TSTP Solution File: ALG350-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG350-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 17:54:32 EDT 2022
% Result : Unsatisfiable 0.98s 1.32s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG350-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 22:53:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.09 ============================== Prover9 ===============================
% 0.80/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.09 Process 14095 was started by sandbox2 on n019.cluster.edu,
% 0.80/1.09 Wed Jun 8 22:53:56 2022
% 0.80/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13941_n019.cluster.edu".
% 0.80/1.09 ============================== end of head ===========================
% 0.80/1.09
% 0.80/1.09 ============================== INPUT =================================
% 0.80/1.09
% 0.80/1.09 % Reading from file /tmp/Prover9_13941_n019.cluster.edu
% 0.80/1.09
% 0.80/1.09 set(prolog_style_variables).
% 0.80/1.09 set(auto2).
% 0.80/1.09 % set(auto2) -> set(auto).
% 0.80/1.09 % set(auto) -> set(auto_inference).
% 0.80/1.09 % set(auto) -> set(auto_setup).
% 0.80/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.09 % set(auto) -> set(auto_limits).
% 0.80/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.09 % set(auto) -> set(auto_denials).
% 0.80/1.09 % set(auto) -> set(auto_process).
% 0.80/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.09 % set(auto2) -> assign(stats, some).
% 0.80/1.09 % set(auto2) -> clear(echo_input).
% 0.80/1.09 % set(auto2) -> set(quiet).
% 0.80/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.09 % set(auto2) -> clear(print_given).
% 0.80/1.09 assign(lrs_ticks,-1).
% 0.80/1.09 assign(sos_limit,10000).
% 0.80/1.09 assign(order,kbo).
% 0.80/1.09 set(lex_order_vars).
% 0.80/1.09 clear(print_given).
% 0.80/1.09
% 0.80/1.09 % formulas(sos). % not echoed (380 formulas)
% 0.80/1.09
% 0.80/1.09 ============================== end of input ==========================
% 0.80/1.09
% 0.80/1.09 % From the command line: assign(max_seconds, 300).
% 0.80/1.09
% 0.80/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.09
% 0.80/1.09 % Formulas that are not ordinary clauses:
% 0.80/1.09
% 0.80/1.09 ============================== end of process non-clausal formulas ===
% 0.80/1.09
% 0.80/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.09
% 0.80/1.09 ============================== PREDICATE ELIMINATION =================
% 0.80/1.09 1 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 0.80/1.09 2 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_norm__minus__cancel_0) # label(axiom). [assumption].
% 0.80/1.09 3 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_abs__norm__cancel_0) # label(axiom). [assumption].
% 0.80/1.09 4 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_norm__minus__commute_0) # label(axiom). [assumption].
% 0.80/1.09 5 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__triangle__ineq_0) # label(axiom). [assumption].
% 0.80/1.09 6 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(C,A),E,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,A),D,tc_RealDef_Oreal) # label(cls_norm__add__less_0) # label(axiom). [assumption].
% 0.80/1.09 7 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__triangle__ineq4_0) # label(axiom). [assumption].
% 0.80/1.10 8 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A),A),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,D,A),A),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(C,E,A),A),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__diff__triangle__ineq_0) # label(axiom). [assumption].
% 0.80/1.10 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal). [resolve(1,a,2,a)].
% 0.80/1.10 Derived: c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal). [resolve(1,a,3,a)].
% 0.80/1.10 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,4,a)].
% 0.80/1.10 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,5,a)].
% 0.80/1.10 Derived: c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(1,a,6,a)].
% 0.80/1.10 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,7,a)].
% 0.80/1.10 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,8,a)].
% 0.80/1.10 9 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 0.80/1.10 10 -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].
% 0.80/1.10 11 -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].
% 0.80/1.10 12 -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].
% 0.80/1.10 13 -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].
% 0.80/1.10 14 -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].
% 0.80/1.10 15 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 0.80/1.10 16 -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].
% 0.80/1.10 17 -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].
% 0.80/1.10 18 -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].
% 0.80/1.10 19 -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].
% 0.80/1.10 20 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 0.80/1.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(9,a,10,a)].
% 0.80/1.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(9,a,11,a)].
% 0.80/1.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(9,a,12,a)].
% 0.80/1.10 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(9,a,13,a)].
% 0.80/1.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(9,a,14,a)].
% 0.80/1.10 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(9,a,15,a)].
