label(axiom). [assumption].
% 2.08/2.32 377 -class_OrderedGroup_Oab__group__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),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 2.08/2.32 378 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 2.08/2.32 379 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 2.08/2.32 380 -class_OrderedGroup_Oab__group__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_add__cancel__21_1) # label(axiom). [assumption].
% 2.08/2.32 381 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 2.08/2.32 382 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 2.08/2.32 383 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 2.08/2.34 384 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(374,a,375,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBB(A,hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),B),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))). [resolve(374,a,376,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) = D. [resolve(374,a,377,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(374,a,378,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(374,a,379,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C) | B = C. [resolve(374,a,381,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),C) | A = B. [resolve(374,a,382,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(374,a,383,a)].
% 2.08/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)). [resolve(374,a,384,a)].
% 2.08/2.34 385 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.08/2.34 386 -class_Ring__and__Field_Oring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) # label(cls_of__nat__diff_0) # label(axiom). [assumption].
% 2.08/2.34 387 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),tc_nat,A,A),D)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_sumr__diff__mult__const2_0) # label(axiom). [assumption].
% 2.08/2.39 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(385,a,386,a)].
% 2.08/2.39 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(385,a,387,a)].
% 2.08/2.39 388 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.08/2.39 389 -class_RealVector_Oreal__normed__algebra__1(A) | c_Series_Osuminf(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),tc_nat,A,A),A) = hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_powser__zero_0) # label(axiom). [assumption].
% 2.08/2.39 Derived: c_Series_Osuminf(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)). [resolve(388,a,389,a)].
% 2.08/2.39 390 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.08/2.39 391 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 2.08/2.39 392 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 2.08/2.39 393 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.08/2.39 394 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.08/2.39 395 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 2.08/2.39 396 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.08/2.39 397 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.08/2.39 398 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.08/2.40 399 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.08/2.40 400 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.08/2.40 401 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(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_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 2.08/2.40 402 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 2.08/2.40 403 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 2.08/2.40 404 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 2.08/2.40 405 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 2.08/2.40 406 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 2.08/2.40 407 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 2.08/2.40 408 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 2.08/2.40 409 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 2.08/2.40 410 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 2.08/2.40 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(400,a,401,a)].
% 2.08/2.40 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B = D | A = C. [resolve(400,a,402,a)].
% 2.19/2.44 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(400,a,404,a)].
% 2.19/2.44 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(400,a,406,a)].
% 2.19/2.44 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(400,a,410,a)].
% 2.19/2.44 411 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.19/2.44 412 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.19/2.44 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(411,a,412,a)].
% 2.19/2.44 413 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.19/2.44 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(413,a,412,a)].
% 2.19/2.44 414 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.19/2.44 415 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.19/2.44 416 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.19/2.44 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(414,a,416,a)].
% 2.19/2.44 417 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.19/2.44 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(417,a,416,a)].
% 2.19/2.44 418 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.19/2.44 419 -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].
% 2.19/2.44 420 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 2.19/2.44 421 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.19/2.44 422 -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].
% 2.19/2.46 423 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.19/2.46 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(418,a,419,a)].
% 2.19/2.46 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(418,a,421,a)].
% 2.19/2.46 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(418,a,422,a)].
% 2.19/2.46 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(418,a,423,a)].
% 2.19/2.46 424 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.19/2.46 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(424,a,419,a)].
% 2.19/2.46 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(424,a,421,a)].
% 2.19/2.46 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(424,a,422,a)].
% 2.19/2.46 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(424,a,423,a)].
% 2.19/2.46 425 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.19/2.46 426 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),F)),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 2.19/2.46 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),E)),D)). [resolve(425,a,426,a)].
% 2.19/2.46 427 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.19/2.46 428 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 2.19/2.47 429 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 2.19/2.47 430 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 2.19/2.47 431 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 2.19/2.47 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C)). [resolve(427,a,428,a)].
% 2.19/2.47 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) = E. [resolve(427,a,429,a)].
% 2.19/2.47 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E). [resolve(427,a,430,a)].
% 2.19/2.47 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D). [resolve(427,a,431,a)].
% 2.19/2.47 432 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.19/2.47 433 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.19/2.47 434 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.28/2.51 435 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.28/2.51 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,435,a)].
% 2.28/2.51 436 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.28/2.51 437 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 2.28/2.51 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(436,a,437,a)].
% 2.28/2.51 438 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.28/2.51 439 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 2.28/2.51 440 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 2.28/2.51 441 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 2.28/2.51 442 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 2.28/2.51 443 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 2.28/2.51 444 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 2.28/2.51 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(438,a,440,a)].
% 2.28/2.51 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(438,a,442,a)].
% 2.28/2.51 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(438,a,444,a)].
% 2.28/2.51 445 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.28/2.51 446 -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].
% 2.28/2.51 447 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.28/2.51 448 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.28/2.51 449 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 2.28/2.51 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(448,a,449,a)].
% 2.96/3.26 450 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.96/3.26 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B)),D). [resolve(450,a,449,a)].
% 2.96/3.26 451 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.96/3.26 452 -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].
% 2.96/3.26 453 -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].
% 2.96/3.26 454 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.96/3.26 455 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.96/3.26 456 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.96/3.26 Derived: A = A. [resolve(455,b,456,a)].
% 2.96/3.26
% 2.96/3.26 ============================== end predicate elimination =============
% 2.96/3.26
% 2.96/3.26 Auto_denials: (non-Horn, no changes).
% 2.96/3.26
% 2.96/3.26 Term ordering decisions:
% 2.96/3.26 Function symbol KB weights: tc_nat=1. tc_Complex_Ocomplex=1. c_Suc=1. tc_bool=1. v_n=1. v_i=1. v_a=1. hAPP=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_Finite__Set_Osetsum=1. tc_fun=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Series_Osuminf=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Ominus__class_Ominus=1. c_Power_Opower__class_Opower=1. c_HOL_Oinverse__class_Odivide=1. c_HOL_Oone__class_Oone=1. c_FFT__Mirabelle_Oroot=1. c_HOL_OIf=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_FFT__Mirabelle_ODFT=1. c_FFT__Mirabelle_OIDFT=1. c_COMBC=1. c_COMBB=1. c_COMBS=1.
% 2.96/3.26
% 2.96/3.26 ============================== end of process initial clauses ========
% 2.96/3.26
% 2.96/3.26 ============================== CLAUSES FOR SEARCH ====================
% 2.96/3.26
% 2.96/3.26 ============================== end of clauses for search =============
% 2.96/3.26
% 2.96/3.26 ============================== SEARCH ================================
% 2.96/3.26
% 2.96/3.26 % Starting search at 1.17 seconds.
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=79.000, iters=3526
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=77.000, iters=3505
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=71.000, iters=3443
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=64.000, iters=3337
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=61.000, iters=3356
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=58.000, iters=3339
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=56.000, iters=3417
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=53.000, iters=3412
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=52.000, iters=3358
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=51.000, iters=3377
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=50.000, iters=3417
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=49.000, iters=3416
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=48.000, iters=3389
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=47.000, iters=3385
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=46.000, iters=3346
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=45.000, iters=3362
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=44.000, iters=3351
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=43.000, iters=3394
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=42.000, iters=3410
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=41.000, iters=3451
% 2.96/3.26
% 2.96/3.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 57 (0.00 of 1.73 sec).
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=40.000, iters=3375
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=39.000, iters=3394
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=38.000, iters=3413
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=36.000, iters=3372
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wt=34.000, iters=3335
% 2.96/3.26
% 2.96/3.26 Low Water (keep): wCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------