TSTP Solution File: ALG392-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG392-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:54:41 EDT 2022
% Result : Timeout 300.07s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG392-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 10:50:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.06/1.53 ============================== Prover9 ===============================
% 1.06/1.53 Prover9 (32) version 2009-11A, November 2009.
% 1.06/1.53 Process 3260 was started by sandbox2 on n018.cluster.edu,
% 1.06/1.53 Wed Jun 8 10:50:38 2022
% 1.06/1.53 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3106_n018.cluster.edu".
% 1.06/1.53 ============================== end of head ===========================
% 1.06/1.53
% 1.06/1.53 ============================== INPUT =================================
% 1.06/1.53
% 1.06/1.53 % Reading from file /tmp/Prover9_3106_n018.cluster.edu
% 1.06/1.53
% 1.06/1.53 set(prolog_style_variables).
% 1.06/1.53 set(auto2).
% 1.06/1.53 % set(auto2) -> set(auto).
% 1.06/1.53 % set(auto) -> set(auto_inference).
% 1.06/1.53 % set(auto) -> set(auto_setup).
% 1.06/1.53 % set(auto_setup) -> set(predicate_elim).
% 1.06/1.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.06/1.53 % set(auto) -> set(auto_limits).
% 1.06/1.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.06/1.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.06/1.53 % set(auto) -> set(auto_denials).
% 1.06/1.53 % set(auto) -> set(auto_process).
% 1.06/1.53 % set(auto2) -> assign(new_constants, 1).
% 1.06/1.53 % set(auto2) -> assign(fold_denial_max, 3).
% 1.06/1.53 % set(auto2) -> assign(max_weight, "200.000").
% 1.06/1.53 % set(auto2) -> assign(max_hours, 1).
% 1.06/1.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.06/1.53 % set(auto2) -> assign(max_seconds, 0).
% 1.06/1.53 % set(auto2) -> assign(max_minutes, 5).
% 1.06/1.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.06/1.53 % set(auto2) -> set(sort_initial_sos).
% 1.06/1.53 % set(auto2) -> assign(sos_limit, -1).
% 1.06/1.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.06/1.53 % set(auto2) -> assign(max_megs, 400).
% 1.06/1.53 % set(auto2) -> assign(stats, some).
% 1.06/1.53 % set(auto2) -> clear(echo_input).
% 1.06/1.53 % set(auto2) -> set(quiet).
% 1.06/1.53 % set(auto2) -> clear(print_initial_clauses).
% 1.06/1.53 % set(auto2) -> clear(print_given).
% 1.06/1.53 assign(lrs_ticks,-1).
% 1.06/1.53 assign(sos_limit,10000).
% 1.06/1.53 assign(order,kbo).
% 1.06/1.53 set(lex_order_vars).
% 1.06/1.53 clear(print_given).
% 1.06/1.53
% 1.06/1.53 % formulas(sos). % not echoed (1185 formulas)
% 1.06/1.53
% 1.06/1.53 ============================== end of input ==========================
% 1.06/1.53
% 1.06/1.53 % From the command line: assign(max_seconds, 300).
% 1.06/1.53
% 1.06/1.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.06/1.53
% 1.06/1.53 % Formulas that are not ordinary clauses:
% 1.06/1.53
% 1.06/1.53 ============================== end of process non-clausal formulas ===
% 1.06/1.53
% 1.06/1.53 ============================== PROCESS INITIAL CLAUSES ===============
% 1.06/1.53
% 1.06/1.53 ============================== PREDICATE ELIMINATION =================
% 1.06/1.53 1 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 1.06/1.53 2 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__less__le_2) # label(axiom). [assumption].
% 1.06/1.53 3 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 1.06/1.53 4 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__le__neq__trans_0) # label(axiom). [assumption].
% 1.06/1.53 5 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | B = C # label(cls_order__neq__le__trans_0) # label(axiom). [assumption].
% 1.06/1.53 6 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | C = B # label(cls_xt1_I12_J_0) # label(axiom). [assumption].
% 1.06/1.53 7 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | -c_lessequals(B,C,A) # label(cls_xt1_I11_J_0) # label(axiom). [assumption].
% 1.06/1.53 8 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom). [assumption].
% 1.06/1.53 9 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 1.06/1.53 10 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 1.06/1.53 11 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I10_J_0) # label(axiom). [assumption].
% 1.06/1.53 12 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 1.06/1.54 13 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__le__less_1) # label(axiom). [assumption].
% 1.06/1.54 14 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 1.06/1.54 15 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I8_J_0) # label(axiom). [assumption].
% 1.06/1.54 16 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I7_J_0) # label(axiom). [assumption].
% 1.06/1.54 17 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom). [assumption].
% 1.06/1.54 18 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom). [assumption].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | A = B | -c_lessequals(A,B,tc_nat). [resolve(1,a,2,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat) | B = A. [resolve(1,a,6,a)].
% 1.06/1.54 Derived: A = B | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(1,a,8,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(1,a,11,a)].
% 1.06/1.54 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,12,a)].
% 1.06/1.54 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,13,a)].
% 1.06/1.54 Derived: c_lessequals(A,A,tc_nat). [resolve(1,a,14,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(1,a,15,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(1,a,16,a)].
% 1.06/1.54 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(1,a,17,a)].
% 1.06/1.54 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,18,a)].
% 1.06/1.54 19 class_Orderings_Oorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Oorder) # label(axiom). [assumption].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | A = B | -c_lessequals(A,B,tc_Int_Oint). [resolve(19,a,2,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | B = A. [resolve(19,a,6,a)].
% 1.06/1.54 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(19,a,8,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint). [resolve(19,a,11,a)].
% 1.06/1.54 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(19,a,12,a)].