% 0.80/1.10 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(9,a,16,a)].
% 0.80/1.10 Derived: -c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(9,a,18,a)].
% 0.80/1.10 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(9,a,19,a)].
% 0.80/1.10 Derived: c_lessequals(A,A,tc_RealDef_Oreal). [resolve(9,a,20,a)].
% 0.80/1.10 21 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 0.80/1.10 22 -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].
% 0.80/1.10 23 -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].
% 0.80/1.10 24 -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].
% 0.80/1.10 25 -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].
% 0.80/1.10 26 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 0.80/1.10 27 -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].
% 0.80/1.10 28 -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].
% 0.80/1.10 29 -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].
% 0.80/1.10 30 -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].
% 0.80/1.10 31 -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].
% 0.80/1.10 32 -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].
% 0.80/1.10 33 -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].
% 0.80/1.10 34 -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].
% 0.80/1.11 35 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 0.80/1.11 36 -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].
% 0.80/1.11 37 -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].
% 0.80/1.11 38 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 0.80/1.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | B = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(21,a,28,a)].
% 0.80/1.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | A = B. [resolve(21,a,30,a)].
% 0.80/1.11 Derived: A = B | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(21,a,36,a)].
% 0.80/1.11 39 class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.80/1.11 40 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.80/1.11 41 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.80/1.11 42 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.80/1.11 43 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.80/1.11 44 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.80/1.11 45 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.80/1.11 46 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.80/1.11 47 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.80/1.11 48 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.80/1.11 49 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.80/1.11 50 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.80/1.11 51 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.80/1.11 52 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.80/1.11 53 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.80/1.11 54 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.80/1.11 55 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.80/1.11 56 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.80/1.11 57 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.80/1.11 58 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.80/1.11 59 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.80/1.11 60 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_RealDef_Oreal) = A. [resolve(39,a,40,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(39,a,41,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(39,a,42,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal). [resolve(39,a,43,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal). [resolve(39,a,44,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = A | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(39,a,45,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) != B | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(39,a,46,a)].
% 0.80/1.11 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = B | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(39,a,47,a)].
% 0.80/1.11 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(39,a,48,a)].
% 0.80/1.11 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(39,a,49,a)].
% 0.80/1.11 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(39,a,50,a)].
% 0.80/1.11 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(39,a,52,a)].
% 0.80/1.11 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(39,a,53,a)].
% 0.80/1.11 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(39,a,55,a)].
% 0.80/1.11 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(39,a,56,a)].
% 0.80/1.11 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(39,a,57,a)].
% 0.80/1.12 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(39,a,58,a)].
% 0.80/1.12 61 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 0.80/1.12 62 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) # label(axiom). [assumption].
% 0.80/1.12 63 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) # label(axiom). [assumption].
% 0.80/1.12 64 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) # label(cls_add__eq__inf__sup_0) # label(axiom). [assumption].
% 0.80/1.12 65 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A),A) # label(cls_inf__eq__neg__sup_0) # label(axiom). [assumption].
% 0.80/1.12 66 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_neg__inf__eq__sup_0) # label(axiom). [assumption].
% 0.80/1.12 67 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_neg__sup__eq__inf_0) # label(axiom). [assumption].
% 0.80/1.12 68 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) # label(axiom). [assumption].
% 0.80/1.12 69 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) # label(axiom). [assumption].
% 0.80/1.12 70 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A),A) # label(cls_sup__eq__neg__inf_0) # label(axiom). [assumption].
% 0.80/1.12 Derived: c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,62,a)].
% 0.80/1.12 Derived: c_HOL_Oplus__class_Oplus(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,63,a)].
% 0.80/1.12 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,64,a)].
% 0.80/1.13 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,65,a)].
% 0.80/1.13 Derived: c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,66,a)].
% 0.80/1.13 Derived: c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,67,a)].
% 0.80/1.13 Derived: c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,68,a)].
% 0.80/1.13 Derived: c_HOL_Oplus__class_Oplus(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,69,a)].
% 0.80/1.13 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(61,a,70,a)].
% 0.80/1.13 71 class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 0.80/1.13 72 -class_OrderedGroup_Olordered__ab__group__add__join(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__sup__distrib__left_0) # label(axiom). [assumption].
% 0.80/1.13 73 -class_OrderedGroup_Olordered__ab__group__add__join(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__sup__distrib__right_0) # label(axiom). [assumption].
