TSTP Solution File: SWW208+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW208+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %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 : 300s
% DateTime : Mon Jun 24 18:06:24 EDT 2024
% Result : Theorem 7.14s 7.07s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW208+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %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 : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:23:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.51/0.56 start to proof:theBenchmark
% 6.91/7.00 %-------------------------------------------
% 6.91/7.00 % File :CSE---1.7
% 6.91/7.00 % Problem :theBenchmark
% 6.91/7.00 % Transform :cnf
% 6.91/7.00 % Format :tptp:raw
% 6.91/7.00 % Command :java -jar mcs_scs.jar %d %s
% 6.91/7.00
% 6.91/7.00 % Result :Theorem 5.570000s
% 6.91/7.00 % Output :CNFRefutation 5.570000s
% 6.91/7.00 %-------------------------------------------
% 6.91/7.00 %------------------------------------------------------------------------------
% 6.91/7.00 % File : SWW208+1 : TPTP v8.2.0. Released v5.2.0.
% 6.91/7.00 % Domain : Software Verification
% 6.91/7.00 % Problem : Fundamental Theorem of Algebra 436796, 1000 axioms selected
% 6.91/7.00 % Version : Especial.
% 6.91/7.00 % English :
% 6.91/7.00
% 6.91/7.00 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 6.91/7.00 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 6.91/7.00 % Source : [Bla11]
% 6.91/7.00 % Names : fta_436796.1000.p [Bla11]
% 6.91/7.00
% 6.91/7.00 % Status : Theorem
% 6.91/7.00 % Rating : 0.33 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.38 v7.4.0, 0.33 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v7.0.0, 0.40 v6.4.0, 0.38 v6.2.0, 0.36 v6.1.0, 0.53 v6.0.0, 0.43 v5.5.0, 0.59 v5.4.0, 0.61 v5.3.0, 0.63 v5.2.0
% 6.91/7.00 % Syntax : Number of formulae : 1269 ( 428 unt; 0 def)
% 6.91/7.00 % Number of atoms : 2891 ( 732 equ)
% 6.91/7.00 % Maximal formula atoms : 13 ( 2 avg)
% 6.91/7.00 % Number of connectives : 1773 ( 151 ~; 57 |; 113 &)
% 6.91/7.00 % ( 216 <=>;1236 =>; 0 <=; 0 <~>)
% 6.91/7.00 % Maximal formula depth : 13 ( 4 avg)
% 6.91/7.00 % Maximal term depth : 10 ( 2 avg)
% 6.91/7.00 % Number of predicates : 78 ( 77 usr; 0 prp; 1-2 aty)
% 6.91/7.00 % Number of functors : 52 ( 52 usr; 12 con; 0-5 aty)
% 6.91/7.00 % Number of variables : 2667 (2625 !; 42 ?)
% 6.91/7.00 % SPC : FOF_THM_RFO_SEQ
% 6.91/7.00
% 6.91/7.00 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 6.91/7.00 % 2011-03-01 11:30:54
% 6.91/7.00 %------------------------------------------------------------------------------
% 6.91/7.00 %----Relevant facts (997)
% 6.91/7.00 fof(fact_ext,axiom,
% 6.91/7.00 ! [V_gb_2,V_fa_2] :
% 6.91/7.00 ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_gb_2,B_x)
% 6.91/7.00 => V_fa_2 = V_gb_2 ) ).
% 6.91/7.00
% 6.91/7.00 fof(fact_rp,axiom,
% 6.91/7.00 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ).
% 6.91/7.00
% 6.91/7.00 fof(fact_f_I1_J,axiom,
% 6.91/7.00 c_SEQ_Osubseq(v_f____) ).
% 6.91/7.00
% 6.91/7.00 fof(fact_th,axiom,
% 6.91/7.00 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ).
% 6.91/7.00
% 6.91/7.00 fof(fact_g_I1_J,axiom,
% 6.91/7.01 c_SEQ_Osubseq(v_ga____) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_assms,axiom,
% 6.91/7.01 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_abs__add__one__gt__zero,axiom,
% 6.91/7.01 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_abs__add__one__not__less__self,axiom,
% 6.91/7.01 ! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_zero__less__two,axiom,
% 6.91/7.01 ! [T_a] :
% 6.91/7.01 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__pos__nonneg,axiom,
% 6.91/7.01 ! [V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__nonneg__pos,axiom,
% 6.91/7.01 ! [V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__strict__increasing,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__strict__increasing2,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__neg__nonpos,axiom,
% 6.91/7.01 ! [V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__nonpos__neg,axiom,
% 6.91/7.01 ! [V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_abs__triangle__ineq,axiom,
% 6.91/7.01 ! [V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_abs__not__less__zero,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.01 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_zero__less__abs__iff,axiom,
% 6.91/7.01 ! [V_a_2,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
% 6.91/7.01 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact__096cmod_A_Is_A0_J_A_060_061_Ar_096,axiom,
% 6.91/7.01 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_complex__mod__triangle__sub,axiom,
% 6.91/7.01 ! [V_z,V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_zero__reorient,axiom,
% 6.91/7.01 ! [V_x_2,T_a] :
% 6.91/7.01 ( class_Groups_Ozero(T_a)
% 6.91/7.01 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 6.91/7.01 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_linorder__neqE__linordered__idom,axiom,
% 6.91/7.01 ! [V_y,V_x,T_a] :
% 6.91/7.01 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.01 => ( V_x != V_y
% 6.91/7.01 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__right__imp__eq,axiom,
% 6.91/7.01 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.01 ( class_Groups_Ocancel__semigroup__add(T_a)
% 6.91/7.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
% 6.91/7.01 => V_b = V_c ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__imp__eq,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 6.91/7.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 6.91/7.01 => V_b = V_c ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__left__imp__eq,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Ocancel__semigroup__add(T_a)
% 6.91/7.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 6.91/7.01 => V_b = V_c ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__right__cancel,axiom,
% 6.91/7.01 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 6.91/7.01 ( class_Groups_Ocancel__semigroup__add(T_a)
% 6.91/7.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
% 6.91/7.01 <=> V_b_2 = V_c_2 ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__left__cancel,axiom,
% 6.91/7.01 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 6.91/7.01 ( class_Groups_Ocancel__semigroup__add(T_a)
% 6.91/7.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)
% 6.91/7.01 <=> V_b_2 = V_c_2 ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oab__semigroup__add(T_a)
% 6.91/7.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_one__reorient,axiom,
% 6.91/7.01 ! [V_x_2,T_a] :
% 6.91/7.01 ( class_Groups_Oone(T_a)
% 6.91/7.01 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 6.91/7.01 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_real__le__antisym,axiom,
% 6.91/7.01 ! [V_w,V_z] :
% 6.91/7.01 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
% 6.91/7.01 => V_z = V_w ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_real__le__trans,axiom,
% 6.91/7.01 ! [V_k,V_j,V_i] :
% 6.91/7.01 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_real__le__linear,axiom,
% 6.91/7.01 ! [V_w,V_z] :
% 6.91/7.01 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 6.91/7.01 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_real__le__refl,axiom,
% 6.91/7.01 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_abs__idempotent,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.01 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add_Ocomm__neutral,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Ocomm__monoid__add(T_a)
% 6.91/7.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__0__right,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Omonoid__add(T_a)
% 6.91/7.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_double__zero__sym,axiom,
% 6.91/7.01 ! [V_a_2,T_a] :
% 6.91/7.01 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.01 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 6.91/7.01 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__0,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Ocomm__monoid__add(T_a)
% 6.91/7.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__0__left,axiom,
% 6.91/7.01 ! [V_a,T_a] :
% 6.91/7.01 ( class_Groups_Omonoid__add(T_a)
% 6.91/7.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__le__imp__le__left,axiom,
% 6.91/7.01 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__le__imp__le__right,axiom,
% 6.91/7.01 ! [V_b,V_c,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__mono,axiom,
% 6.91/7.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__left__mono,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__right__mono,axiom,
% 6.91/7.01 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.01 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__le__cancel__left,axiom,
% 6.91/7.01 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 6.91/7.01 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 6.91/7.01
% 6.91/7.01 fof(fact_add__le__cancel__right,axiom,
% 6.91/7.01 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 6.91/7.01 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.01 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 6.91/7.01 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__less__imp__less__left,axiom,
% 6.91/7.02 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__less__imp__less__right,axiom,
% 6.91/7.02 ! [V_b,V_c,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__strict__mono,axiom,
% 6.91/7.02 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__strict__left__mono,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__strict__right__mono,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__less__cancel__left,axiom,
% 6.91/7.02 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__less__cancel__right,axiom,
% 6.91/7.02 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__neq__one,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Ozero__neq__one(T_a)
% 6.91/7.02 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_one__neq__zero,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Ozero__neq__one(T_a)
% 6.91/7.02 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__eq__0,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.02 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__zero,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__le__D1,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__ge__self,axiom,
% 6.91/7.02 ! [V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_less__eq__real__def,axiom,
% 6.91/7.02 ! [V_y_2,V_x_2] :
% 6.91/7.02 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 6.91/7.02 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
% 6.91/7.02 | V_x_2 = V_y_2 ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_real__less__def,axiom,
% 6.91/7.02 ! [V_y_2,V_x_2] :
% 6.91/7.02 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
% 6.91/7.02 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 6.91/7.02 & V_x_2 != V_y_2 ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__add__abs,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__one,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.02 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_real__zero__not__eq__one,axiom,
% 6.91/7.02 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_real__add__left__mono,axiom,
% 6.91/7.02 ! [V_z,V_y,V_x] :
% 6.91/7.02 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__nonpos__nonpos,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__increasing2,axiom,
% 6.91/7.02 ! [V_a,V_b,V_c,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__increasing,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__nonneg__eq__0__iff,axiom,
% 6.91/7.02 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 6.91/7.02 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.02 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.02 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__nonneg__nonneg,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__neg__neg,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_pos__add__strict,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__pos__pos,axiom,
% 6.91/7.02 ! [V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__le__less__mono,axiom,
% 6.91/7.02 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_add__less__le__mono,axiom,
% 6.91/7.02 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__le__one,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_not__one__le__zero,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__less__one,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_not__one__less__zero,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_less__add__one,axiom,
% 6.91/7.02 ! [V_a,T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__of__nonneg,axiom,
% 6.91/7.02 ! [V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__le__zero__iff,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__ge__zero,axiom,
% 6.91/7.02 ! [V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__of__pos,axiom,
% 6.91/7.02 ! [V_a,T_a] :
% 6.91/7.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.02 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_abs__Im__le__cmod,axiom,
% 6.91/7.02 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__add__less,axiom,
% 6.91/7.02 ! [V_s,V_y,V_r,V_x,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__triangle__ineq,axiom,
% 6.91/7.02 ! [V_y,V_x,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_zero__less__norm__iff,axiom,
% 6.91/7.02 ! [V_x_2,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))
% 6.91/7.02 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__le__zero__iff,axiom,
% 6.91/7.02 ! [V_x_2,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.02 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__one,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 6.91/7.02 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__not__less__zero,axiom,
% 6.91/7.02 ! [V_x,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__ge__zero,axiom,
% 6.91/7.02 ! [V_x,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__eq__zero,axiom,
% 6.91/7.02 ! [V_x_2,T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.02 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_norm__zero,axiom,
% 6.91/7.02 ! [T_a] :
% 6.91/7.02 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.02 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_even__less__0__iff,axiom,
% 6.91/7.02 ! [V_a_2,T_a] :
% 6.91/7.02 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.02 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_order__refl,axiom,
% 6.91/7.02 ! [V_x,T_a] :
% 6.91/7.02 ( class_Orderings_Opreorder(T_a)
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_real__norm__def,axiom,
% 6.91/7.02 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_le__fun__def,axiom,
% 6.91/7.02 ! [V_gb_2,V_fa_2,T_a,T_b] :
% 6.91/7.02 ( class_Orderings_Oord(T_b)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 6.91/7.02 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_linorder__linear,axiom,
% 6.91/7.02 ! [V_y,V_x,T_a] :
% 6.91/7.02 ( class_Orderings_Olinorder(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.02 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_order__eq__iff,axiom,
% 6.91/7.02 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.02 ( class_Orderings_Oorder(T_a)
% 6.91/7.02 => ( V_x_2 = V_y_2
% 6.91/7.02 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.02 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_order__eq__refl,axiom,
% 6.91/7.02 ! [V_y,V_x,T_a] :
% 6.91/7.02 ( class_Orderings_Opreorder(T_a)
% 6.91/7.02 => ( V_x = V_y
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_le__funD,axiom,
% 6.91/7.02 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
% 6.91/7.02 ( class_Orderings_Oord(T_b)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_order__antisym__conv,axiom,
% 6.91/7.02 ! [V_x_2,V_y_2,T_a] :
% 6.91/7.02 ( class_Orderings_Oorder(T_a)
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.02 <=> V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_ord__eq__le__trans,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Orderings_Oord(T_a)
% 6.91/7.02 => ( V_a = V_b
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 6.91/7.02 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 6.91/7.02
% 6.91/7.02 fof(fact_xt1_I3_J,axiom,
% 6.91/7.02 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.02 ( class_Orderings_Oorder(T_a)
% 6.91/7.02 => ( V_a = V_b
% 6.91/7.02 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_ord__le__eq__trans,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oord(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.03 => ( V_b = V_c
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I4_J,axiom,
% 6.91/7.03 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.03 => ( V_b = V_c
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__antisym,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => V_x = V_y ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__trans,axiom,
% 6.91/7.03 ! [V_z,V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I5_J,axiom,
% 6.91/7.03 ! [V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => V_x = V_y ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I6_J,axiom,
% 6.91/7.03 ! [V_z,V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__funE,axiom,
% 6.91/7.03 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
% 6.91/7.03 ( class_Orderings_Oord(T_b)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__le__cases,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__irrefl,axiom,