% 1.06/1.54 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(19,a,13,a)].
% 1.06/1.54 Derived: c_lessequals(A,A,tc_Int_Oint). [resolve(19,a,14,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(19,a,15,a)].
% 1.06/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint). [resolve(19,a,16,a)].
% 1.06/1.54 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(19,a,17,a)].
% 1.06/1.54 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(19,a,18,a)].
% 1.06/1.54 20 class_Orderings_Oorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Oorder) # label(axiom). [assumption].
% 1.06/1.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | B = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(20,a,2,a)].
% 1.06/1.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | C = B. [resolve(20,a,6,a)].
% 1.06/1.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(20,a,8,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)). [resolve(20,a,11,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(20,a,12,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(20,a,13,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,tc_Polynomial_Opoly(A)). [resolve(20,a,14,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(20,a,15,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)). [resolve(20,a,16,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(20,a,17,a)].
% 1.06/1.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(20,a,18,a)].
% 1.06/1.57 21 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.06/1.57 22 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.06/1.57 23 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.06/1.57 24 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.06/1.57 25 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.06/1.57 26 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.06/1.57 27 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.06/1.57 28 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.06/1.57 29 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.06/1.57 30 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.06/1.57 31 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.06/1.57 32 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.06/1.57 33 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.06/1.57 34 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.06/1.57 35 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.06/1.57 36 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 1.06/1.63 37 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 1.06/1.63 38 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.06/1.63 39 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.06/1.63 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(21,a,24,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(21,a,28,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(21,a,31,a)].
% 1.06/1.63 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(21,a,38,a)].
% 1.06/1.63 40 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 1.06/1.63 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(40,a,24,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(40,a,28,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(40,a,31,a)].
% 1.06/1.63 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(40,a,38,a)].
% 1.06/1.63 41 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(41,a,24,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(41,a,28,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(41,a,31,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(41,a,38,a)].
% 1.06/1.63 42 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.06/1.63 43 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A),A) # label(cls_of__nat__fact__gt__zero_0) # label(axiom). [assumption].
% 1.06/1.63 44 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.06/1.63 45 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.06/1.63 46 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.06/1.63 47 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A),A) # label(cls_of__nat__fact__ge__zero_0) # label(axiom). [assumption].
% 1.06/1.63 48 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.06/1.63 49 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.06/1.63 50 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.06/1.63 51 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.06/1.63 52 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.06/1.63 53 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.06/1.63 54 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.06/1.63 55 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.06/1.63 56 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.06/1.63 57 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.06/1.63 58 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.06/1.63 59 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.06/1.63 60 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.06/1.63 61 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.06/1.63 62 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.06/1.63 63 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.06/1.63 64 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.06/1.63 65 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.06/1.63 66 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.06/1.63 67 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.06/1.63 68 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat),tc_nat). [resolve(42,a,43,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(42,a,44,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(42,a,45,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(42,a,48,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(42,a,49,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(42,a,50,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(42,a,51,a)].
% 1.06/1.63 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(42,a,52,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(42,a,53,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(42,a,54,a)].
% 1.06/1.63 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(42,a,55,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(42,a,56,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(42,a,57,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(42,a,58,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(42,a,59,a)].
% 1.06/1.63 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(42,a,60,a)].
% 1.06/1.63 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat),tc_nat). [resolve(42,a,61,a)].
% 1.06/1.63 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(42,a,62,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(42,a,63,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(42,a,64,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(42,a,65,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(42,a,66,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(42,a,67,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(42,a,68,a)].
% 1.06/1.63 69 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint),tc_Int_Oint). [resolve(69,a,43,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,44,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(69,a,45,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,48,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(69,a,49,a)].
% 1.06/1.63 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,50,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,51,a)].
% 1.06/1.63 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,52,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,53,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,54,a)].
% 1.06/1.63 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(69,a,55,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,56,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,57,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(69,a,58,a)].
% 1.06/1.63 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,59,a)].
% 1.06/1.63 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(69,a,60,a)].
% 1.06/1.63 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Int_Oint),tc_Int_Oint). [resolve(69,a,61,a)].
% 1.06/1.63 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Int_Oint) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,62,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(69,a,63,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,64,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(69,a,65,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,66,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,67,a)].
% 1.06/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(69,a,68,a)].
% 1.06/1.63 70 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,43,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,44,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,45,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,48,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(70,a,49,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,50,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,51,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,52,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,53,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,54,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(70,a,55,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,56,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,57,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,58,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,59,a)].
% 1.06/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = D. [resolve(70,a,60,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,c_Suc(D),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,61,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)) != c_Power_Opower__class_Opower(D,c_Suc(C),tc_Polynomial_Opoly(A)) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,62,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,63,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,64,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(70,a,65,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,66,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,67,a)].
% 1.42/1.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(70,a,68,a)].
% 1.42/1.66 71 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 1.42/1.66 72 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__neg_0) # label(axiom). [assumption].
% 1.42/1.66 73 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__neg__div_0) # label(axiom). [assumption].
% 1.42/1.66 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(71,a,72,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(71,a,73,a)].
% 1.45/1.69 74 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.45/1.69 75 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__dvd__div_0) # label(axiom). [assumption].
% 1.45/1.69 76 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__dvd__div_1) # label(axiom). [assumption].
% 1.45/1.69 77 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__mult__div__if__dvd_0) # label(axiom). [assumption].
% 1.45/1.69 78 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__add_0) # label(axiom). [assumption].
% 1.45/1.69 79 -class_Divides_Osemiring__div(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__power_0) # label(axiom). [assumption].
% 1.45/1.69 80 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult_0) # label(axiom). [assumption].
% 1.45/1.69 81 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult__div__cancel_0) # label(axiom). [assumption].