% 0.80/1.13 74 class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) # label(axiom). [assumption].
% 0.80/1.13 75 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__sup__distrib1_0) # label(axiom). [assumption].
% 0.80/1.13 76 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,D,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__sup__distrib2_0) # label(axiom). [assumption].
% 0.80/1.13 77 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__inf__distrib1_0) # label(axiom). [assumption].
% 0.80/1.13 78 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__inf__distrib2_0) # label(axiom). [assumption].
% 0.80/1.14 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(74,a,75,a)].
% 0.80/1.14 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(74,a,76,a)].
% 0.80/1.14 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(74,a,77,a)].
% 0.80/1.14 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(74,a,78,a)].
% 0.80/1.14 79 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 0.80/1.14 80 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 0.80/1.14 81 -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].
% 0.80/1.14 82 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oplus__class_Oplus(B,C,A) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 0.80/1.14 83 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 0.80/1.14 84 -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].
% 0.80/1.14 85 -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].
% 0.80/1.14 86 -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].
% 0.80/1.14 87 -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].
% 0.80/1.14 88 -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].
% 0.80/1.14 89 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 0.80/1.14 90 -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].
% 0.80/1.14 91 -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].
% 0.80/1.14 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(79,a,80,a)].
% 0.80/1.14 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(79,a,81,a)].
% 0.80/1.14 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal). [resolve(79,a,82,a)].
% 0.80/1.14 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(79,a,83,a)].
% 0.80/1.14 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(79,a,84,a)].
% 0.80/1.14 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(79,a,85,a)].
% 0.80/1.14 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal) = B. [resolve(79,a,88,a)].
% 0.80/1.14 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(79,a,89,a)].
% 0.80/1.14 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = B. [resolve(79,a,90,a)].
% 0.80/1.14 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(79,a,91,a)].
% 0.80/1.14 92 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 0.80/1.14 93 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(B,C,A),A) = c_Orderings_Oord__class_Omin(B,C,A) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 0.80/1.14 94 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 0.80/1.14 95 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 0.80/1.14 96 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 0.80/1.14 97 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,D,A),c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 0.80/1.14 98 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,B,A) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 0.80/1.14 99 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.80/1.14 100 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.80/1.14 101 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.80/1.14 102 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.80/1.14 103 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,B,A) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 0.80/1.14 104 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(B,C,A),A) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 0.80/1.14 105 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 0.80/1.14 106 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 0.80/1.14 107 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 0.80/1.14 108 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 0.80/1.14 109 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 0.80/1.14 110 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 0.80/1.14 111 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = c_Orderings_Oord__class_Omin(C,B,A) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 0.80/1.14 112 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 0.80/1.14 113 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 0.80/1.14 114 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 0.80/1.14 115 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 0.80/1.14 116 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 0.80/1.14 117 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 0.80/1.14 118 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 0.80/1.14 119 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 0.80/1.14 120 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 0.80/1.14 121 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 0.80/1.14 122 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 0.80/1.14 123 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 0.80/1.14 124 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 0.80/1.14 125 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 0.80/1.14 126 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 0.80/1.14 127 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 0.80/1.14 128 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 0.80/1.14 129 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 0.80/1.14 130 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 0.80/1.14 131 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 0.80/1.14 132 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 0.80/1.14 133 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 0.80/1.14 134 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 0.80/1.14 135 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 0.80/1.14 136 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 0.80/1.14 137 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 0.80/1.14 138 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 0.80/1.14 139 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) != C | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 0.80/1.14 140 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 0.80/1.14 141 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 0.80/1.14 142 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 0.80/1.14 143 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,D,A),c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 0.80/1.14 144 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A) = c_Orderings_Oord__class_Omax(B,C,A) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 0.80/1.14 145 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(B,C,A),A) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 0.80/1.14 146 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A),c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A),A) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 0.80/1.14 147 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = c_Orderings_Oord__class_Omax(C,B,A) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 0.80/1.14 148 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 0.80/1.14 149 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(C,c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 0.80/1.14 150 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 0.80/1.14 151 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 0.80/1.14 152 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.80/1.14 153 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A),A) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 0.80/1.14 154 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.80/1.14 155 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 0.80/1.14 156 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 0.80/1.14 157 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.80/1.14 158 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.80/1.14 159 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 0.80/1.14 160 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 0.80/1.14 161 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 0.80/1.14 162 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(B,C,A),A) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 0.80/1.14 163 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,B,A),A) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 0.80/1.14 164 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 0.80/1.14 165 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 0.80/1.14 166 