% 6.91/7.03 ! [V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__neq__iff,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( V_x_2 != V_y_2
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_not__less__iff__gr__or__eq,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
% 6.91/7.03 | V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__less__linear,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 | V_x = V_y
% 6.91/7.03 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__antisym__conv3,axiom,
% 6.91/7.03 ! [V_x_2,V_y_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__neqE,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( V_x != V_y
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__imp__neq,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => V_x != V_y ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__not__sym,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__imp__not__less,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__imp__not__eq,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => V_x != V_y ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__imp__not__eq2,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => V_y != V_x ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__asym_H,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I9_J,axiom,
% 6.91/7.03 ! [V_a,V_b,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_ord__eq__less__trans,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oord(T_a)
% 6.91/7.03 => ( V_a = V_b
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I1_J,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( V_a = V_b
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_ord__less__eq__trans,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oord(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.03 => ( V_b = V_c
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I2_J,axiom,
% 6.91/7.03 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 6.91/7.03 => ( V_b = V_c
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__trans,axiom,
% 6.91/7.03 ! [V_z,V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I10_J,axiom,
% 6.91/7.03 ! [V_z,V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__asym,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__cases,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ( V_x != V_y
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__not__less,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__not__le,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__le__less__linear,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__le,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 & V_x_2 != V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__le__not__le,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__le__less,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 | V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_leI,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_not__leE,axiom,
% 6.91/7.03 ! [V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__antisym__conv1,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__neq__le__trans,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( V_a != V_b
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I12_J,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( V_a != V_b
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_leD,axiom,
% 6.91/7.03 ! [V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__imp__le,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__antisym__conv2,axiom,
% 6.91/7.03 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.03 ( class_Orderings_Olinorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 6.91/7.03 <=> V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__le__imp__less__or__eq,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 | V_x = V_y ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__le__neq__trans,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.03 => ( V_a != V_b
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I11_J,axiom,
% 6.91/7.03 ! [V_a,V_b,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.03 => ( V_a != V_b
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__less__le__trans,axiom,
% 6.91/7.03 ! [V_z,V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I7_J,axiom,
% 6.91/7.03 ! [V_z,V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_order__le__less__trans,axiom,
% 6.91/7.03 ! [V_z,V_y,V_x,T_a] :
% 6.91/7.03 ( class_Orderings_Opreorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_xt1_I8_J,axiom,
% 6.91/7.03 ! [V_z,V_x,V_y,T_a] :
% 6.91/7.03 ( class_Orderings_Oorder(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_double__eq__0__iff,axiom,
% 6.91/7.03 ! [V_a_2,T_a] :
% 6.91/7.03 ( class_Groups_Olinordered__ab__group__add(T_a)
% 6.91/7.03 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.03 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_Im_Ozero,axiom,
% 6.91/7.03 hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_complex__Im__one,axiom,
% 6.91/7.03 hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_abs__norm__cancel,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.03 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_Im_Oadd,axiom,
% 6.91/7.03 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le0,axiom,
% 6.91/7.03 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__zeroE,axiom,
% 6.91/7.03 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__0__iff,axiom,
% 6.91/7.03 ! [V_a_2,V_b_2,T_a] :
% 6.91/7.03 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 6.91/7.03 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 6.91/7.03 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_norm__sgn,axiom,
% 6.91/7.03 ! [V_x,T_a] :
% 6.91/7.03 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.03 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.03 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 6.91/7.03 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.03 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_psize__eq__0__iff,axiom,
% 6.91/7.03 ! [V_p_2,T_a] :
% 6.91/7.03 ( class_Groups_Ozero(T_a)
% 6.91/7.03 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.03 <=> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_convex__bound__lt,axiom,
% 6.91/7.03 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 6.91/7.03 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 6.91/7.03 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_g_I2_J,axiom,
% 6.91/7.03 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_f_I2_J,axiom,
% 6.91/7.03 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_not__add__less1,axiom,
% 6.91/7.03 ! [V_j,V_i] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_not__add__less2,axiom,
% 6.91/7.03 ! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__add2,axiom,
% 6.91/7.03 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__add1,axiom,
% 6.91/7.03 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_norm__mult,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 6.91/7.03 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__iff__add,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__fun__def,axiom,
% 6.91/7.03 ! [V_gb_2,V_fa_2,T_a,T_b] :
% 6.91/7.03 ( class_Orderings_Oord(T_b)
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 6.91/7.03 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__add__left__cancel__less,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.03 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__add__left__cancel__le,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.03 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_trans__less__add1,axiom,
% 6.91/7.03 ! [V_m,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_trans__less__add2,axiom,
% 6.91/7.03 ! [V_m,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_trans__le__add1,axiom,
% 6.91/7.03 ! [V_m,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_trans__le__add2,axiom,
% 6.91/7.03 ! [V_m,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__less__mono1,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__le__mono1,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__less__mono,axiom,
% 6.91/7.03 ! [V_l,V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__le__mono,axiom,
% 6.91/7.03 ! [V_l,V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__add__eq__less,axiom,
% 6.91/7.03 ! [V_n,V_m,V_l,V_k] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
% 6.91/7.03 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__lessD1,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__leD2,axiom,
% 6.91/7.03 ! [V_n,V_k,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__leD1,axiom,
% 6.91/7.03 ! [V_n,V_k,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_add__leE,axiom,
% 6.91/7.03 ! [V_n,V_k,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 6.91/7.03 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_sgn__mult,axiom,
% 6.91/7.03 ! [V_y,V_x,T_a] :
% 6.91/7.03 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 6.91/7.03 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 6.91/7.03 ! [V_ry,V_rx,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 6.91/7.03 ! [V_ry,V_rx,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 6.91/7.03 ! [V_rx,V_ly,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 6.91/7.03 ! [V_rx,V_ly,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 6.91/7.03 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 6.91/7.03 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 6.91/7.03 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__less__cases,axiom,
% 6.91/7.03 ! [V_P_2,V_n_2,V_m_2] :
% 6.91/7.03 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 6.91/7.03 => ( ( V_m_2 = V_n_2
% 6.91/7.03 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 6.91/7.03 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 6.91/7.03 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 6.91/7.03 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__or__eq__imp__le,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 | V_m = V_n )
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_mult__le__mono,axiom,
% 6.91/7.03 ! [V_l,V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__antisym,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.03 => V_m = V_n ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__trans,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__neq__implies__less,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 => ( V_m != V_n
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_mult__le__mono2,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_mult__le__mono1,axiom,
% 6.91/7.03 ! [V_k,V_j,V_i] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__imp__le__nat,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_eq__imp__le,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( V_m = V_n
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__not__refl3,axiom,
% 6.91/7.03 ! [V_t,V_s] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))
% 6.91/7.03 => V_s != V_t ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__not__refl2,axiom,
% 6.91/7.03 ! [V_m,V_n] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
% 6.91/7.03 => V_m != V_n ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__irrefl__nat,axiom,
% 6.91/7.03 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_linorder__neqE__nat,axiom,
% 6.91/7.03 ! [V_y,V_x] :
% 6.91/7.03 ( V_x != V_y
% 6.91/7.03 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 6.91/7.03 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Groups_Oab__semigroup__mult(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__eq__less__or__eq,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 | V_m_2 = V_n_2 ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__less__le,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 & V_m_2 != V_n_2 ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__le__linear,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.03 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_nat__neq__iff,axiom,
% 6.91/7.03 ! [V_n_2,V_m_2] :
% 6.91/7.03 ( V_m_2 != V_n_2
% 6.91/7.03 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.03 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_sgn__times,axiom,
% 6.91/7.03 ! [V_b,V_a,T_a] :
% 6.91/7.03 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.03 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_sgn__sgn,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.03 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__cube,axiom,
% 6.91/7.03 ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__square,axiom,
% 6.91/7.03 ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_le__refl,axiom,
% 6.91/7.03 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_less__not__refl,axiom,
% 6.91/7.03 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_crossproduct__eq,axiom,
% 6.91/7.03 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 6.91/7.03 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 6.91/7.03 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 6.91/7.03 <=> ( V_w_2 = V_x_2
% 6.91/7.03 | V_y_2 = V_z_2 ) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 6.91/7.03 ! [V_b,V_m,V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 6.91/7.03 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_crossproduct__noteq,axiom,
% 6.91/7.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 6.91/7.03 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 6.91/7.03 => ( ( V_a_2 != V_b_2
% 6.91/7.03 & V_c_2 != V_d_2 )
% 6.91/7.03 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 6.91/7.03 ! [V_z,V_y,V_x,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_abs__sgn,axiom,
% 6.91/7.03 ! [V_k,T_a] :
% 6.91/7.03 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.03 => c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_mult__sgn__abs,axiom,
% 6.91/7.03 ! [V_x,T_a] :
% 6.91/7.03 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 6.91/7.03 ! [V_a,T_a] :
% 6.91/7.03 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.03 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 6.91/7.03
% 6.91/7.03 fof(fact_mult__eq__self__implies__10,axiom,
% 6.91/7.03 ! [V_n,V_m] :
% 6.91/7.03 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 6.91/7.04 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 6.91/7.04 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__mono2,axiom,
% 6.91/7.04 ! [V_k,V_j,V_i] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__mono1,axiom,
% 6.91/7.04 ! [V_k,V_j,V_i] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__cancel2,axiom,
% 6.91/7.04 ! [V_n_2,V_k_2,V_m_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 6.91/7.04 <=> ( V_m_2 = V_n_2
% 6.91/7.04 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 6.91/7.04 <=> ( V_m_2 = V_n_2
% 6.91/7.04 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__cancel2,axiom,
% 6.91/7.04 ! [V_n_2,V_k_2,V_m_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel2,axiom,
% 6.91/7.04 ! [V_n_2,V_k_2,V_m_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__is__0,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__0__right,axiom,
% 6.91/7.04 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__0__less__mult__iff,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__0,axiom,
% 6.91/7.04 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_norm__mult__ineq,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_norm__mult__less,axiom,
% 6.91/7.04 ! [V_s,V_y,V_r,V_x,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_divisors__zero,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ono__zero__divisors(T_a)
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_no__zero__divisors,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ono__zero__divisors(T_a)
% 6.91/7.04 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__eq__0__iff,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Oring__no__zero__divisors(T_a)
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__zero__right,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Omult__zero(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__zero__left,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Omult__zero(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right_Ozero,axiom,
% 6.91/7.04 ! [V_x,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Ozero__right,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left_Ozero,axiom,
% 6.91/7.04 ! [V_y,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Ozero__left,axiom,
% 6.91/7.04 ! [V_b,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_combine__common__factor,axiom,
% 6.91/7.04 ! [V_c,V_b,V_e,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Osemiring(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__class_Odistrib,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left_Oadd,axiom,
% 6.91/7.04 ! [V_ya,V_y,V_x,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Oadd__left,axiom,
% 6.91/7.04 ! [V_b,V_a_H,V_a,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right_Oadd,axiom,
% 6.91/7.04 ! [V_y,V_x,V_xa,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Oadd__right,axiom,
% 6.91/7.04 ! [V_b_H,V_b,V_a,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Ocomm__neutral,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Groups_Ocomm__monoid__mult(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__1__right,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__1,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Groups_Ocomm__monoid__mult(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__1__left,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__left__cancel,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2] :