% 1.45/1.69 82 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult__self_0) # label(axiom). [assumption].
% 1.45/1.69 83 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 1.45/1.69 84 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 1.45/1.69 85 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 1.45/1.69 86 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 1.45/1.69 87 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 1.45/1.69 88 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 1.45/1.69 89 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 1.45/1.69 90 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 1.45/1.69 91 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 1.45/1.69 92 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,A),A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 1.45/1.69 93 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A) = c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 1.45/1.69 94 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,A),c_HOL_Oone__class_Oone(A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 1.45/1.69 95 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,C,A),c_HOL_Oone__class_Oone(A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 1.45/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(74,a,75,a)].
% 1.45/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(74,a,76,a)].
% 1.45/1.69 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,D,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(74,a,77,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(74,a,78,a)].
% 1.45/1.69 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(74,a,79,a)].
% 1.45/1.69 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(74,a,80,a)].
% 1.45/1.69 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(74,a,81,a)].
% 1.45/1.69 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(74,a,82,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,83,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,84,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,85,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,86,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,87,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,88,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,89,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,90,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(74,a,91,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_nat),tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,92,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,93,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,94,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,95,a)].
% 1.45/1.69 96 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.45/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(96,a,75,a)].
% 1.45/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(96,a,76,a)].
% 1.45/1.69 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,D,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(96,a,77,a)].
% 1.45/1.69 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(96,a,78,a)].
% 1.45/1.69 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(96,a,79,a)].
% 1.45/1.72 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(96,a,80,a)].
% 1.45/1.72 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(96,a,81,a)].
% 1.45/1.72 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(96,a,82,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,83,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,84,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,85,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,86,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,87,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,88,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,89,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,90,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(96,a,91,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,92,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,93,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,94,a)].
% 1.45/1.72 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(96,a,95,a)].
% 1.45/1.72 97 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.45/1.72 98 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.45/1.72 99 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.45/1.72 100 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.45/1.72 101 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.45/1.72 102 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.45/1.72 103 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.45/1.72 104 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.45/1.72 105 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.45/1.72 106 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 1.45/1.72 107 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.45/1.72 108 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.45/1.72 109 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.45/1.72 110 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.45/1.72 111 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.45/1.72 112 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.45/1.72 113 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.45/1.72 114 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.45/1.72 115 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.45/1.72 116 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.45/1.72 117 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 1.45/1.72 118 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.45/1.72 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,98,a)].
% 1.45/1.72 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(97,a,99,a)].
% 1.45/1.72 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(97,a,100,a)].
% 1.45/1.72 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(97,a,101,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(97,a,102,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,103,a)].
% 1.45/1.72 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,104,a)].
% 1.45/1.72 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(97,a,105,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(97,a,106,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(97,a,107,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),A,tc_Int_Oint). [resolve(97,a,108,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,110,a)].
% 1.45/1.72 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),A,tc_Int_Oint). [resolve(97,a,112,a)].
% 1.45/1.72 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,114,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,116,a)].
% 1.45/1.72 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(97,a,117,a)].
% 1.45/1.72 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(97,a,118,a)].
% 1.45/1.72 119 class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,98,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,99,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(119,a,100,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,101,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(119,a,102,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,103,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,104,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(119,a,105,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(119,a,106,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,107,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(119,a,108,a)].
% 1.45/1.72 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,110,a)].
% 1.52/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(119,a,112,a)].
% 1.52/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,114,a)].
% 1.52/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,116,a)].
% 1.52/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,117,a)].
% 1.52/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(119,a,118,a)].
% 1.52/1.77 120 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ogroup__add(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.52/1.77 121 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.52/1.77 122 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.52/1.77 123 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.52/1.77 124 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.52/1.77 125 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.52/1.77 126 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.52/1.77 127 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.52/1.77 128 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.52/1.77 129 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.52/1.77 130 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_minus__add_0) # label(axiom). [assumption].
% 1.52/1.77 131 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 1.52/1.77 132 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 1.52/1.77 133 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 1.52/1.78 134 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 1.52/1.78 135 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 1.52/1.78 136 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 1.52/1.78 137 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C. [resolve(120,b,121,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B. [resolve(120,b,122,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A). [resolve(120,b,123,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A). [resolve(120,b,126,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A). [resolve(120,b,127,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A). [resolve(120,b,128,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B. [resolve(120,b,129,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A). [resolve(120,b,130,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A) = C. [resolve(120,b,131,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = C. [resolve(120,b,132,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A). [resolve(120,b,133,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ozero__class_Ozero(A). [resolve(120,b,134,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C. [resolve(120,b,136,a)].
% 1.52/1.78 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A). [resolve(120,b,137,a)].
% 1.52/1.78 138 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.52/1.78 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint) | A = B. [resolve(138,a,121,a)].
% 1.52/1.78 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = A. [resolve(138,a,122,a)].
% 1.52/1.78 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(138,a,123,a)].
% 1.52/1.78 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(138,a,126,a)].
% 1.52/1.78 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(138,a,127,a)].
% 1.52/1.78 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(138,a,128,a)].
% 1.52/1.78 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) | c_HOL_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(138,a,129,a)].
% 1.52/1.78 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(138,a,130,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) = B. [resolve(138,a,131,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = B. [resolve(138,a,132,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(138,a,133,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(138,a,134,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) = B. [resolve(138,a,136,a)].
% 1.52/1.78 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint). [resolve(138,a,137,a)].
% 1.52/1.78 139 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(139,a,121,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(139,a,122,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(139,a,123,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(139,a,126,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(139,a,127,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(139,a,128,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(139,a,129,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(139,a,130,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(139,a,131,a)].
% 1.52/1.78 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(139,a,132,a)].