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 0.80/1.15 167 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 0.80/1.15 168 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 0.80/1.15 169 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.80/1.15 170 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.80/1.15 171 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.80/1.15 172 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.80/1.15 173 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.80/1.15 174 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.80/1.15 175 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.80/1.15 176 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal). [resolve(92,a,93,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(92,a,94,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(92,a,95,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,96,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,97,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,A,tc_RealDef_Oreal) = A. [resolve(92,a,98,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | B = A. [resolve(92,a,99,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,A,tc_RealDef_Oreal) = A. [resolve(92,a,103,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(92,a,104,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,105,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,106,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(92,a,107,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(92,a,108,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(B,A,tc_RealDef_Oreal). [resolve(92,a,111,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(92,a,112,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(92,a,113,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,114,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,115,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,118,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,119,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,120,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,121,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(92,a,122,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,123,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(C,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,128,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,129,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,130,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(92,a,131,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(92,a,132,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,137,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = A | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(92,a,138,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) != B | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,139,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = B | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,140,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = B | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(92,a,141,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,142,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,143,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal). [resolve(92,a,144,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(92,a,145,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,146,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(B,A,tc_RealDef_Oreal). [resolve(92,a,147,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,148,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,149,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,150,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,151,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,153,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) != A | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,155,a)].
% 0.80/1.15 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,156,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(92,a,159,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,162,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(92,a,163,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(92,a,164,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(92,a,167,a)].
% 0.80/1.15 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(92,a,168,a)].
% 0.80/1.15 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(92,a,169,a)].
% 0.80/1.15 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(92,a,176,a)].
% 0.80/1.15 177 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.80/1.15 178 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 0.80/1.15 179 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 0.80/1.15 180 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 0.80/1.15 181 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 0.80/1.15 182 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 0.80/1.15 183 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 0.80/1.15 184 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 0.80/1.15 185 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 0.80/1.15 186 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 0.80/1.15 187 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,A),A),A),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 0.80/1.15 188 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 0.80/1.15 189 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 0.80/1.15 190 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 0.80/1.15 191 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 0.80/1.15 192 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 0.80/1.15 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,178,a)].
% 0.80/1.15 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,179,a)].
% 0.80/1.15 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,180,a)].
% 0.80/1.15 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(177,a,181,a)].
% 0.80/1.15 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,182,a)].
% 0.80/1.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,183,a)].
% 0.80/1.16 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(177,a,184,a)].
% 0.80/1.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(177,a,186,a)].
% 0.80/1.16 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,187,a)].
% 0.80/1.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(177,a,188,a)].
% 0.80/1.16 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,189,a)].
% 0.80/1.16 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,190,a)].
% 0.80/1.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(177,a,191,a)].
% 0.80/1.16 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(177,a,192,a)].
% 0.80/1.16 193 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 0.80/1.16 194 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 0.80/1.16 195 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 0.80/1.16 196 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(D,B,A),A),C,A) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 0.80/1.16 197 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(C,D,A),B,A) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 0.80/1.16 198 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 0.80/1.16 199 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 0.80/1.16 200 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(193,a,194,a)].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(193,a,196,a)].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(193,a,197,a)].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(193,a,198,a)].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(193,a,199,a)].
% 0.80/1.17 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(193,a,200,a)].
% 0.80/1.17 201 class_Lattices_Olattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Olattice) # label(axiom). [assumption].
% 0.80/1.17 202 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__sup__aci_I2_J_0) # label(axiom). [assumption].
% 0.80/1.17 203 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__sup__aci_I3_J_0) # label(axiom). [assumption].
% 0.80/1.17 204 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),A) # label(cls_distrib__sup__le_0) # label(axiom). [assumption].
% 0.80/1.17 205 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = B # label(cls_inf__sup__absorb_0) # label(axiom). [assumption].
% 0.80/1.17 206 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_inf__sup__aci_I7_J_0) # label(axiom). [assumption].
% 0.80/1.17 207 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_inf__sup__aci_I6_J_0) # label(axiom). [assumption].
% 0.80/1.17 208 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__sup__aci_I1_J_0) # label(axiom). [assumption].
% 0.80/1.17 209 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_inf__sup__aci_I5_J_0) # label(axiom). [assumption].