% 6.91/7.04 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
% 6.91/7.04 <=> V_a_2 = V_b_2 ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__right__cancel,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2] :
% 6.91/7.04 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
% 6.91/7.04 <=> V_a_2 = V_b_2 ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__mult__self,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__mult,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__1,axiom,
% 6.91/7.04 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__add__mult__distrib,axiom,
% 6.91/7.04 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__scale__eq__noteq,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 6.91/7.04 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 6.91/7.04 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 => ( ( V_a = V_b
% 6.91/7.04 & V_c != V_d )
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 6.91/7.04 ! [V_m,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 6.91/7.04 ! [V_a,V_m,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 6.91/7.04 ! [V_m,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__0__0,axiom,
% 6.91/7.04 ! [V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn0,axiom,
% 6.91/7.04 ! [T_a] :
% 6.91/7.04 ( class_Groups_Osgn__if(T_a)
% 6.91/7.04 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__zero__iff,axiom,
% 6.91/7.04 ! [V_x_2,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.04 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__zero,axiom,
% 6.91/7.04 ! [T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.04 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__one,axiom,
% 6.91/7.04 ! [T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 6.91/7.04 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_split__mult__neg__le,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__cancel__semiring(T_a)
% 6.91/7.04 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_split__mult__pos__le,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.04 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__mono,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__mono_H,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left__mono__neg,axiom,
% 6.91/7.04 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right__mono__neg,axiom,
% 6.91/7.04 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__mult__left__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__comm__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__nonpos__nonpos,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__nonpos__nonneg,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__cancel__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__nonneg__nonpos2,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__cancel__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__nonneg__nonpos,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__cancel__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__nonneg__nonneg,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__cancel__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__0__iff,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_zero__le__mult__iff,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))
% 6.91/7.04 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_zero__le__square,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring(T_a)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__left__mono__neg,axiom,
% 6.91/7.04 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__right__mono__neg,axiom,
% 6.91/7.04 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__mult__strict__left__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__left__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__right__mono,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__neg__neg,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__neg__pos,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel__left__neg,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_zero__less__mult__pos2,axiom,
% 6.91/7.04 ! [V_a,V_b,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_zero__less__mult__pos,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__pos__neg2,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__pos__neg,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__pos__pos,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel__left__pos,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel__left__disj,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 6.91/7.04 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__cancel__right__disj,axiom,
% 6.91/7.04 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
% 6.91/7.04 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
% 6.91/7.04 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_not__square__less__zero,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring(T_a)
% 6.91/7.04 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_less__1__mult,axiom,
% 6.91/7.04 ! [V_n,V_m,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__mult__less,axiom,
% 6.91/7.04 ! [V_d,V_b,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__less__mono2,axiom,
% 6.91/7.04 ! [V_y,V_x,V_z] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__order,axiom,
% 6.91/7.04 ! [V_y,V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__less__iff1,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,V_z_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__two__squares__add__zero__iff,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.04 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.04 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__less,axiom,
% 6.91/7.04 ! [V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__greater,axiom,
% 6.91/7.04 ! [V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left__le__imp__le,axiom,
% 6.91/7.04 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right__le__imp__le,axiom,
% 6.91/7.04 ! [V_b,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__imp__less__left,axiom,
% 6.91/7.04 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left__less__imp__less,axiom,
% 6.91/7.04 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__imp__less__right,axiom,
% 6.91/7.04 ! [V_b,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right__less__imp__less,axiom,
% 6.91/7.04 ! [V_b,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__less__imp__less,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__less__le__imp__less,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__mono_H,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__strict__mono,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__cancel__left__neg,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__le__cancel__left__pos,axiom,
% 6.91/7.04 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left__le__one__le,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right__le__one__le,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__eq__mult,axiom,
% 6.91/7.04 ! [V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Oordered__ring__abs(T_a)
% 6.91/7.04 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 6.91/7.04 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.04 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 6.91/7.04 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__mult__pos,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 6.91/7.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__le__cancel__iff2,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,V_z_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__le__cancel__iff1,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,V_z_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 6.91/7.04 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 6.91/7.04 ! [V_c,V_b,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 6.91/7.04 ! [V_d,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 6.91/7.04 ! [V_d,V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 6.91/7.04 ! [V_c,V_a,T_a] :
% 6.91/7.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.04 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_gr0I,axiom,
% 6.91/7.04 ! [V_n] :
% 6.91/7.04 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__eq__self__zero,axiom,
% 6.91/7.04 ! [V_n,V_m] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 6.91/7.04 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_gr__implies__not0,axiom,
% 6.91/7.04 ! [V_n,V_m] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.04 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__is__0,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_le__0__eq,axiom,
% 6.91/7.04 ! [V_n_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 6.91/7.04 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Nat_Oadd__0__right,axiom,
% 6.91/7.04 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 6.91/7.04
% 6.91/7.04 fof(fact_less__nat__zero__code,axiom,
% 6.91/7.04 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__gr__0,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
% 6.91/7.04 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 6.91/7.04 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_plus__nat_Oadd__0,axiom,
% 6.91/7.04 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 6.91/7.04
% 6.91/7.04 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 6.91/7.04 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_neq0__conv,axiom,
% 6.91/7.04 ! [V_n_2] :
% 6.91/7.04 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_not__less0,axiom,
% 6.91/7.04 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__sgn__pos,axiom,
% 6.91/7.04 ! [V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.04 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__pos,axiom,
% 6.91/7.04 ! [V_a,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.04 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sgn__1__pos,axiom,
% 6.91/7.04 ! [V_a_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.04 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_convex__bound__le,axiom,
% 6.91/7.04 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__semiring__1(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 6.91/7.04 ~ ! [B_g] :
% 6.91/7.04 ( c_SEQ_Osubseq(B_g)
% 6.91/7.04 => ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_norm__ratiotest__lemma,axiom,
% 6.91/7.04 ! [V_y,V_x,V_c,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y))))
% 6.91/7.04 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sum__squares__gt__zero__iff,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
% 6.91/7.04 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_not__sum__squares__lt__zero,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring(T_a)
% 6.91/7.04 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sum__squares__le__zero__iff,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
% 6.91/7.04 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sum__squares__ge__zero,axiom,
% 6.91/7.04 ! [V_y,V_x,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring(T_a)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_monoseq__def,axiom,
% 6.91/7.04 ! [V_X_2,T_a] :
% 6.91/7.04 ( class_Orderings_Oorder(T_a)
% 6.91/7.04 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 6.91/7.04 <=> ( ! [B_m,B_n] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 6.91/7.04 | ! [B_m,B_n] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_rabs__ratiotest__lemma,axiom,
% 6.91/7.04 ! [V_y,V_x,V_c] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))))
% 6.91/7.04 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__add__commute,axiom,
% 6.91/7.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__add__left__commute,axiom,
% 6.91/7.04 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__mult__distrib2,axiom,
% 6.91/7.04 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__add__assoc,axiom,
% 6.91/7.04 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_add__mult__distrib,axiom,
% 6.91/7.04 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__add__left__cancel,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
% 6.91/7.04 <=> V_m_2 = V_n_2 ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__add__right__cancel,axiom,
% 6.91/7.04 ! [V_n_2,V_k_2,V_m_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
% 6.91/7.04 <=> V_m_2 = V_n_2 ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__commute,axiom,
% 6.91/7.04 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__assoc,axiom,
% 6.91/7.04 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__assoc,axiom,
% 6.91/7.04 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__eq__1__iff,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 6.91/7.04 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 6.91/7.04 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_real__mult__commute,axiom,
% 6.91/7.04 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__1__right,axiom,
% 6.91/7.04 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__1__eq__mult__iff,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2] :
% 6.91/7.04 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 6.91/7.04 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 6.91/7.04 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__1,axiom,
% 6.91/7.04 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 6.91/7.04
% 6.91/7.04 fof(fact_expand__complex__eq,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2] :
% 6.91/7.04 ( V_x_2 = V_y_2
% 6.91/7.04 <=> ( hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2)
% 6.91/7.04 & hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_complex__equality,axiom,
% 6.91/7.04 ! [V_y,V_x] :
% 6.91/7.04 ( hAPP(c_Complex_ORe,V_x) = hAPP(c_Complex_ORe,V_y)
% 6.91/7.04 => ( hAPP(c_Complex_OIm,V_x) = hAPP(c_Complex_OIm,V_y)
% 6.91/7.04 => V_x = V_y ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_complex__Im__mult,axiom,
% 6.91/7.04 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_complex__Re__le__cmod,axiom,
% 6.91/7.04 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Re_Ozero,axiom,
% 6.91/7.04 hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Re_Oadd,axiom,
% 6.91/7.04 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_complex__Re__one,axiom,
% 6.91/7.04 hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_abs__Re__le__cmod,axiom,
% 6.91/7.04 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_le__Suc__ex__iff,axiom,
% 6.91/7.04 ! [V_l_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2))
% 6.91/7.04 <=> ? [B_n] : V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_subseq__def,axiom,
% 6.91/7.04 ! [V_fa_2] :
% 6.91/7.04 ( c_SEQ_Osubseq(V_fa_2)
% 6.91/7.04 <=> ! [B_m,B_n] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_seq__suble,axiom,
% 6.91/7.04 ! [V_n_2,V_fa_2] :
% 6.91/7.04 ( c_SEQ_Osubseq(V_fa_2)
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_sum__squares__eq__zero__iff,axiom,
% 6.91/7.04 ! [V_y_2,V_x_2,T_a] :
% 6.91/7.04 ( class_Rings_Olinordered__ring__strict(T_a)
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.04 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_conv1,axiom,
% 6.91/7.04 c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__le__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_not__real__square__gt__zero,axiom,
% 6.91/7.04 ! [V_x_2] :
% 6.91/7.04 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)))
% 6.91/7.04 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__eq__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 6.91/7.04 <=> V_m_2 = V_n_2 ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__less__cancel1,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 6.91/7.04 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 6.91/7.04 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_convergent__const,axiom,
% 6.91/7.04 ! [V_c_2,T_a] :
% 6.91/7.04 ( class_RealVector_Ometric__space(T_a)
% 6.91/7.04 => c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right_Oconvergent,axiom,
% 6.91/7.04 ! [V_x_2,V_X_2,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_X_2)
% 6.91/7.04 => c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left_Oconvergent,axiom,
% 6.91/7.04 ! [V_y_2,V_X_2,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_X_2)
% 6.91/7.04 => c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Oconvergent,axiom,
% 6.91/7.04 ! [V_Y_2,V_X_2,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_X_2)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_Y_2)
% 6.91/7.04 => c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_convergent__add,axiom,
% 6.91/7.04 ! [V_Y_2,V_X_2,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_X_2)
% 6.91/7.04 => ( c_SEQ_Oconvergent(T_a,V_Y_2)
% 6.91/7.04 => c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2)) ) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 6.91/7.04 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.04 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 6.91/7.04 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.04 | V_m_2 = V_n_2 ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_left__add__mult__distrib,axiom,
% 6.91/7.04 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Im_Opos__bounded,axiom,
% 6.91/7.04 ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Re_Opos__bounded,axiom,
% 6.91/7.04 ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Im_Ononneg__bounded,axiom,