% 1.58/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(139,a,133,a)].
% 1.58/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(139,a,134,a)].
% 1.58/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = C. [resolve(139,a,136,a)].
% 1.58/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)). [resolve(139,a,137,a)].
% 1.58/1.82 140 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.58/1.82 141 -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].
% 1.58/1.82 142 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__fact__not__zero_0) # label(axiom). [assumption].
% 1.58/1.82 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(140,a,141,a)].
% 1.58/1.82 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(140,a,142,a)].
% 1.58/1.82 143 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.58/1.82 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B. [resolve(143,a,141,a)].
% 1.58/1.82 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(143,a,142,a)].
% 1.58/1.82 144 class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.58/1.82 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)) != c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(144,a,141,a)].
% 1.58/1.82 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(144,a,142,a)].
% 1.58/1.82 145 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 1.58/1.82 146 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__trans_0) # label(axiom). [assumption].
% 1.58/1.82 147 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 1.58/1.82 148 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 1.58/1.82 149 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_less__le__not__le_2) # label(axiom). [assumption].
% 1.58/1.82 150 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__less__imp__le_0) # label(axiom). [assumption].
% 1.58/1.82 151 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 1.58/1.82 152 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 1.58/1.84 153 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__le__trans_0) # label(axiom). [assumption].
% 1.58/1.84 154 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 1.58/1.84 155 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom). [assumption].
% 1.58/1.84 156 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom). [assumption].
% 1.58/1.84 157 class_Orderings_Opreorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Opreorder) # label(axiom). [assumption].
% 1.58/1.84 158 class_Orderings_Opreorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom). [assumption].
% 1.58/1.84 159 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.58/1.84 160 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A) # label(cls_of__nat__power_0) # label(axiom). [assumption].
% 1.58/1.84 161 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),A) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 1.58/1.84 162 -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].
% 1.58/1.84 163 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.58/1.84 164 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.58/1.84 165 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A). [resolve(159,b,160,a)].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),A) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A). [resolve(159,b,161,a)].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A). [resolve(159,b,162,a)].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A). [resolve(159,b,163,a)].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A). [resolve(159,b,164,a)].
% 1.58/1.84 Derived: -class_Ring__and__Field_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A). [resolve(159,b,165,a)].
% 1.58/1.84 166 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),B,tc_nat). [resolve(166,a,160,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(166,a,161,a)].
% 1.58/1.85 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(166,a,162,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(166,a,163,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(166,a,164,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(166,a,165,a)].
% 1.58/1.85 167 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_Int_Oint) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(167,a,160,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(167,a,161,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(167,a,162,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(167,a,163,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(167,a,164,a)].
% 1.58/1.85 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(167,a,165,a)].
% 1.58/1.85 168 class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.58/1.85 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),tc_Polynomial_Opoly(A)) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(168,a,160,a)].
% 1.58/1.85 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(168,a,161,a)].
% 1.58/1.85 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(168,a,162,a)].
% 1.58/1.85 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(168,a,163,a)].
% 1.58/1.85 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(168,a,164,a)].
% 1.63/1.87 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(168,a,165,a)].
% 1.63/1.87 169 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.63/1.87 170 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.63/1.87 171 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.63/1.87 172 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.63/1.87 173 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.63/1.87 174 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__eq__neg_1) # label(axiom). [assumption].
% 1.63/1.87 175 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_le__eq__neg_0) # label(axiom). [assumption].
% 1.63/1.87 176 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.63/1.87 177 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.63/1.87 178 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.63/1.87 179 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.63/1.87 180 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.63/1.87 181 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.63/1.87 182 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.63/1.87 183 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.63/1.89 184 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.63/1.89 185 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.63/1.89 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(169,a,170,a)].
% 1.63/1.89 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,171,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint). [resolve(169,a,172,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(169,a,173,a)].
% 1.63/1.89 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,174,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(169,a,175,a)].
% 1.63/1.89 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,176,a)].
% 1.63/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,177,a)].
% 1.63/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(169,a,178,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(169,a,180,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(169,a,181,a)].
% 1.63/1.89 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,182,a)].
% 1.63/1.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(169,a,183,a)].
% 1.63/1.89 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(169,a,184,a)].
% 1.63/1.89 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(169,a,185,a)].
% 1.63/1.89 186 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.63/1.89 187 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 1.63/1.89 188 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 1.71/1.95 189 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 1.71/1.95 190 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 1.71/1.95 191 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 1.71/1.95 192 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 1.71/1.95 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != A | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(186,a,192,a)].
% 1.71/1.95 193 class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(193,a,187,a)].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(193,a,188,a)].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(193,a,189,a)].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(193,a,190,a)].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(193,a,191,a)].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != B | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(193,a,192,a)].
% 1.71/1.95 194 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 1.71/1.95 195 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 1.71/1.95 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(194,a,195,a)].
% 1.71/1.95 196 class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom). [assumption].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)) != c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(196,a,195,a)].
% 1.71/1.95 197 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.71/1.95 198 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.71/1.95 199 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.71/1.95 200 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.71/1.95 201 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.71/1.95 202 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(197,a,198,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(197,a,199,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(197,a,200,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(197,a,201,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(197,a,202,a)].
% 1.71/1.95 203 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(203,a,198,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(203,a,199,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(203,a,200,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(203,a,201,a)].
% 1.71/1.95 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(203,a,202,a)].
% 1.71/1.95 204 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.71/1.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(204,a,198,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(204,a,199,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(204,a,200,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(204,a,201,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(204,a,202,a)].