% 0.80/1.17 210 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_inf__sup__aci_I8_J_0) # label(axiom). [assumption].
% 0.80/1.17 211 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A),c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A),A) # label(cls_distrib__inf__le_0) # label(axiom). [assumption].
% 0.80/1.17 212 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = B # label(cls_sup__inf__absorb_0) # label(axiom). [assumption].
% 0.80/1.17 213 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__sup__aci_I4_J_0) # label(axiom). [assumption].
% 0.80/1.17 214 -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_inf__sup__ord_I4_J_0) # label(axiom). [assumption].
% 0.80/1.17 215 -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_inf__sup__ord_I3_J_0) # label(axiom). [assumption].
% 0.80/1.17 216 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__sup__ord_I2_J_0) # label(axiom). [assumption].
% 0.80/1.17 217 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__sup__ord_I1_J_0) # label(axiom). [assumption].
% 0.80/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,202,a)].
% 0.80/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,203,a)].
% 0.80/1.17 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,204,a)].
% 0.80/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(201,a,205,a)].
% 0.80/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_RealDef_Oreal). [resolve(201,a,208,a)].
% 0.80/1.17 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,211,a)].
% 0.80/1.17 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(201,a,212,a)].
% 0.80/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal). [resolve(201,a,213,a)].
% 0.80/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(201,a,216,a)].
% 0.80/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(201,a,217,a)].
% 0.80/1.17 218 class_Lattices_Olower__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.80/1.17 219 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.80/1.17 220 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.80/1.17 221 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.80/1.17 222 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.80/1.17 223 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.80/1.17 224 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.80/1.17 225 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.80/1.17 226 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.80/1.17 227 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.80/1.17 228 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.80/1.17 229 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.80/1.17 230 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.80/1.17 231 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.80/1.17 232 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.80/1.17 233 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.80/1.17 234 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.80/1.17 235 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.80/1.17 236 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.80/1.17 237 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.80/1.17 238 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.80/1.18 239 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(218,a,222,a)].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(218,a,223,a)].
% 0.80/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_RealDef_Oreal) = A. [resolve(218,a,225,a)].
% 0.80/1.18 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(218,a,226,a)].
% 0.80/1.18 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(218,a,227,a)].
% 0.80/1.18 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(218,a,228,a)].
% 0.80/1.18 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(218,a,229,a)].
% 0.80/1.18 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(218,a,232,a)].
% 0.80/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = B | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(218,a,237,a)].
% 0.80/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) != A | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(218,a,238,a)].
% 0.80/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(218,a,239,a)].
% 0.80/1.18 240 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 0.80/1.18 241 -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].
% 0.80/1.18 242 -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].
% 0.80/1.18 243 -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].
% 0.80/1.18 244 -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].
% 0.80/1.18 245 -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].
% 0.80/1.18 246 -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].
% 0.80/1.18 247 -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].
% 0.80/1.18 248 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 0.80/1.18 249 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 0.80/1.18 250 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_max__diff__distrib__left_0) # label(axiom). [assumption].
% 0.80/1.18 251 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_min__diff__distrib__left_0) # label(axiom). [assumption].
% 0.80/1.18 252 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 0.80/1.18 253 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 0.80/1.18 254 -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].
% 0.80/1.18 255 -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].
% 0.80/1.18 256 -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].
% 0.80/1.18 257 -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].
% 0.80/1.18 258 -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].
% 0.80/1.18 259 -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].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,241,a)].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(240,a,242,a)].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(240,a,243,a)].
% 0.80/1.18 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,245,a)].
% 0.80/1.18 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,247,a)].
% 0.80/1.18 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal). [resolve(240,a,248,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(240,a,249,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,250,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,251,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(240,a,252,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal). [resolve(240,a,253,a)].
% 0.93/1.19 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,254,a)].
% 0.93/1.19 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(240,a,255,a)].
% 0.93/1.19 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(240,a,256,a)].
% 0.93/1.19 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,258,a)].
% 0.93/1.19 260 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.93/1.19 261 -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_abs__lattice_0) # label(axiom). [assumption].
% 0.93/1.19 262 -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,c_HOL_Oabs__class_Oabs(D,A),A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_estimate__by__abs_0) # label(axiom). [assumption].
% 0.93/1.19 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(260,a,261,a)].