% 6.91/7.04 ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Re_Ononneg__bounded,axiom,
% 6.91/7.04 ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__left_Opos__bounded,axiom,
% 6.91/7.04 ! [V_y,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Re_Oconvergent,axiom,
% 6.91/7.04 ! [V_X_2] :
% 6.91/7.04 ( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)
% 6.91/7.04 => c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_Im_Oconvergent,axiom,
% 6.91/7.04 ! [V_X_2] :
% 6.91/7.04 ( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)
% 6.91/7.04 => c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult_Opos__bounded,axiom,
% 6.91/7.04 ! [T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_mult__right_Opos__bounded,axiom,
% 6.91/7.04 ! [V_x,T_a] :
% 6.91/7.04 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.04 => ? [B_K] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.04 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_termination__basic__simps_I4_J,axiom,
% 6.91/7.04 ! [V_y,V_z,V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_termination__basic__simps_I3_J,axiom,
% 6.91/7.04 ! [V_z,V_y,V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_termination__basic__simps_I5_J,axiom,
% 6.91/7.04 ! [V_y,V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_termination__basic__simps_I1_J,axiom,
% 6.91/7.04 ! [V_z,V_y,V_x] :
% 6.91/7.04 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 6.91/7.04 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 6.91/7.04
% 6.91/7.04 fof(fact_termination__basic__simps_I2_J,axiom,
% 6.91/7.05 ! [V_y,V_z,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Im_Obounded,axiom,
% 6.91/7.05 ? [B_K] :
% 6.91/7.05 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Re_Obounded,axiom,
% 6.91/7.05 ? [B_K] :
% 6.91/7.05 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_decseq__def,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_Orderings_Oorder(T_a)
% 6.91/7.05 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 6.91/7.05 <=> ! [B_m,B_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_ex__least__nat__less,axiom,
% 6.91/7.05 ! [V_n_2,V_P_2] :
% 6.91/7.05 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 6.91/7.05 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 6.91/7.05 => ? [B_k] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2))
% 6.91/7.05 & ! [B_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k))
% 6.91/7.05 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 6.91/7.05 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult_Ononneg__bounded,axiom,
% 6.91/7.05 ! [T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.05 => ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_decseq__imp__monoseq,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_Orderings_Oorder(T_a)
% 6.91/7.05 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 6.91/7.05 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult__left_Ononneg__bounded,axiom,
% 6.91/7.05 ! [V_y,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.05 => ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult__right_Ononneg__bounded,axiom,
% 6.91/7.05 ! [V_x,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.05 => ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__def,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,V_X_2)
% 6.91/7.05 <=> ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_incseq__def,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_Orderings_Oorder(T_a)
% 6.91/7.05 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 6.91/7.05 <=> ! [B_m,B_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__offset,axiom,
% 6.91/7.05 ! [V_k_2,V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))
% 6.91/7.05 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__ignore__initial__segment,axiom,
% 6.91/7.05 ! [V_k_2,V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,V_X_2)
% 6.91/7.05 => c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__monoseq__convergent,axiom,
% 6.91/7.05 ! [V_X_2] :
% 6.91/7.05 ( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2)
% 6.91/7.05 => ( c_SEQ_Omonoseq(tc_RealDef_Oreal,V_X_2)
% 6.91/7.05 => c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_incseq__imp__monoseq,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_Orderings_Oorder(T_a)
% 6.91/7.05 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 6.91/7.05 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_BseqI,axiom,
% 6.91/7.05 ! [V_X_2,V_K_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2))
% 6.91/7.05 => ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2))
% 6.91/7.05 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_BseqD,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,V_X_2)
% 6.91/7.05 => ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_expi__zero,axiom,
% 6.91/7.05 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__add__one,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__zero,axiom,
% 6.91/7.05 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__le__natceiling,axiom,
% 6.91/7.05 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__mono,axiom,
% 6.91/7.05 ! [V_y,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__one,axiom,
% 6.91/7.05 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__neg,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.05 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__le__eq__one,axiom,
% 6.91/7.05 ! [V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_expi__add,axiom,
% 6.91/7.05 ! [V_b,V_a] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__add__one,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__eq,axiom,
% 6.91/7.05 ! [V_x,V_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 6.91/7.05 => c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__mult__natfloor,axiom,
% 6.91/7.05 ! [V_b,V_a] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__mono__convergent,axiom,
% 6.91/7.05 ! [V_X_2] :
% 6.91/7.05 ( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2)
% 6.91/7.05 => ( ! [B_m,B_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 6.91/7.05 => c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__ge__zero,axiom,
% 6.91/7.05 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__real__of__nat,axiom,
% 6.91/7.05 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__real__of__nat,axiom,
% 6.91/7.05 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__natfloor,axiom,
% 6.91/7.05 ! [V_a,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__natfloor__le,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__inject,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
% 6.91/7.05 <=> V_n_2 = V_m_2 ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_abs__real__of__nat__cancel,axiom,
% 6.91/7.05 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__natfloor__eq,axiom,
% 6.91/7.05 ! [V_a_2,V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__natfloor__add__one__gt,axiom,
% 6.91/7.05 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__zero,axiom,
% 6.91/7.05 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__zero__iff,axiom,
% 6.91/7.05 ! [V_n_2] :
% 6.91/7.05 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.05 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_not__real__of__nat__less__zero,axiom,
% 6.91/7.05 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__less__iff,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__le__iff,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__natfloor,axiom,
% 6.91/7.05 ! [V_n,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__mult,axiom,
% 6.91/7.05 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__add,axiom,
% 6.91/7.05 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__add,axiom,
% 6.91/7.05 ! [V_a,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 6.91/7.05 ! [V_n,V_z] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__1,axiom,
% 6.91/7.05 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__eq,axiom,
% 6.91/7.05 ! [V_x,V_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 6.91/7.05 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__natceiling__ge,axiom,
% 6.91/7.05 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__zero,axiom,
% 6.91/7.05 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__le__natfloor,axiom,
% 6.91/7.05 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__mono,axiom,
% 6.91/7.05 ! [V_y,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__one,axiom,
% 6.91/7.05 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 6.91/7.05 ! [V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.05 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__le,axiom,
% 6.91/7.05 ! [V_a,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__neg,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.05 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 6.91/7.05 ! [V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__less__real__le,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__le__real__less,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__le__eq,axiom,
% 6.91/7.05 ! [V_a_2,V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__natfloor__eq__one,axiom,
% 6.91/7.05 ! [V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natceiling__add,axiom,
% 6.91/7.05 ! [V_a,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 6.91/7.05 ! [V_n,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_BseqI2_H,axiom,
% 6.91/7.05 ! [V_K_2,V_X_2,V_N_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( ! [B_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)) )
% 6.91/7.05 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_lemma__NBseq__def,axiom,
% 6.91/7.05 ! [V_X_2,T_b] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_b)
% 6.91/7.05 => ( ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) )
% 6.91/7.05 <=> ? [B_N] :
% 6.91/7.05 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_lemma__NBseq__def2,axiom,
% 6.91/7.05 ! [V_X_2,T_b] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_b)
% 6.91/7.05 => ( ? [B_K] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 6.91/7.05 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) )
% 6.91/7.05 <=> ? [B_N] :
% 6.91/7.05 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_lessI,axiom,
% 6.91/7.05 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__mono,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__less__Suc,axiom,
% 6.91/7.05 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_realpow__Suc__le__self,axiom,
% 6.91/7.05 ! [V_n,V_r,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 6.91/7.05 ! [V_q,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 6.91/7.05 ! [V_q,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 6.91/7.05 ! [V_q,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 6.91/7.05 ! [V_q,V_p,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 6.91/7.05 ! [V_q,V_y,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 6.91/7.05 ! [V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__less__SucD,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__lessD,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__SucE,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
% 6.91/7.05 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => V_m = V_n ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__trans__Suc,axiom,
% 6.91/7.05 ! [V_k,V_j,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__lessI,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => ( c_Nat_OSuc(V_m) != V_n
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__SucI,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__antisym,axiom,
% 6.91/7.05 ! [V_m,V_n] :
% 6.91/7.05 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m)))
% 6.91/7.05 => V_m = V_n ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_not__less__less__Suc__eq,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
% 6.91/7.05 <=> V_n_2 = V_m_2 ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__less__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__Suc__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 | V_m_2 = V_n_2 ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_not__less__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_add__Suc__shift,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_add__Suc,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_add__Suc__right,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__leD,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__SucE,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
% 6.91/7.05 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__SucI,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__le__mono,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__Suc__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_not__less__eq__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__n__not__le__n,axiom,
% 6.91/7.05 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__mult__cancel1,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.05 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 6.91/7.05 <=> V_m_2 = V_n_2 ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_norm__power,axiom,
% 6.91/7.05 ! [V_n,V_x,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 6.91/7.05 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_n__not__Suc__n,axiom,
% 6.91/7.05 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__n__not__n,axiom,
% 6.91/7.05 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat_Oinject,axiom,
% 6.91/7.05 ! [V_nat_H_2,V_nat_2] :
% 6.91/7.05 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 6.91/7.05 <=> V_nat_2 = V_nat_H_2 ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__inject,axiom,
% 6.91/7.05 ! [V_y,V_x] :
% 6.91/7.05 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 6.91/7.05 => V_x = V_y ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__neq__Zero,axiom,
% 6.91/7.05 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Zero__neq__Suc,axiom,
% 6.91/7.05 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat_Osimps_I3_J,axiom,
% 6.91/7.05 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__not__Zero,axiom,
% 6.91/7.05 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat_Osimps_I2_J,axiom,
% 6.91/7.05 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Zero__not__Suc,axiom,
% 6.91/7.05 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_norm__power__ineq,axiom,
% 6.91/7.05 ! [V_n,V_x,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 6.91/7.05 ! [V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 6.91/7.05 ! [V_q,V_p,V_x,T_a] :
% 6.91/7.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_gr0__conv__Suc,axiom,
% 6.91/7.05 ! [V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 6.91/7.05 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__Suc0,axiom,
% 6.91/7.05 ! [V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 6.91/7.05 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__Suc__eq__0__disj,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 6.91/7.05 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 | ? [B_j] :
% 6.91/7.05 ( V_m_2 = c_Nat_OSuc(B_j)
% 6.91/7.05 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_one__is__add,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
% 6.91/7.05 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 6.91/7.05 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_add__is__1,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 6.91/7.05 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult__eq__1__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__iff__Suc__add,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__add__Suc2,axiom,
% 6.91/7.05 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__add__Suc1,axiom,
% 6.91/7.05 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__eq__Suc__le,axiom,
% 6.91/7.05 ! [V_m_2,V_n_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__Suc__eq__le,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__le__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__imp__less__Suc,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__leI,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__less__Suc__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
% 6.91/7.05 <=> V_n_2 = V_m_2 ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__le__lessD,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_One__nat__def,axiom,
% 6.91/7.05 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__mult__less__cancel1,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult__Suc__right,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_mult__Suc,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__mult__le__cancel1,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__eq__plus1__left,axiom,
% 6.91/7.05 ! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Suc__eq__plus1,axiom,
% 6.91/7.05 ! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_monoseq__Suc,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_Orderings_Oorder(T_a)
% 6.91/7.05 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 6.91/7.05 <=> ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n))))
% 6.91/7.05 | ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_subseq__Suc__iff,axiom,
% 6.91/7.05 ! [V_fa_2] :
% 6.91/7.05 ( c_SEQ_Osubseq(V_fa_2)
% 6.91/7.05 <=> ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_less__eq__Suc__le__raw,axiom,
% 6.91/7.05 ! [V_n_2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_one__less__mult,axiom,
% 6.91/7.05 ! [V_m,V_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_n__less__n__mult__m,axiom,