% 1.75/2.00 205 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.75/2.00 206 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.75/2.00 207 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.75/2.00 208 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.75/2.00 209 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.75/2.00 210 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.75/2.00 211 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.75/2.00 212 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.75/2.00 213 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.75/2.00 214 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.75/2.00 215 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.75/2.00 216 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.75/2.00 217 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.75/2.00 218 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.75/2.00 219 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.75/2.00 220 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.75/2.00 221 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(205,a,206,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(205,a,207,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(205,a,208,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(205,a,209,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(205,a,210,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). [resolve(205,a,211,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(205,a,212,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(205,a,213,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(205,a,214,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(205,a,216,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(205,a,217,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(205,a,218,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(205,a,219,a)].
% 1.75/2.00 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(205,a,220,a)].
% 1.75/2.00 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(205,a,221,a)].
% 1.75/2.00 222 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(222,a,206,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(222,a,207,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(222,a,208,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(222,a,209,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(222,a,210,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,211,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,212,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(222,a,213,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(222,a,214,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(222,a,216,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,217,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,218,a)].
% 1.75/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(222,a,219,a)].
% 1.75/2.00 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,220,a)].
% 1.75/2.00 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,221,a)].
% 1.75/2.00 223 class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(223,a,206,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(223,a,207,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(223,a,208,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(223,a,209,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(223,a,210,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,211,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,212,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,213,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(223,a,214,a)].
% 1.75/2.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(223,a,216,a)].
% 1.75/2.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,217,a)].
% 1.75/2.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,218,a)].
% 1.75/2.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(223,a,219,a)].
% 1.75/2.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,220,a)].
% 1.75/2.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(223,a,221,a)].
% 1.75/2.02 224 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.75/2.02 225 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.75/2.02 226 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.75/2.02 227 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.75/2.02 228 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.75/2.02 229 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.75/2.02 230 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.75/2.02 231 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.75/2.02 232 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.75/2.02 233 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.75/2.02 234 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.75/2.02 235 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.75/2.02 236 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.75/2.02 237 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.75/2.02 238 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.75/2.02 239 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.75/2.02 240 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.75/2.02 241 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.75/2.02 242 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.75/2.02 243 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.75/2.02 244 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.75/2.02 245 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.75/2.02 246 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.75/2.02 247 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.75/2.02 248 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.75/2.02 249 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.75/2.02 250 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.75/2.02 251 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.75/2.02 252 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.75/2.02 253 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.75/2.02 254 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.75/2.02 255 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.75/2.02 256 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.75/2.02 257 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.75/2.02 258 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.75/2.02 259 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.75/2.02 260 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.75/2.02 261 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.75/2.02 262 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.75/2.02 263 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.75/2.02 264 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.75/2.02 265 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.75/2.02 266 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.75/2.02 267 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.75/2.02 268 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.75/2.02 269 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.75/2.03 270 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 1.75/2.03 271 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 1.75/2.03 272 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,225,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,226,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(224,a,227,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,A,tc_Int_Oint). [resolve(224,a,232,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,235,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,237,a)].
% 1.75/2.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,238,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,240,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(224,a,241,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,242,a)].
% 1.75/2.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,244,a)].
% 1.75/2.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,245,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(224,a,247,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,249,a)].
% 1.75/2.03 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,250,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,251,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,252,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,253,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,254,a)].
% 1.75/2.03 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,255,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(224,a,256,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,257,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,258,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,259,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,260,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(224,a,261,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(224,a,262,a)].
% 1.75/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(224,a,263,a)].
% 1.75/2.03 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,264,a)].
% 1.75/2.03 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,265,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(224,a,266,a)].
% 1.75/2.03 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,267,a)].
% 1.75/2.03 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(224,a,268,a)].
% 1.75/2.03 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(224,a,269,a)].
% 1.75/2.03 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(224,a,270,a)].
% 1.75/2.03 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(224,a,271,a)].
% 1.75/2.03 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(224,a,272,a)].
% 1.75/2.03 273 class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,225,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,226,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(273,a,227,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,B,tc_Polynomial_Opoly(A)). [resolve(273,a,232,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,235,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,237,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,238,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,240,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(273,a,241,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,242,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,244,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,245,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(273,a,247,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,249,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,250,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,251,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,252,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,253,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,254,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,255,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(273,a,256,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,257,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,258,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,259,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,260,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,261,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(273,a,262,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(273,a,263,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,264,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,265,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,266,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,267,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,268,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(273,a,269,a)].
% 1.75/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(273,a,270,a)].
% 1.82/2.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(273,a,271,a)].
% 1.82/2.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(273,a,272,a)].
% 1.82/2.10 274 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.82/2.10 275 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.82/2.10 276 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.82/2.10 277 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.82/2.10 278 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.82/2.10 279 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.82/2.10 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(278,a,279,a)].
% 1.82/2.10 280 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.82/2.10 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(280,a,279,a)].
% 1.82/2.10 281 class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.82/2.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(281,a,279,a)].
% 1.82/2.10 282 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.82/2.10 283 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.82/2.10 284 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.88/2.13 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(282,a,284,a)].
% 1.88/2.13 285 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.88/2.13 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(285,a,284,a)].
% 1.88/2.13 286 class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.88/2.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(286,a,284,a)].
% 1.88/2.13 287 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.88/2.13 288 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 1.88/2.13 289 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 1.88/2.13 290 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 1.88/2.13 291 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 1.88/2.13 292 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.88/2.13 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(287,a,288,a)].
% 1.88/2.13 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,A,tc_Int_Oint). [resolve(287,a,289,a)].
% 1.88/2.13 293 class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.88/2.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(293,a,288,a)].
% 1.88/2.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,B,tc_Polynomial_Opoly(A)). [resolve(293,a,289,a)].
% 1.94/2.18 294 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.94/2.18 295 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.94/2.18 296 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.94/2.18 297 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.94/2.18 298 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.94/2.18 299 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.94/2.18 300 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.94/2.18 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(294,a,295,a)].