% 0.93/1.19 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,c_HOL_Oabs__class_Oabs(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(260,a,262,a)].
% 0.93/1.19 263 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.93/1.19 264 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.93/1.19 265 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.93/1.19 266 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(263,a,264,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(263,a,265,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(B,A,tc_RealDef_Oreal). [resolve(263,a,266,a)].
% 0.93/1.19 267 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.93/1.19 268 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.93/1.19 269 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.93/1.19 270 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.93/1.19 271 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.93/1.19 272 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.93/1.19 273 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.93/1.19 274 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.93/1.19 275 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(267,a,268,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(267,a,270,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(267,a,273,a)].
% 0.93/1.19 276 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 0.93/1.19 277 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 0.93/1.19 278 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 0.93/1.19 279 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 0.93/1.19 280 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 0.93/1.19 281 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != C | B = c_HOL_Ouminus__class_Ouminus(D,A) # label(cls_add__cancel__end_0) # label(axiom). [assumption].
% 0.93/1.19 282 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Ominus__class_Ominus(C,B,A) # label(cls_minus__diff__eq_0) # label(axiom). [assumption].
% 0.93/1.19 283 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_diff__def_0) # label(axiom). [assumption].
% 0.93/1.19 284 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_ab__diff__minus_0) # label(axiom). [assumption].
% 0.93/1.19 285 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != c_HOL_Oplus__class_Oplus(C,E,A) | c_HOL_Oplus__class_Oplus(B,D,A) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 0.93/1.19 286 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oplus__class_Oplus(C,B,A),A) = C # label(cls_add__cancel__end_1) # label(axiom). [assumption].
% 0.93/1.19 287 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(B,C,A),A) # label(cls_Lim_Ominus__diff__minus_0) # label(axiom). [assumption].
% 0.93/1.19 288 -class_OrderedGroup_Oab__group__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(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__add__distrib_0) # label(axiom). [assumption].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal) | B = C. [resolve(276,a,278,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,C,tc_RealDef_Oreal) | A = B. [resolve(276,a,279,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(276,a,280,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) != B | A = c_HOL_Ouminus__class_Ouminus(C,tc_RealDef_Oreal). [resolve(276,a,281,a)].
% 0.93/1.19 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal). [resolve(276,a,282,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) = D. [resolve(276,a,285,a)].
% 0.93/1.19 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal) = B. [resolve(276,a,286,a)].
% 0.93/1.19 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(276,a,287,a)].
% 0.93/1.19 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(276,a,288,a)].
% 0.93/1.20 289 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.93/1.20 290 -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].
% 0.93/1.20 291 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.93/1.20 292 -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].
% 0.93/1.20 293 -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].
% 0.93/1.20 294 -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].
% 0.93/1.20 295 -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].
% 0.93/1.20 296 -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].
% 0.93/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(291,a,292,a)].
% 0.93/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(291,a,293,a)].
% 0.93/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(291,a,294,a)].
% 0.93/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(291,a,295,a)].
% 0.93/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(291,a,296,a)].
% 0.93/1.20 297 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.93/1.20 298 -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].
% 0.93/1.20 299 -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].
% 0.93/1.20 300 -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].
% 0.95/1.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(297,a,298,a)].
% 0.95/1.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(297,a,299,a)].
% 0.95/1.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(297,a,300,a)].
% 0.95/1.20 301 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.95/1.20 302 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 0.95/1.20 303 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 0.95/1.20 304 -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].
% 0.95/1.20 305 -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].
% 0.95/1.20 306 -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].
% 0.95/1.20 307 -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].
% 0.95/1.20 308 -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].
% 0.95/1.20 309 -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].
% 0.95/1.20 310 -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].
% 0.95/1.20 311 -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].
% 0.95/1.20 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,302,a)].
% 0.95/1.20 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,303,a)].
% 0.95/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,304,a)].
% 0.95/1.22 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,306,a)].
% 0.95/1.22 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,309,a)].
% 0.95/1.22 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(301,a,311,a)].
% 0.95/1.22 312 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 0.95/1.22 313 -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_class__ring_Osub__add_0) # label(axiom). [assumption].
% 0.95/1.22 314 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 0.95/1.22 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(312,a,314,b)].
% 0.95/1.22 315 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.95/1.22 316 -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].
% 0.95/1.22 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(315,a,316,a)].
% 0.95/1.22 317 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.95/1.22 318 -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].
% 0.95/1.22 319 -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].