% 6.91/7.05 ! [V_m,V_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_n__less__m__mult__n,axiom,
% 6.91/7.05 ! [V_m,V_n] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_one__le__mult__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 6.91/7.05 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 6.91/7.05 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__one,axiom,
% 6.91/7.05 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__Suc,axiom,
% 6.91/7.05 ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__iff,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,V_X_2)
% 6.91/7.05 <=> ? [B_N] :
% 6.91/7.05 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__iff1a,axiom,
% 6.91/7.05 ! [V_X_2,T_a] :
% 6.91/7.05 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.05 => ( c_SEQ_OBseq(T_a,V_X_2)
% 6.91/7.05 <=> ? [B_N] :
% 6.91/7.05 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_monoseq__realpow,axiom,
% 6.91/7.05 ! [V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.05 => c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_convergent__realpow,axiom,
% 6.91/7.05 ! [V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.05 => c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_Bseq__realpow,axiom,
% 6.91/7.05 ! [V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.05 => c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__strict__mono,axiom,
% 6.91/7.05 ! [V_n,V_b,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_one__less__power,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__increasing__iff,axiom,
% 6.91/7.05 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__le__imp__le__exp,axiom,
% 6.91/7.05 ! [V_n,V_m,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zpower__zadd__distrib,axiom,
% 6.91/7.05 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zpower__zpower,axiom,
% 6.91/7.05 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__Suc__0,axiom,
% 6.91/7.05 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 6.91/7.05 ! [V_m_2,V_x_2] :
% 6.91/7.05 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 6.91/7.05 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__less__zpower__abs__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))
% 6.91/7.05 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.05 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__power__less__imp__less,axiom,
% 6.91/7.05 ! [V_n,V_m,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__zero__less__power__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 6.91/7.05 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__one__le__power,axiom,
% 6.91/7.05 ! [V_n,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_real__of__nat__power,axiom,
% 6.91/7.05 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__real__of__nat,axiom,
% 6.91/7.05 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_natfloor__power,axiom,
% 6.91/7.05 ! [V_n,V_x] :
% 6.91/7.05 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 6.91/7.05 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_field__power__not__zero,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 6.91/7.05 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__mult__distrib,axiom,
% 6.91/7.05 ! [V_n,V_b,V_a,T_a] :
% 6.91/7.05 ( class_Groups_Ocomm__monoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__commutes,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__one,axiom,
% 6.91/7.05 ! [V_n,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__abs,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.05 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__mult,axiom,
% 6.91/7.05 ! [V_n,V_m,V_a,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__one__right,axiom,
% 6.91/7.05 ! [V_a,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__le__power,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__mono,axiom,
% 6.91/7.05 ! [V_n,V_b,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__less__power,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_one__le__power,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__eq__0__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_a_2,T_a] :
% 6.91/7.05 ( ( class_Power_Opower(T_a)
% 6.91/7.05 & class_Rings_Omult__zero(T_a)
% 6.91/7.05 & class_Rings_Ono__zero__divisors(T_a)
% 6.91/7.05 & class_Rings_Ozero__neq__one(T_a) )
% 6.91/7.05 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.05 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.05 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__inject__exp,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 6.91/7.05 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 6.91/7.05 <=> V_m_2 = V_n_2 ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__0__Suc,axiom,
% 6.91/7.05 ! [V_n,T_a] :
% 6.91/7.05 ( ( class_Power_Opower(T_a)
% 6.91/7.05 & class_Rings_Osemiring__0(T_a) )
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__Suc2,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__Suc,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Power_Opower(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__0,axiom,
% 6.91/7.05 ! [V_a,T_a] :
% 6.91/7.05 ( class_Power_Opower(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__add,axiom,
% 6.91/7.05 ! [V_n,V_m,V_a,T_a] :
% 6.91/7.05 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__less__imp__less__base,axiom,
% 6.91/7.05 ! [V_b,V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__le__imp__le__base,axiom,
% 6.91/7.05 ! [V_b,V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__inject__base,axiom,
% 6.91/7.05 ! [V_b,V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.05 => V_a = V_b ) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__less__power__Suc,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__gt1__lemma,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__0__left,axiom,
% 6.91/7.05 ! [V_n,T_a] :
% 6.91/7.05 ( ( class_Power_Opower(T_a)
% 6.91/7.05 & class_Rings_Osemiring__0(T_a) )
% 6.91/7.05 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 6.91/7.05 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__le__power__abs,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__gt1,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__strict__increasing,axiom,
% 6.91/7.05 ! [V_a,V_N,V_n,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__less__imp__less__exp,axiom,
% 6.91/7.05 ! [V_n,V_m,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__strict__increasing__iff,axiom,
% 6.91/7.05 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__increasing,axiom,
% 6.91/7.05 ! [V_a,V_N,V_n,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__Suc__less,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__Suc__less__one,axiom,
% 6.91/7.05 ! [V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__strict__decreasing,axiom,
% 6.91/7.05 ! [V_a,V_N,V_n,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__eq__imp__eq__base,axiom,
% 6.91/7.05 ! [V_b,V_n,V_a,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.05 => V_a = V_b ) ) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__decreasing,axiom,
% 6.91/7.05 ! [V_a,V_N,V_n,T_a] :
% 6.91/7.05 ( class_Rings_Olinordered__semidom(T_a)
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_reduce__poly__simple,axiom,
% 6.91/7.05 ! [V_n,V_b] :
% 6.91/7.05 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 6.91/7.05 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 => ? [B_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 6.91/7.05 ! [V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
% 6.91/7.05 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power__power__power,axiom,
% 6.91/7.05 ! [T_a] :
% 6.91/7.05 ( class_Power_Opower(T_a)
% 6.91/7.05 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__le__zpower__abs,axiom,
% 6.91/7.05 ! [V_n,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zmult__1,axiom,
% 6.91/7.05 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zmult__1__right,axiom,
% 6.91/7.05 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__zmult__distrib2,axiom,
% 6.91/7.05 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__zmult__distrib,axiom,
% 6.91/7.05 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_pos__zmult__eq__1__iff,axiom,
% 6.91/7.05 ! [V_n_2,V_m_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 6.91/7.05 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 6.91/7.05 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 6.91/7.05 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zmult__zless__mono2,axiom,
% 6.91/7.05 ! [V_k,V_j,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_abs__zmult__eq__1,axiom,
% 6.91/7.05 ! [V_n,V_m] :
% 6.91/7.05 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 6.91/7.05 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zmult__assoc,axiom,
% 6.91/7.05 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zmult__commute,axiom,
% 6.91/7.05 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__zless__mono,axiom,
% 6.91/7.05 ! [V_z,V_z_H,V_w,V_w_H] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__strict__right__mono,axiom,
% 6.91/7.05 ! [V_k,V_j,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zless__imp__add1__zle,axiom,
% 6.91/7.05 ! [V_z,V_w] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_le__imp__0__less,axiom,
% 6.91/7.05 ! [V_z] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_odd__less__0,axiom,
% 6.91/7.05 ! [V_z_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_add1__zle__eq,axiom,
% 6.91/7.05 ! [V_z_2,V_w_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zabs__less__one__iff,axiom,
% 6.91/7.05 ! [V_z_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 6.91/7.05 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zless__add1__eq,axiom,
% 6.91/7.05 ! [V_z_2,V_w_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))
% 6.91/7.05 | V_w_2 = V_z_2 ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zle__add1__eq__le,axiom,
% 6.91/7.05 ! [V_z_2,V_w_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zless__linear,axiom,
% 6.91/7.05 ! [V_y,V_x] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))
% 6.91/7.05 | V_x = V_y
% 6.91/7.05 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zless__le,axiom,
% 6.91/7.05 ! [V_w_2,V_z_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))
% 6.91/7.05 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2))
% 6.91/7.05 & V_z_2 != V_w_2 ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__0__right,axiom,
% 6.91/7.05 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 6.91/7.05
% 6.91/7.05 fof(fact_int__one__le__iff__zero__less,axiom,
% 6.91/7.05 ! [V_z_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 6.91/7.05 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__0,axiom,
% 6.91/7.05 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 6.91/7.05
% 6.91/7.05 fof(fact_int__0__less__1,axiom,
% 6.91/7.05 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_odd__nonzero,axiom,
% 6.91/7.05 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_int__0__neq__1,axiom,
% 6.91/7.05 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power_Opower_Opower__0,axiom,
% 6.91/7.05 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 6.91/7.05
% 6.91/7.05 fof(fact_power_Opower_Opower__Suc,axiom,
% 6.91/7.05 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zero__less__power__nat__eq,axiom,
% 6.91/7.05 ! [V_n_2,V_x_2] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 6.91/7.05 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.05 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_self__quotient__aux2,axiom,
% 6.91/7.05 ! [V_q,V_r,V_a] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 6.91/7.05 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_self__quotient__aux1,axiom,
% 6.91/7.05 ! [V_q,V_r,V_a] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 6.91/7.05 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_q__pos__lemma,axiom,
% 6.91/7.05 ! [V_r_H,V_q_H,V_b_H] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__left__mono,axiom,
% 6.91/7.05 ! [V_k,V_j,V_i] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 6.91/7.05 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__assoc,axiom,
% 6.91/7.05 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__left__commute,axiom,
% 6.91/7.05 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zadd__commute,axiom,
% 6.91/7.05 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zle__antisym,axiom,
% 6.91/7.05 ! [V_w,V_z] :
% 6.91/7.05 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 6.91/7.05 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
% 6.91/7.05 => V_z = V_w ) ) ).
% 6.91/7.05
% 6.91/7.05 fof(fact_zle__trans,axiom,
% 6.91/7.05 ! [V_k,V_j,V_i] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zle__linear,axiom,
% 6.91/7.06 ! [V_w,V_z] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 6.91/7.06 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zle__refl,axiom,
% 6.91/7.06 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 6.91/7.06 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 6.91/7.06 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_unique__quotient__lemma__neg,axiom,
% 6.91/7.06 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono2__lemma,axiom,
% 6.91/7.06 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 6.91/7.06 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_unique__quotient__lemma,axiom,
% 6.91/7.06 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_q__neg__lemma,axiom,
% 6.91/7.06 ! [V_r_H,V_q_H,V_b_H] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 6.91/7.06 ! [V_n,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 6.91/7.06 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 6.91/7.06 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_DeMoivre2,axiom,
% 6.91/7.06 ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_reals__Archimedean6a,axiom,
% 6.91/7.06 ! [V_r] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
% 6.91/7.06 => ? [B_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__pos__nth__unique,axiom,
% 6.91/7.06 ! [V_a,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 6.91/7.06 => ? [B_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x))
% 6.91/7.06 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 6.91/7.06 & ! [B_y] :
% 6.91/7.06 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y))
% 6.91/7.06 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 6.91/7.06 => B_y = B_x ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__mod__rcis,axiom,
% 6.91/7.06 ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_rcis__zero__mod,axiom,
% 6.91/7.06 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_rcis__mult,axiom,
% 6.91/7.06 ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__pos__nth,axiom,
% 6.91/7.06 ! [V_a,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 6.91/7.06 => ? [B_r] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))
% 6.91/7.06 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cis__real__of__nat__Suc__mult,axiom,
% 6.91/7.06 ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_reals__Archimedean4,axiom,
% 6.91/7.06 ! [V_x,V_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => ? [B_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cis__mult,axiom,
% 6.91/7.06 ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cis__zero,axiom,
% 6.91/7.06 c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cis__rcis__eq,axiom,
% 6.91/7.06 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_DeMoivre,axiom,
% 6.91/7.06 ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__realpow,axiom,
% 6.91/7.06 ! [V_n,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__n__Re__cis__pow__n,axiom,
% 6.91/7.06 ! [V_a,V_n] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__n__Im__cis__pow__n,axiom,
% 6.91/7.06 ! [V_a,V_n] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__add,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__cos__squared__add3,axiom,
% 6.91/7.06 ! [V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__zero__abs__cos__one,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.06 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__one__sin__zero,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 6.91/7.06 => c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__zero,axiom,
% 6.91/7.06 c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__le__one,axiom,
% 6.91/7.06 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__le__one,axiom,
% 6.91/7.06 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__zero,axiom,
% 6.91/7.06 c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Im__cis,axiom,
% 6.91/7.06 ! [V_a] : hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Re__cis,axiom,
% 6.91/7.06 ! [V_a] : hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__less__cancel__iff,axiom,
% 6.91/7.06 ! [V_y_2,V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__inj__iff,axiom,
% 6.91/7.06 ! [V_y_2,V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 6.91/7.06 => ( c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2)
% 6.91/7.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__less__self,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__one,axiom,
% 6.91/7.06 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__sin__le__one,axiom,
% 6.91/7.06 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__cos__le__one,axiom,
% 6.91/7.06 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Im__rcis,axiom,
% 6.91/7.06 ! [V_a,V_r] : hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Re__rcis,axiom,
% 6.91/7.06 ! [V_a,V_r] : hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__le__cancel__iff,axiom,