% 1.94/2.18 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(294,a,296,a)].
% 1.94/2.18 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(294,a,297,a)].
% 1.94/2.18 301 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.94/2.18 302 class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.94/2.18 303 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.94/2.18 304 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 1.94/2.18 305 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(303,a,304,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(303,a,305,a)].
% 1.94/2.22 306 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(306,a,304,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(306,a,305,a)].
% 1.94/2.22 307 class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.94/2.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(307,a,304,a)].
% 1.94/2.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(307,a,305,a)].
% 1.94/2.22 308 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.94/2.22 309 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.94/2.22 310 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.94/2.22 311 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.94/2.22 312 class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.94/2.22 313 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.94/2.23 314 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.94/2.23 315 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.94/2.23 316 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.94/2.23 317 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.94/2.23 318 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.94/2.23 319 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.94/2.23 320 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.94/2.23 321 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.94/2.23 322 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.94/2.23 323 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.94/2.23 324 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.94/2.23 325 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(313,a,314,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(313,a,315,a)].
% 1.94/2.23 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(313,a,317,a)].
% 1.94/2.23 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(313,a,319,a)].
% 1.94/2.23 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(313,a,320,a)].
% 1.94/2.23 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(313,a,321,a)].
% 1.94/2.23 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(313,a,322,a)].
% 1.94/2.23 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(313,a,323,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(313,a,324,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(313,a,325,a)].
% 1.94/2.23 326 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(326,a,314,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(326,a,315,a)].
% 1.94/2.23 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(326,a,317,a)].
% 1.94/2.23 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(326,a,319,a)].
% 1.94/2.23 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(326,a,320,a)].
% 1.94/2.23 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(326,a,321,a)].
% 1.94/2.23 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(326,a,322,a)].
% 1.94/2.23 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(326,a,323,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(326,a,324,a)].
% 1.94/2.23 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(326,a,325,a)].
% 1.94/2.23 327 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.94/2.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(327,a,314,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(327,a,315,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(327,a,317,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(327,a,319,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(327,a,320,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(327,a,321,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(327,a,322,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(327,a,323,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(327,a,324,a)].
% 1.94/2.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(327,a,325,a)].
% 1.94/2.25 328 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.94/2.25 329 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.94/2.25 330 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.94/2.25 331 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.94/2.25 332 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.94/2.25 333 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.94/2.25 334 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.94/2.25 335 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.94/2.25 336 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.94/2.25 337 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.94/2.25 338 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.94/2.25 339 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(328,a,329,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(328,a,330,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(328,a,331,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(328,a,332,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(328,a,333,a)].
% 1.94/2.25 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(328,a,334,a)].
% 1.94/2.25 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(328,a,335,a)].
% 1.94/2.25 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(328,a,336,a)].
% 1.94/2.25 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(328,a,337,a)].
% 1.94/2.25 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(328,a,339,a)].
% 1.94/2.25 340 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(340,a,329,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(340,a,330,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(340,a,331,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(340,a,332,a)].
% 1.94/2.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(340,a,333,a)].
% 1.94/2.25 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(340,a,335,a)].
% 1.94/2.25 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(340,a,336,a)].
% 1.94/2.25 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(340,a,337,a)].
% 1.94/2.25 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(340,a,339,a)].
% 1.94/2.25 341 class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(341,a,329,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(341,a,330,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(341,a,331,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(341,a,332,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(341,a,333,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(341,a,334,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(341,a,335,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(341,a,336,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(341,a,337,a)].
% 2.03/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(341,a,339,a)].
% 2.03/2.28 342 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.03/2.28 343 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 2.03/2.28 344 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 2.03/2.28 345 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 2.03/2.28 346 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 2.03/2.28 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A). [resolve(342,b,343,a)].
% 2.03/2.28 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A). [resolve(342,b,344,a)].
% 2.03/2.28 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A). [resolve(342,b,345,a)].
% 2.03/2.28 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A). [resolve(342,b,346,a)].
% 2.03/2.28 347 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.03/2.28 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(347,a,343,a)].
% 2.03/2.28 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint). [resolve(347,a,344,a)].
% 2.03/2.28 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(347,a,345,a)].
% 2.03/2.28 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(347,a,346,a)].
% 2.03/2.28 348 class_Ring__and__Field_Oring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.03/2.28 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(348,a,343,a)].
% 2.03/2.28 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)). [resolve(348,a,344,a)].
% 2.03/2.28 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(348,a,345,a)].
% 2.11/2.38 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(348,a,346,a)].
% 2.11/2.38 349 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Odvd(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.11/2.38 350 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvdI_0) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A). [resolve(349,b,350,a)].
% 2.11/2.38 351 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.11/2.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(351,a,350,a)].
% 2.11/2.38 352 class_Ring__and__Field_Odvd(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.11/2.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(352,a,350,a)].
% 2.11/2.38 353 class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(353,a,350,a)].
% 2.11/2.38 354 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.11/2.38 355 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.11/2.38 356 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.11/2.38 357 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.11/2.38 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(354,a,355,a)].
% 2.11/2.38 358 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.11/2.38 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(358,a,355,a)].
% 2.11/2.38 359 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(359,a,355,a)].
% 2.11/2.38 360 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.11/2.38 361 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 2.11/2.38 362 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 2.11/2.38 363 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A),E,A) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A). [resolve(360,b,361,a)].
% 2.11/2.38 Derived: -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A). [resolve(360,b,362,a)].
% 2.11/2.38 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A),E,A). [resolve(360,b,363,a)].
% 2.11/2.38 364 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Int_Onumber(tc_nat) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),B,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(364,a,361,a)].