% 0.95/1.22 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal) | A = C. [resolve(317,a,319,a)].
% 0.95/1.22 320 class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom). [assumption].
% 0.95/1.22 321 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__inf__distrib__left_0) # label(axiom). [assumption].
% 0.95/1.22 322 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__inf__distrib__right_0) # label(axiom). [assumption].
% 0.95/1.22
% 0.95/1.22 ============================== end predicate elimination =============
% 0.95/1.22
% 0.95/1.22 Auto_denials: (non-Horn, no changes).
% 0.95/1.22
% 0.95/1.22 Term ordering decisions:
% 0.95/1.22 Function symbol KB weights: tc_RealDef_Oreal=1. v_P=1. v_Y____=1. v_x____=1. t_a=1. v_L____=1. v_xa=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Oabs__class_Oabs=1. c_RealVector_Onorm__class_Onorm=1. c_Transcendental_Oexp=1. hAPP=1. c_COMBI=1. c_NthRoot_Osqrt=1. c_Transcendental_Oarctan=1. c_HOL_Oplus__class_Oplus=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Orderings_Oord__class_Omax=1. c_Orderings_Oord__class_Omin=1. c_HOL_Ominus__class_Ominus=1.
% 0.98/1.32
% 0.98/1.32 ============================== end of process initial clauses ========
% 0.98/1.32
% 0.98/1.32 ============================== CLAUSES FOR SEARCH ====================
% 0.98/1.32
% 0.98/1.32 ============================== end of clauses for search =============
% 0.98/1.32
% 0.98/1.32 ============================== SEARCH ================================
% 0.98/1.32
% 0.98/1.32 % Starting search at 0.17 seconds.
% 0.98/1.32
% 0.98/1.32 ============================== PROOF =================================
% 0.98/1.32 % SZS status Unsatisfiable
% 0.98/1.32 % SZS output start Refutation
% 0.98/1.32
% 0.98/1.32 % Proof 1 at 0.27 (+ 0.00) seconds.
% 0.98/1.32 % Length of proof is 10.
% 0.98/1.32 % Level of proof is 2.
% 0.98/1.32 % Maximum clause weight is 8.000.
% 0.98/1.32 % Given clauses 207.
% 0.98/1.32
% 0.98/1.32 9 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 0.98/1.32 18 -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].
% 0.98/1.32 346 c_HOL_Oord__class_Oless(A,v_Y____,tc_RealDef_Oreal) | -hBOOL(hAPP(v_P,A)) # label(cls_Y_0) # label(axiom). [assumption].
% 0.98/1.32 347 c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) # label(cls_real__le__linear_0) # label(axiom). [assumption].
% 0.98/1.32 351 hBOOL(hAPP(v_P,v_xa)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 0.98/1.32 352 -c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.98/1.32 366 -c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(9,a,18,a)].
% 0.98/1.32 610 c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal). [resolve(351,a,346,b)].
% 0.98/1.32 612 c_lessequals(v_Y____,v_xa,tc_RealDef_Oreal). [resolve(352,a,347,b)].
% 0.98/1.32 1895 $F. [resolve(610,a,366,b),unit_del(a,612)].
% 0.98/1.32
% 0.98/1.32 % SZS output end Refutation
% 0.98/1.32 ============================== end of proof ==========================
% 0.98/1.32
% 0.98/1.32 ============================== STATISTICS ============================
% 0.98/1.32
% 0.98/1.32 Given=207. Generated=3659. Kept=1518. proofs=1.
% 0.98/1.32 Usable=206. Sos=1239. Demods=351. Limbo=12, Disabled=646. Hints=0.
% 0.98/1.32 Megabytes=2.30.
% 0.98/1.32 User_CPU=0.27, System_CPU=0.00, Wall_clock=0.
% 0.98/1.32
% 0.98/1.32 ============================== end of statistics =====================
% 0.98/1.32
% 0.98/1.32 ============================== end of search =========================
% 0.98/1.32
% 0.98/1.32 THEOREM PROVED
% 0.98/1.32 % SZS status Unsatisfiable
% 0.98/1.32
% 0.98/1.32 Exiting with 1 proof.
% 0.98/1.32
% 0.98/1.32 Process 14095 exit (max_proofs) Wed Jun 8 22:53:56 2022
% 0.98/1.32 Prover9 interrupted
%------------------------------------------------------------------------------