% 6.91/7.06 ! [V_y_2,V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__ge__zero,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__gt__zero__imp__gt__one,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__less__zero,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__less__zero__iff,axiom,
% 6.91/7.06 ! [V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__eq__zero__iff,axiom,
% 6.91/7.06 ! [V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.06 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__gt__zero__iff,axiom,
% 6.91/7.06 ! [V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__gt__zero,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__ge__zero__imp__ge__one,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__ge__zero__iff,axiom,
% 6.91/7.06 ! [V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__mult,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 6.91/7.06 => c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_ln__add__one__self__le__self,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__arccos__abs,axiom,
% 6.91/7.06 ! [V_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.06 => c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_reals__Archimedean3,axiom,
% 6.91/7.06 ! [V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => ! [B_y] :
% 6.91/7.06 ? [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__pos__nth2,axiom,
% 6.91/7.06 ! [V_n,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 6.91/7.06 => ? [B_r] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))
% 6.91/7.06 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n)) = V_a ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__left_Obounded,axiom,
% 6.91/7.06 ! [V_y,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => ? [B_K] :
% 6.91/7.06 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__right_Obounded,axiom,
% 6.91/7.06 ! [V_x,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => ? [B_K] :
% 6.91/7.06 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult_Obounded,axiom,
% 6.91/7.06 ! [T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => ? [B_K] :
% 6.91/7.06 ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__minus__mult,axiom,
% 6.91/7.06 ! [V_x,V_n,T_a] :
% 6.91/7.06 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__1,axiom,
% 6.91/7.06 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 6.91/7.06 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__triangle__ineq3,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__iff__diff__le__0,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__triangle__ineq2,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__eq__diff__less__eq,axiom,
% 6.91/7.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add(T_a)
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__cancel,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Ogroup__add(T_a)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b) = V_a ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_add__diff__cancel,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Ogroup__add(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = V_a ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__le__self,axiom,
% 6.91/7.06 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__le__mono2,axiom,
% 6.91/7.06 ! [V_l,V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__le__mono,axiom,
% 6.91/7.06 ! [V_l,V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__diff__cancel,axiom,
% 6.91/7.06 ! [V_n,V_i] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_eq__diff__iff,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
% 6.91/7.06 <=> V_m_2 = V_n_2 ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat_Odiff__diff__eq,axiom,
% 6.91/7.06 ! [V_n,V_m,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__diff__iff,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__inverse2,axiom,
% 6.91/7.06 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n) = V_m ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__inverse,axiom,
% 6.91/7.06 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n) = V_m ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__diff__left,axiom,
% 6.91/7.06 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__cancel,axiom,
% 6.91/7.06 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__cancel2,axiom,
% 6.91/7.06 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__iff__diff__less__0,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult_Oprod__diff__prod,axiom,
% 6.91/7.06 ! [V_b,V_a,V_y,V_x,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_eq__add__iff1,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oring(T_a)
% 6.91/7.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 6.91/7.06 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_eq__add__iff2,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oring(T_a)
% 6.91/7.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 6.91/7.06 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__diff__mult,axiom,
% 6.91/7.06 ! [V_b,V_a,V_y,V_x,T_a] :
% 6.91/7.06 ( class_Rings_Oring(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__triangle__ineq2__sym,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__triangle__ineq2,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__triangle__ineq3,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__commute,axiom,
% 6.91/7.06 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__eq__diff__eq,axiom,
% 6.91/7.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oab__group__add(T_a)
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 6.91/7.06 => ( V_a_2 = V_b_2
% 6.91/7.06 <=> V_c_2 = V_d_2 ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__minus__commute,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Suc__diff__diff,axiom,
% 6.91/7.06 ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__Suc,axiom,
% 6.91/7.06 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__0__right,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Groups_Ogroup__add(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__self,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Groups_Ogroup__add(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_eq__iff__diff__eq__0,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oab__group__add(T_a)
% 6.91/7.06 => ( V_a_2 = V_b_2
% 6.91/7.06 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_right__minus__eq,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Ogroup__add(T_a)
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 <=> V_a_2 = V_b_2 ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__eq__diff__less,axiom,
% 6.91/7.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add(T_a)
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__0__eq__0,axiom,
% 6.91/7.06 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_minus__nat_Odiff__0,axiom,
% 6.91/7.06 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__self__eq__0,axiom,
% 6.91/7.06 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diffs0__imp__equal,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => V_m = V_n ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__minus__commute,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__imp__diff__less,axiom,
% 6.91/7.06 ! [V_n,V_k,V_j] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__less__mono2,axiom,
% 6.91/7.06 ! [V_l,V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__mult__distrib2,axiom,
% 6.91/7.06 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__mult__distrib,axiom,
% 6.91/7.06 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__left_Odiff,axiom,
% 6.91/7.06 ! [V_ya,V_y,V_x,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult_Odiff__left,axiom,
% 6.91/7.06 ! [V_b,V_a_H,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__right_Odiff,axiom,
% 6.91/7.06 ! [V_y,V_x,V_xa,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult_Odiff__right,axiom,
% 6.91/7.06 ! [V_b_H,V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__algebra(T_a)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__diff__right,axiom,
% 6.91/7.06 ! [V_i,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__diff__conv,axiom,
% 6.91/7.06 ! [V_i_2,V_k_2,V_j_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__add__diff,axiom,
% 6.91/7.06 ! [V_m,V_n,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__add__diff__inverse,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_add__diff__assoc,axiom,
% 6.91/7.06 ! [V_i,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__diff__conv2,axiom,
% 6.91/7.06 ! [V_i_2,V_j_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__add__diff__inverse2,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n) = V_m ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__imp__diff__is__add,axiom,
% 6.91/7.06 ! [V_k_2,V_j_2,V_i_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 6.91/7.06 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 6.91/7.06 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__assoc,axiom,
% 6.91/7.06 ! [V_i,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_add__diff__assoc2,axiom,
% 6.91/7.06 ! [V_i,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__assoc2,axiom,
% 6.91/7.06 ! [V_i,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__diff__iff,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__less__mono,axiom,
% 6.91/7.06 ! [V_c,V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__diff__conv,axiom,
% 6.91/7.06 ! [V_k_2,V_j_2,V_i_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_add__diff__inverse,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Suc__diff__le,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__is__0__eq_H,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__is__0__eq,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2] :
% 6.91/7.06 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__add__0,axiom,
% 6.91/7.06 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__less__Suc,axiom,
% 6.91/7.06 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__less,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zero__less__diff,axiom,
% 6.91/7.06 ! [V_m_2,V_n_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__add__iff2,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__add__iff1,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__add__iff2,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__add__iff1,axiom,
% 6.91/7.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 6.91/7.06 ( class_Rings_Oordered__ring(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_real__squared__diff__one__factored,axiom,
% 6.91/7.06 ! [V_x,T_a] :
% 6.91/7.06 ( class_Rings_Oring__1(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__triangle__ineq4,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__diff__triangle__ineq,axiom,
% 6.91/7.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_abs__diff__less__iff,axiom,
% 6.91/7.06 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 6.91/7.06 ( class_Rings_Olinordered__idom(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))
% 6.91/7.06 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__triangle__ineq4,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Suc__pred,axiom,
% 6.91/7.06 ! [V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__less,axiom,
% 6.91/7.06 ! [V_i,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__diff__split__asm,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,V_P_2] :
% 6.91/7.06 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 6.91/7.06 <=> ~ ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))
% 6.91/7.06 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 6.91/7.06 | ? [B_d] :
% 6.91/7.06 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 6.91/7.06 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__diff__split,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2,V_P_2] :
% 6.91/7.06 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 6.91/7.06 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))
% 6.91/7.06 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 6.91/7.06 & ! [B_d] :
% 6.91/7.06 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 6.91/7.06 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__diff__eq2,axiom,
% 6.91/7.06 ! [V_m,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_diff__Suc__diff__eq1,axiom,
% 6.91/7.06 ! [V_m,V_j,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__eq__add__iff2,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 6.91/7.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 6.91/7.06 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__diff__add__eq2,axiom,
% 6.91/7.06 ! [V_n,V_m,V_u,V_j,V_i] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__le__add__iff2,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__eq__add__iff1,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 6.91/7.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 6.91/7.06 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__diff__add__eq1,axiom,
% 6.91/7.06 ! [V_n,V_m,V_u,V_i,V_j] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i))
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__le__add__iff1,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__diff__triangle__ineq,axiom,
% 6.91/7.06 ! [V_d,V_c,V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_lemma__realpow__diff,axiom,
% 6.91/7.06 ! [V_y,V_n,V_p,T_a] :
% 6.91/7.06 ( class_Groups_Omonoid__mult(T_a)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p),V_n))
% 6.91/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Suc__pred_H,axiom,
% 6.91/7.06 ! [V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Suc__diff__1,axiom,
% 6.91/7.06 ! [V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_add__eq__if,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 6.91/7.06 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__less__add__iff1,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__less__add__iff2,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_mult__eq__if,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 6.91/7.06 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_power__eq__if,axiom,
% 6.91/7.06 ! [V_p,V_m] :
% 6.91/7.06 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 6.91/7.06 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__two__diff,axiom,
% 6.91/7.06 ! [V_y,V_x,T_a] :
% 6.91/7.06 ( class_Rings_Ocomm__ring__1(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_realpow__num__eq__if,axiom,
% 6.91/7.06 ! [V_m,V_n,T_a] :
% 6.91/7.06 ( class_Power_Opower(T_a)
% 6.91/7.06 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 6.91/7.06 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_reals__Archimedean6,axiom,
% 6.91/7.06 ! [V_r] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
% 6.91/7.06 => ? [B_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_lemmaCauchy,axiom,
% 6.91/7.06 ! [V_X_2,V_M_2,T_a,T_b] :
% 6.91/7.06 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 6.91/7.06 & class_Orderings_Oord(T_a) )
% 6.91/7.06 => ( ! [B_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
% 6.91/7.06 => ! [B_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_real__le__eq__diff,axiom,
% 6.91/7.06 ! [V_y_2,V_x_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Im_Odiff,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Re_Odiff,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiff__zmult__distrib2,axiom,
% 6.91/7.06 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiff__zmult__distrib,axiom,
% 6.91/7.06 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_less__bin__lemma,axiom,
% 6.91/7.06 ! [V_l_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_norm__diff__ineq,axiom,
% 6.91/7.06 ! [V_b,V_a,T_a] :
% 6.91/7.06 ( class_RealVector_Oreal__normed__vector(T_a)
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_metric__bound__lemma,axiom,
% 6.91/7.06 ! [V_y,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zle__diff1__eq,axiom,
% 6.91/7.06 ! [V_z_2,V_w_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_real__of__nat__diff,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.06 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__diff,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_sin__diff2,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__mod__triangle__ineq2,axiom,
% 6.91/7.06 ! [V_a,V_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__add,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__diff,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__diff2,axiom,
% 6.91/7.06 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_natfloor__subtract,axiom,
% 6.91/7.06 ! [V_x,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))
% 6.91/7.06 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_real__natfloor__gt__diff__one,axiom,
% 6.91/7.06 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_natceiling__subtract,axiom,
% 6.91/7.06 ! [V_x,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))
% 6.91/7.06 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__Re__mult,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_decr__lemma,axiom,
% 6.91/7.06 ! [V_z,V_x,V_d] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_incr__lemma,axiom,
% 6.91/7.06 ! [V_x,V_z,V_d] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_unimodular__reduce__norm,axiom,
% 6.91/7.06 ! [V_z] :
% 6.91/7.06 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.06 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.06 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 6.91/7.06 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_tsub__def,axiom,