% 2.11/2.38 Derived: -class_Int_Onumber(tc_nat) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(364,a,362,a)].
% 2.11/2.38 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat),D,tc_nat). [resolve(364,a,363,a)].
% 2.11/2.38 365 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.11/2.38 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(365,a,361,a)].
% 2.11/2.38 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(365,a,362,a)].
% 2.17/2.41 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint). [resolve(365,a,363,a)].
% 2.17/2.41 366 class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(366,a,361,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(366,a,362,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(366,a,363,a)].
% 2.17/2.41 367 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ozero__neq__one(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.17/2.41 368 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 2.17/2.41 369 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 2.17/2.41 370 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 2.17/2.41 371 -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].
% 2.17/2.41 372 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 2.17/2.41 373 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.17/2.41 374 -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].
% 2.17/2.41 375 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A). [resolve(367,b,368,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A). [resolve(367,b,369,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(367,b,370,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A). [resolve(367,b,371,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(367,b,372,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A). [resolve(367,b,373,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A). [resolve(367,b,374,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Oidom(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A). [resolve(367,b,375,a)].
% 2.17/2.41 376 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,368,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,369,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,370,a)].
% 2.17/2.41 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(376,a,371,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,372,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,373,a)].
% 2.17/2.41 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,374,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(376,a,375,a)].
% 2.17/2.41 377 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,368,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,369,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(377,a,370,a)].
% 2.17/2.41 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(377,a,371,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(377,a,372,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,373,a)].
% 2.17/2.41 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,374,a)].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,375,a)].
% 2.17/2.41 378 class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.17/2.41 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(378,a,368,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(378,a,369,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(378,a,370,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(378,a,371,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(378,a,372,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(378,a,373,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(378,a,374,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(378,a,375,a)].
% 2.17/2.44 379 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.17/2.44 380 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.17/2.44 381 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left__number__of_1) # label(axiom). [assumption].
% 2.17/2.44 382 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom). [assumption].
% 2.17/2.44 383 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 2.17/2.44 384 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 2.17/2.44 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A). [resolve(379,b,380,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(379,b,381,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Oone__class_Oone(A). [resolve(379,b,382,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A). [resolve(379,b,383,a)].
% 2.17/2.44 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(379,b,384,a)].
% 2.17/2.44 385 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.17/2.44 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(385,a,380,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(385,a,381,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(385,a,382,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(385,a,383,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(385,a,384,a)].
% 2.17/2.44 386 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.17/2.44 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(A),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(386,a,380,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(386,a,381,a)].
% 2.17/2.44 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(386,a,382,a)].
% 2.23/2.46 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(386,a,383,a)].
% 2.23/2.46 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(386,a,384,a)].
% 2.23/2.46 387 class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.23/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Suc(B),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(387,a,380,a)].
% 2.23/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(387,a,381,a)].
% 2.23/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(387,a,382,a)].
% 2.23/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(387,a,383,a)].
% 2.23/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(387,a,384,a)].
% 2.23/2.46 388 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.23/2.46 389 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 2.23/2.46 390 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A) # label(cls_power__mult_0) # label(axiom). [assumption].
% 2.23/2.46 391 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 2.23/2.46 392 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 2.23/2.46 393 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 2.23/2.46 394 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 2.23/2.46 395 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 2.23/2.46 396 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) # label(cls_power__add_0) # label(axiom). [assumption].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A). [resolve(388,b,389,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A). [resolve(388,b,390,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). [resolve(388,b,391,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B. [resolve(388,b,392,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A). [resolve(388,b,393,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B. [resolve(388,b,394,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B. [resolve(388,b,395,a)].
% 2.23/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A). [resolve(388,b,396,a)].
% 2.23/2.47 397 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_nat),A,tc_nat). [resolve(397,a,389,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat). [resolve(397,a,390,a)].
% 2.23/2.47 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_nat),A,tc_nat) = c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat). [resolve(397,a,391,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(397,a,392,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(397,a,393,a)].
% 2.23/2.47 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(397,a,394,a)].
% 2.23/2.47 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = A. [resolve(397,a,395,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat). [resolve(397,a,396,a)].
% 2.23/2.47 398 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),A,tc_Int_Oint). [resolve(398,a,389,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_Int_Oint) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(398,a,390,a)].
% 2.23/2.47 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(398,a,391,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = A. [resolve(398,a,392,a)].
% 2.23/2.47 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(398,a,393,a)].
% 2.23/2.47 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(398,a,394,a)].
% 2.23/2.50 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(398,a,395,a)].
% 2.23/2.50 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(398,a,396,a)].
% 2.23/2.50 399 class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(399,a,389,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_Polynomial_Opoly(A)) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(399,a,390,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(399,a,391,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),tc_Polynomial_Opoly(A)) = B. [resolve(399,a,392,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(399,a,393,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(399,a,394,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(399,a,395,a)].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(399,a,396,a)].
% 2.23/2.50 400 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.23/2.50 401 -class_Ring__and__Field_Oring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),C,A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__minus_0) # label(axiom). [assumption].
% 2.23/2.50 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),C,A),c_Power_Opower__class_Opower(B,C,A),A). [resolve(400,b,401,a)].
% 2.23/2.50 402 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.23/2.50 Derived: c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(402,a,401,a)].
% 2.23/2.50 403 class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.23/2.50 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(403,a,401,a)].
% 2.23/2.55 404 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.23/2.55 405 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.23/2.55 406 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.23/2.55 407 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != 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].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A). [resolve(404,b,405,a)].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A). [resolve(404,b,406,a)].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A). [resolve(404,b,407,a)].
% 2.23/2.55 408 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.23/2.55 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(408,a,405,a)].