% 6.91/7.06 ! [V_x,V_y] :
% 6.91/7.06 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 6.91/7.06 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 6.91/7.06 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 6.91/7.06 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__Re__i,axiom,
% 6.91/7.06 hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__i__not__zero,axiom,
% 6.91/7.06 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__i__not__one,axiom,
% 6.91/7.06 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__Im__i,axiom,
% 6.91/7.06 hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_tsub__eq,axiom,
% 6.91/7.06 ! [V_x,V_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 6.91/7.06 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_int__power__div__base,axiom,
% 6.91/7.06 ! [V_k,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Deriv_Oadd__diff__add,axiom,
% 6.91/7.06 ! [V_d,V_b,V_c,V_a,T_a] :
% 6.91/7.06 ( class_Groups_Oab__group__add(T_a)
% 6.91/7.06 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_int__div__less__self,axiom,
% 6.91/7.06 ! [V_k,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__zmult2__eq,axiom,
% 6.91/7.06 ! [V_b,V_a,V_c] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__mult1__if,axiom,
% 6.91/7.06 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 6.91/7.06 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self2__is__id,axiom,
% 6.91/7.06 ! [V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self1__is__id,axiom,
% 6.91/7.06 ! [V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__mult2,axiom,
% 6.91/7.06 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__mult1,axiom,
% 6.91/7.06 ! [V_b,V_a,V_c,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__self,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__zero,axiom,
% 6.91/7.06 ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__by__0,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__0,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__neg__pos__less0,axiom,
% 6.91/7.06 ! [V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 6.91/7.06 ! [V_a_2,V_b_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 6.91/7.06 ! [V_a_2,V_b_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__self,axiom,
% 6.91/7.06 ! [V_a] :
% 6.91/7.06 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__by__1,axiom,
% 6.91/7.06 ! [V_a,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono1__neg,axiom,
% 6.91/7.06 ! [V_b,V_a_H,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono1,axiom,
% 6.91/7.06 ! [V_b,V_a_H,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__neg__neg__trivial,axiom,
% 6.91/7.06 ! [V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono2__neg,axiom,
% 6.91/7.06 ! [V_b,V_b_H,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__nonpos__pos__le0,axiom,
% 6.91/7.06 ! [V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 6.91/7.06 ! [V_a_2,V_b_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__pos__pos__trivial,axiom,
% 6.91/7.06 ! [V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__nonneg__neg__le0,axiom,
% 6.91/7.06 ! [V_b,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__mono2,axiom,
% 6.91/7.06 ! [V_b,V_b_H,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 6.91/7.06 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 6.91/7.06 ! [V_i_2,V_k_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 6.91/7.06 ! [V_a_2,V_b_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 6.91/7.06 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_zdiv__eq__0__iff,axiom,
% 6.91/7.06 ! [V_k_2,V_i_2] :
% 6.91/7.06 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.06 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.06 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)) )
% 6.91/7.06 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self2,axiom,
% 6.91/7.06 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self1,axiom,
% 6.91/7.06 ! [V_c,V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__add__self2,axiom,
% 6.91/7.06 ! [V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__add__self1,axiom,
% 6.91/7.06 ! [V_a,V_b,T_a] :
% 6.91/7.06 ( class_Divides_Osemiring__div(T_a)
% 6.91/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_split__zdiv,axiom,
% 6.91/7.06 ! [V_k_2,V_n_2,V_P_2] :
% 6.91/7.06 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
% 6.91/7.06 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.06 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 6.91/7.06 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 6.91/7.06 => ! [B_i] :
% 6.91/7.06 ( ? [B_j] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))
% 6.91/7.06 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 6.91/7.06 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 6.91/7.06 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 => ! [B_i] :
% 6.91/7.06 ( ? [B_j] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 6.91/7.06 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 6.91/7.06 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_divmod__int__rel__div__eq,axiom,
% 6.91/7.06 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 6.91/7.06 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 6.91/7.06 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1)) ) )
% 6.91/7.06 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 6.91/7.06 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__mult__def,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_lemma__interval,axiom,
% 6.91/7.06 ! [V_b,V_x,V_a] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_b))
% 6.91/7.06 => ? [B_d] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_d))
% 6.91/7.06 & ! [B_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y))),B_d))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b)) ) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult2__eq,axiom,
% 6.91/7.06 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__less,axiom,
% 6.91/7.06 ! [V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__1,axiom,
% 6.91/7.06 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__le__dividend,axiom,
% 6.91/7.06 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__le__mono,axiom,
% 6.91/7.06 ! [V_k,V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__mult__div__cancel__disj,axiom,
% 6.91/7.06 ! [V_n,V_m,V_k] :
% 6.91/7.06 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 6.91/7.06 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__less__dividend,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self__is__m,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__mult__self1__is__m,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_nat__mult__div__cancel1,axiom,
% 6.91/7.06 ! [V_n,V_m,V_k] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__le__mono2,axiom,
% 6.91/7.06 ! [V_k,V_n,V_m] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__diff,axiom,
% 6.91/7.06 ! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__surj,axiom,
% 6.91/7.06 ! [V_z] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z)) = V_z ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex_Oinject,axiom,
% 6.91/7.06 ! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
% 6.91/7.06 ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
% 6.91/7.06 <=> ( V_real1_2 = V_real1_H_2
% 6.91/7.06 & V_real2_2 = V_real2_H_2 ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Im,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Re,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__add,axiom,
% 6.91/7.06 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Complex__eq__0,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2] :
% 6.91/7.06 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 6.91/7.06 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.06 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__zero__def,axiom,
% 6.91/7.06 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Complex__eq__i,axiom,
% 6.91/7.06 ! [V_y_2,V_x_2] :
% 6.91/7.06 ( c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii
% 6.91/7.06 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.06 & V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_i__def,axiom,
% 6.91/7.06 c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_Complex__eq__1,axiom,
% 6.91/7.06 ! [V_b_2,V_a_2] :
% 6.91/7.06 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
% 6.91/7.06 <=> ( V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 6.91/7.06 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__one__def,axiom,
% 6.91/7.06 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cis__def,axiom,
% 6.91/7.06 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__geq,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_div__if,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 6.91/7.06 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_split__div,axiom,
% 6.91/7.06 ! [V_k_2,V_n_2,V_P_2] :
% 6.91/7.06 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
% 6.91/7.06 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 6.91/7.06 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 => ! [B_i,B_j] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))
% 6.91/7.06 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 6.91/7.06 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__mult,axiom,
% 6.91/7.06 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cmod__unit__one,axiom,
% 6.91/7.06 ! [V_a] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex__add__def,axiom,
% 6.91/7.06 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_split__div_H,axiom,
% 6.91/7.06 ! [V_n_2,V_m_2,V_P_2] :
% 6.91/7.06 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
% 6.91/7.06 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 6.91/7.06 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 6.91/7.06 | ? [B_q] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))
% 6.91/7.06 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_split__div__lemma,axiom,
% 6.91/7.06 ! [V_m_2,V_q_2,V_n_2] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 6.91/7.06 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))
% 6.91/7.06 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))) )
% 6.91/7.06 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_le__div__geq,axiom,
% 6.91/7.06 ! [V_m,V_n] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 6.91/7.06 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex_Osize_I1_J,axiom,
% 6.91/7.06 ! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__arg__i__mult__zero__pos,axiom,
% 6.91/7.06 ! [V_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 6.91/7.06 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__arg__i__mult__zero,axiom,
% 6.91/7.06 ! [V_y] :
% 6.91/7.06 ( V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 6.91/7.06 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_cos__arg__i__mult__zero__neg,axiom,
% 6.91/7.06 ! [V_y] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 6.91/7.06 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex_Osize_I2_J,axiom,
% 6.91/7.06 ! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex_Orecs,axiom,
% 6.91/7.06 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_complex_Osimps_I2_J,axiom,
% 6.91/7.06 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_natfloor__div__nat,axiom,
% 6.91/7.06 ! [V_y,V_x] :
% 6.91/7.06 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 6.91/7.06 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))
% 6.91/7.06 => c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 6.91/7.06
% 6.91/7.06 fof(fact_real__sgn__eq,axiom,
% 7.14/7.06 ! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide_Oadd,axiom,
% 7.14/7.06 ! [V_ya,V_y,V_x,T_a] :
% 7.14/7.06 ( class_RealVector_Oreal__normed__field(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_add__divide__distrib,axiom,
% 7.14/7.06 ! [V_c,V_b,V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__1,axiom,
% 7.14/7.06 ! [V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_right__inverse__eq,axiom,
% 7.14/7.06 ! [V_a_2,V_b_2,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 7.14/7.06 <=> V_a_2 = V_b_2 ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__self,axiom,
% 7.14/7.06 ! [V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__self__if,axiom,
% 7.14/7.06 ! [V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 7.14/7.06 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 7.14/7.06 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_nonzero__power__divide,axiom,
% 7.14/7.06 ! [V_n,V_a,V_b,T_a] :
% 7.14/7.06 ( class_Fields_Ofield(T_a)
% 7.14/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_power__one__over,axiom,
% 7.14/7.06 ! [V_n,V_a,T_a] :
% 7.14/7.06 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide_Oconvergent,axiom,
% 7.14/7.06 ! [V_y_2,V_X_2,T_a] :
% 7.14/7.06 ( class_RealVector_Oreal__normed__field(T_a)
% 7.14/7.06 => ( c_SEQ_Oconvergent(T_a,V_X_2)
% 7.14/7.06 => c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_y_2)) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_norm__divide,axiom,
% 7.14/7.06 ! [V_b,V_a,T_a] :
% 7.14/7.06 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.14/7.06 & class_RealVector_Oreal__normed__field(T_a) )
% 7.14/7.06 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_eq__divide__imp,axiom,
% 7.14/7.06 ! [V_b,V_a,V_c,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 7.14/7.06 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__eq__imp,axiom,
% 7.14/7.06 ! [V_a,V_b,V_c,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_nonzero__divide__eq__eq,axiom,
% 7.14/7.06 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
% 7.14/7.06 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_nonzero__eq__divide__eq,axiom,
% 7.14/7.06 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 7.14/7.06 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_nonzero__norm__divide,axiom,
% 7.14/7.06 ! [V_a,V_b,T_a] :
% 7.14/7.06 ( class_RealVector_Oreal__normed__field(T_a)
% 7.14/7.06 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.06 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide_Ozero,axiom,
% 7.14/7.06 ! [V_y,T_a] :
% 7.14/7.06 ( class_RealVector_Oreal__normed__field(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__zero__left,axiom,
% 7.14/7.06 ! [V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_divide__zero,axiom,
% 7.14/7.06 ! [V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_times__divide__eq__right,axiom,
% 7.14/7.06 ! [V_c,V_b,V_a,T_a] :
% 7.14/7.06 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_real__divide__square__eq,axiom,
% 7.14/7.06 ! [V_a,V_r] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a),V_r) ).
% 7.14/7.06
% 7.14/7.06 fof(fact_power__divide,axiom,
% 7.14/7.07 ! [V_n,V_b,V_a,T_a] :
% 7.14/7.07 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.14/7.07 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_real__0__le__divide__iff,axiom,
% 7.14/7.07 ! [V_y_2,V_x_2] :
% 7.14/7.07 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x_2),V_y_2)))
% 7.14/7.07 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 7.14/7.07 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) )
% 7.14/7.07 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 7.14/7.07 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_Im__sgn,axiom,
% 7.14/7.07 ! [V_z] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_Re__sgn,axiom,
% 7.14/7.07 ! [V_z] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_divide_Odiff,axiom,
% 7.14/7.07 ! [V_ya,V_y,V_x,T_a] :
% 7.14/7.07 ( class_RealVector_Oreal__normed__field(T_a)
% 7.14/7.07 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_diff__divide__distrib,axiom,
% 7.14/7.07 ! [V_c,V_b,V_a,T_a] :
% 7.14/7.07 ( class_Rings_Odivision__ring(T_a)
% 7.14/7.07 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_c) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_DERIV__mult__lemma,axiom,
% 7.14/7.07 ! [V_h,V_d,V_c,V_b,V_a,T_a] :
% 7.14/7.07 ( class_RealVector_Oreal__field(T_a)
% 7.14/7.07 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),V_h)),V_d)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_lemma__MVT,axiom,
% 7.14/7.07 ! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_real__of__nat__div4,axiom,
% 7.14/7.07 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)))) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_power__diff,axiom,
% 7.14/7.07 ! [V_m,V_n,V_a,T_a] :
% 7.14/7.07 ( class_Fields_Ofield(T_a)
% 7.14/7.07 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 7.14/7.07 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_ln__div,axiom,
% 7.14/7.07 ! [V_y,V_x] :
% 7.14/7.07 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 7.14/7.07 => c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)) ) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_real__of__nat__div2,axiom,
% 7.14/7.07 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_real__of__nat__div3,axiom,
% 7.14/7.07 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_divide__left__mono__neg,axiom,
% 7.14/7.07 ! [V_c,V_b,V_a,T_a] :
% 7.14/7.07 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 7.14/7.07 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_divide__left__mono,axiom,
% 7.14/7.07 ! [V_c,V_a,V_b,T_a] :
% 7.14/7.07 ( class_Fields_Olinordered__field(T_a)
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 7.14/7.07 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 7.14/7.07 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 7.14/7.07
% 7.14/7.07 fof(fact_cis__divide,axiom,
% 7.14/7.07 ! [V_b,V_a] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b)) ).