% 2.23/2.55 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(408,a,406,a)].
% 2.23/2.55 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(408,a,407,a)].
% 2.23/2.55 409 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(409,a,405,a)].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(409,a,406,a)].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(409,a,407,a)].
% 2.23/2.55 410 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.23/2.55 411 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.23/2.55 412 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.23/2.55 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D. [resolve(410,b,411,a)].
% 2.36/2.61 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D. [resolve(410,b,412,a)].
% 2.36/2.61 413 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(413,a,411,a)].
% 2.36/2.61 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(413,a,412,a)].
% 2.36/2.61 414 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(414,a,411,a)].
% 2.36/2.61 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(414,a,412,a)].
% 2.36/2.61 415 class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)) | B = D. [resolve(415,a,411,a)].
% 2.36/2.61 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(415,a,412,a)].
% 2.36/2.61 416 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 417 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.36/2.61 418 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 419 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 420 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.36/2.61 421 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.36/2.61 422 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.36/2.61 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). [resolve(421,b,422,a)].
% 2.36/2.61 423 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.36/2.61 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(423,a,422,a)].
% 2.36/2.61 424 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.36/2.61 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(424,a,422,a)].
% 2.36/2.61 425 class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(425,a,422,a)].
% 2.41/2.66 426 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.41/2.66 427 -class_OrderedGroup_Oab__semigroup__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A). [resolve(426,b,427,a)].
% 2.41/2.66 428 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.41/2.66 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(428,a,427,a)].
% 2.41/2.66 429 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.41/2.66 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(429,a,427,a)].
% 2.41/2.66 430 class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(430,a,427,a)].
% 2.41/2.66 431 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.41/2.66 432 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 2.41/2.66 433 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A). [resolve(431,b,432,a)].
% 2.41/2.66 434 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.41/2.66 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(434,a,432,a)].
% 2.41/2.66 435 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.41/2.66 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(435,a,432,a)].
% 2.41/2.66 436 class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.48/2.77 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(436,a,432,a)].
% 2.48/2.77 437 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.48/2.77 438 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 2.48/2.77 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A). [resolve(437,b,438,a)].
% 2.48/2.77 439 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.48/2.77 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(439,a,438,a)].
% 2.48/2.77 440 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.48/2.77 Derived: -class_Ring__and__Field_Oidom(A) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(440,a,438,a)].
% 2.48/2.77 441 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.48/2.77 442 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.48/2.77 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). [resolve(441,b,442,a)].
% 2.48/2.77 443 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.48/2.77 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(443,a,442,a)].
% 2.48/2.77 444 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.48/2.77 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(444,a,442,a)].
% 2.48/2.77 445 class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.48/2.77 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(445,a,442,a)].
% 2.48/2.77 446 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__add(A) # label(clsrel_Ring__and__Field_Oidom_OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.48/2.77 447 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.48/2.77 448 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 4.88/5.13 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B. [resolve(446,b,447,a)].
% 4.88/5.13 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B. [resolve(446,b,448,a)].
% 4.88/5.13 449 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.88/5.13 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(449,a,447,a)].
% 4.88/5.13 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(449,a,448,a)].
% 4.88/5.13 450 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.88/5.13 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(450,a,447,a)].
% 4.88/5.13 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(450,a,448,a)].
% 4.88/5.13 451 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.88/5.13 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(451,a,447,a)].
% 4.88/5.13 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(451,a,448,a)].
% 4.88/5.13
% 4.88/5.13 ============================== end predicate elimination =============
% 4.88/5.13
% 4.88/5.13 Auto_denials: (non-Horn, no changes).
% 4.88/5.13
% 4.88/5.13 Term ordering decisions:
% 4.88/5.13 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. t_a=1. c_HOL_Ouminus__class_Ouminus=1. c_Int_Onumber__class_Onumber__of=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Polynomial_Opoly=1. hAPP=1. c_Polynomial_Odegree=1. c_Fact_Ofact__class_Ofact=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. tc_Polynomial_Opoly=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oone__class_Oone=1. c_Suc=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_Divides_Odiv__class_Odiv=1. c_Polynomial_OpCons=1. c_GCD_Ogcd__class_Ogcd=1. c_Polynomial_Osmult=1. c_Polynomial_Ocoeff=1. c_Polynomial_Omonom=1. c_Polynomial_Osynthetic__div=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_Polynomial_Oorder=1. v_x=1.
% 4.88/5.13
% 4.88/5.13 ============================== end of process initial clauses ========
% 4.88/5.13
% 4.88/5.13 ============================== CLAUSES FOR SEARCH ====================
% 4.88/5.13
% 4.88/5.13 ============================== end of clauses for search =============
% 4.88/5.13
% 4.88/5.13 ============================== SEARCH ================================
% 4.88/5.13
% 4.88/5.13 % Starting search at 1.58 seconds.
% 4.88/5.13
% 4.88/5.13 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 1.65 sec).
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=37.000, iters=3542
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=33.000, iters=3477
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=31.000, iters=3370
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=30.000, iters=3391
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=29.000, iters=3405
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=28.000, iters=3370
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=27.000, iters=3388
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=26.000, iters=3337
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=25.000, iters=3341
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=24.000, iters=3337
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=23.000, iters=3359
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=22.000, iters=3339
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=21.000, iters=3335
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=20.000, iters=3385
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=19.000, iters=3342
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=18.000, iters=3345
% 4.88/5.13
% 4.88/5.13 Low Water (keep): wt=17.000, iters=3336
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=5207, wt=58.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11583, wt=45.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11003, wt=44.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11161, wt=40.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11157, wt=39.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11587, wt=38.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace): id=11854, wt=35.000
% 4.88/5.13
% 4.88/5.13 Low Water (displace)Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------