% 7.14/7.07
% 7.14/7.07 %----Arity declarations (267)
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Oidom(T_1)
% 7.14/7.07 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__ring(T_1)
% 7.14/7.07 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 7.14/7.07 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 7.14/7.07 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 7.14/7.07 class_Rings_Oidom(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_fun__Orderings_Opreorder,axiom,
% 7.14/7.07 ! [T_2,T_1] :
% 7.14/7.07 ( class_Orderings_Opreorder(T_1)
% 7.14/7.07 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_fun__Orderings_Oorder,axiom,
% 7.14/7.07 ! [T_2,T_1] :
% 7.14/7.07 ( class_Orderings_Oorder(T_1)
% 7.14/7.07 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_fun__Orderings_Oord,axiom,
% 7.14/7.07 ! [T_2,T_1] :
% 7.14/7.07 ( class_Orderings_Oord(T_1)
% 7.14/7.07 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.14/7.07 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 7.14/7.07 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 7.14/7.07 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 7.14/7.07 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 7.14/7.07 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 7.14/7.07 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 7.14/7.07 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 7.14/7.07 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 7.14/7.07 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 7.14/7.07 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 7.14/7.07 class_Orderings_Opreorder(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 7.14/7.07 class_Orderings_Olinorder(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 7.14/7.07 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 7.14/7.07 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 7.14/7.07 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 7.14/7.07 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 7.14/7.07 class_Rings_Omult__zero(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 7.14/7.07 class_Orderings_Oorder(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 7.14/7.07 class_Rings_Osemiring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 7.14/7.07 class_Orderings_Oord(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 7.14/7.07 class_Groups_Osgn__if(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 7.14/7.07 class_Rings_Oring__1(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Power_Opower,axiom,
% 7.14/7.07 class_Power_Opower(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 7.14/7.07 class_Groups_Ozero(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Rings_Oring,axiom,
% 7.14/7.07 class_Rings_Oring(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Int__Oint__Groups_Oone,axiom,
% 7.14/7.07 class_Groups_Oone(tc_Int_Oint) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.14/7.07 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 7.14/7.07 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 7.14/7.07 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 7.14/7.07 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 7.14/7.07 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 7.14/7.07 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 7.14/7.07 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 7.14/7.07 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 7.14/7.07 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 7.14/7.07 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 7.14/7.07 class_Orderings_Oorder(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 7.14/7.07 class_Rings_Osemiring(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 7.14/7.07 class_Orderings_Oord(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Power_Opower,axiom,
% 7.14/7.07 class_Power_Opower(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 7.14/7.07 class_Groups_Ozero(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 7.14/7.07 class_Groups_Oone(tc_Nat_Onat) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 7.14/7.07 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 7.14/7.07 class_Orderings_Oorder(tc_HOL_Obool) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 7.14/7.07 class_Orderings_Oord(tc_HOL_Obool) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.14/7.07 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 7.14/7.07 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 7.14/7.07 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 7.14/7.07 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 7.14/7.07 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 7.14/7.07 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 7.14/7.07 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 7.14/7.07 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 7.14/7.07 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Ometric__space,axiom,
% 7.14/7.07 class_RealVector_Ometric__space(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 7.14/7.07 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 7.14/7.07 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 7.14/7.07 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 7.14/7.07 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 7.14/7.07 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__RealVector_Oreal__field,axiom,
% 7.14/7.07 class_RealVector_Oreal__field(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 7.14/7.07 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 7.14/7.07 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 7.14/7.07 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 7.14/7.07 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 7.14/7.07 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 7.14/7.07 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 7.14/7.07 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 7.14/7.07 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 7.14/7.07 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 7.14/7.07 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 7.14/7.07 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 7.14/7.07 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 7.14/7.07 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 7.14/7.07 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 7.14/7.07 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 7.14/7.07 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 7.14/7.07 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 7.14/7.07 class_Power_Opower(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 7.14/7.07 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 7.14/7.07 class_Rings_Oring(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 7.14/7.07 class_Groups_Oone(tc_RealDef_Oreal) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.14/7.07 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 7.14/7.07 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 7.14/7.07 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 7.14/7.07 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
% 7.14/7.07 class_RealVector_Ometric__space(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 7.14/7.07 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 7.14/7.07 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 7.14/7.07 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
% 7.14/7.07 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 7.14/7.07 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 7.14/7.07 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 7.14/7.07 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 7.14/7.07 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 7.14/7.07 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 7.14/7.07 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 7.14/7.07 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 7.14/7.07 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 7.14/7.07 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 7.14/7.07 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 7.14/7.07 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 7.14/7.07 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 7.14/7.07 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 7.14/7.07 class_Power_Opower(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 7.14/7.07 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 7.14/7.07 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 7.14/7.07 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Oidom(T_1)
% 7.14/7.07 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Oidom(T_1)
% 7.14/7.07 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Oidom(T_1)
% 7.14/7.07 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocomm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Oidom(T_1)
% 7.14/7.07 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocomm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Fields_Ofield(T_1)
% 7.14/7.07 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Oab__group__add(T_1)
% 7.14/7.07 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__ring__1(T_1)
% 7.14/7.07 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ocomm__monoid__add(T_1)
% 7.14/7.07 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Oab__group__add(T_1)
% 7.14/7.07 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__0(T_1)
% 7.14/7.07 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Olinordered__idom(T_1)
% 7.14/7.07 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__ring__1(T_1)
% 7.14/7.07 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Groups_Ozero(T_1)
% 7.14/7.07 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__ring(T_1)
% 7.14/7.07 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 7.14/7.07 ! [T_1] :
% 7.14/7.07 ( class_Rings_Ocomm__semiring__1(T_1)
% 7.14/7.07 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 7.14/7.07
% 7.14/7.07 %----Helper facts (4)
% 7.14/7.07 fof(help_c__COMBK__1,axiom,
% 7.14/7.07 ! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P ).
% 7.14/7.07
% 7.14/7.07 fof(help_c__COMBB__1,axiom,
% 7.14/7.07 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 7.14/7.07
% 7.14/7.07 fof(help_c__COMBC__1,axiom,
% 7.14/7.07 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 7.14/7.07
% 7.14/7.07 fof(help_c__COMBS__1,axiom,
% 7.14/7.07 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 7.14/7.07
% 7.14/7.07 %----Conjectures (1)
% 7.14/7.07 fof(conj_0,conjecture,
% 7.14/7.07 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 7.14/7.07 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ) ).
% 7.14/7.07
% 7.14/7.07 %------------------------------------------------------------------------------
% 7.14/7.07 %-------------------------------------------
% 7.14/7.07 % Proof found
% 7.14/7.07 % SZS status Theorem for theBenchmark
% 7.14/7.07 % SZS output start Proof
% 7.14/7.07 %ClaNum:1974(EqnAxiom:310)
% 7.14/7.07 %VarNum:8907(SingletonVarNum:3145)
% 7.14/7.07 %MaxLitNum:7
% 7.14/7.07 %MaxfuncDepth:7
% 7.14/7.07 %SharedTerms:369
% 7.14/7.07 %goalClause: 1942
% 7.14/7.07 [311]P1(a1)
% 7.14/7.07 [312]P1(a122)
% 7.14/7.07 [313]P1(a2)
% 7.14/7.07 [314]P7(a82)
% 7.14/7.07 [315]P7(a83)
% 7.14/7.07 [316]P7(a84)
% 7.14/7.07 [317]P8(a82)
% 7.14/7.07 [318]P8(a83)
% 7.14/7.07 [319]P8(a84)
% 7.14/7.07 [320]P9(a82)
% 7.14/7.07 [321]P9(a84)
% 7.14/7.07 [322]P32(a82)
% 7.14/7.07 [323]P32(a85)
% 7.14/7.07 [324]P32(a83)
% 7.14/7.07 [325]P32(a84)
% 7.14/7.07 [326]P34(a82)
% 7.14/7.07 [327]P34(a84)
% 7.14/7.07 [328]P10(a82)
% 7.14/7.07 [329]P10(a85)
% 7.14/7.07 [330]P10(a83)
% 7.14/7.07 [331]P10(a84)
% 7.14/7.07 [332]P11(a82)
% 7.14/7.07 [333]P11(a85)
% 7.14/7.07 [334]P11(a83)
% 7.14/7.07 [335]P11(a84)
% 7.14/7.07 [336]P12(a82)
% 7.14/7.07 [337]P12(a85)
% 7.14/7.07 [338]P12(a83)
% 7.14/7.07 [339]P12(a84)
% 7.14/7.07 [340]P21(a82)
% 7.14/7.07 [341]P21(a85)
% 7.14/7.07 [342]P21(a83)
% 7.14/7.07 [343]P21(a84)
% 7.14/7.07 [344]P22(a82)
% 7.14/7.07 [345]P22(a85)
% 7.14/7.07 [346]P22(a83)
% 7.14/7.07 [347]P22(a84)
% 7.14/7.07 [348]P23(a82)
% 7.14/7.07 [349]P23(a85)
% 7.14/7.07 [350]P23(a83)
% 7.14/7.07 [351]P23(a84)
% 7.14/7.07 [352]P24(a82)
% 7.14/7.07 [353]P24(a84)
% 7.14/7.07 [354]P29(a82)
% 7.14/7.07 [355]P29(a83)
% 7.14/7.07 [356]P29(a84)
% 7.14/7.07 [357]P30(a82)
% 7.14/7.07 [358]P30(a83)
% 7.14/7.07 [359]P30(a84)
% 7.14/7.07 [360]P31(a82)
% 7.14/7.07 [361]P31(a83)
% 7.14/7.07 [362]P31(a84)
% 7.14/7.07 [363]P58(a82)
% 7.14/7.07 [364]P58(a85)
% 7.14/7.07 [365]P58(a83)
% 7.14/7.07 [366]P58(a84)
% 7.14/7.07 [367]P35(a82)
% 7.14/7.07 [368]P35(a85)
% 7.14/7.07 [369]P36(a82)
% 7.14/7.07 [370]P36(a85)
% 7.14/7.07 [371]P37(a82)
% 7.14/7.07 [372]P37(a83)
% 7.14/7.07 [373]P37(a84)
% 7.14/7.07 [374]P37(a119)
% 7.14/7.07 [375]P38(a82)
% 7.14/7.07 [376]P38(a83)
% 7.14/7.07 [377]P38(a84)
% 7.14/7.07 [378]P38(a119)
% 7.14/7.07 [379]P39(a82)
% 7.14/7.07 [380]P39(a83)
% 7.14/7.07 [381]P39(a84)
% 7.14/7.07 [382]P40(a82)
% 7.14/7.07 [383]P40(a83)
% 7.14/7.07 [384]P40(a84)
% 7.14/7.07 [385]P40(a119)
% 7.14/7.07 [386]P47(a82)
% 7.14/7.07 [387]P47(a85)
% 7.14/7.07 [388]P47(a83)
% 7.14/7.07 [389]P47(a84)
% 7.14/7.07 [390]P76(a82)
% 7.14/7.07 [391]P76(a85)
% 7.14/7.07 [392]P76(a83)
% 7.14/7.07 [393]P76(a84)
% 7.14/7.07 [394]P59(a82)
% 7.14/7.07 [395]P59(a84)
% 7.14/7.07 [396]P45(a82)
% 7.14/7.07 [397]P45(a85)
% 7.14/7.07 [398]P19(a82)
% 7.14/7.07 [399]P19(a85)
% 7.14/7.07 [400]P19(a83)
% 7.14/7.07 [401]P19(a84)
% 7.14/7.07 [402]P41(a82)
% 7.14/7.07 [403]P41(a85)
% 7.14/7.07 [404]P62(a82)
% 7.14/7.07 [405]P62(a85)
% 7.14/7.07 [406]P62(a83)
% 7.14/7.07 [407]P62(a84)
% 7.14/7.07 [408]P65(a82)
% 7.14/7.07 [409]P65(a85)
% 7.14/7.07 [410]P65(a84)
% 7.14/7.07 [411]P63(a82)
% 7.14/7.07 [412]P63(a85)
% 7.14/7.07 [413]P63(a83)
% 7.14/7.07 [414]P63(a84)
% 7.14/7.07 [415]P74(a82)
% 7.14/7.07 [416]P74(a85)
% 7.14/7.07 [417]P74(a83)
% 7.14/7.07 [418]P74(a84)
% 7.14/7.07 [419]P48(a82)
% 7.14/7.07 [420]P48(a85)
% 7.14/7.07 [421]P48(a83)
% 7.14/7.07 [422]P48(a84)
% 7.14/7.07 [423]P25(a82)
% 7.14/7.07 [424]P25(a85)
% 7.14/7.07 [425]P25(a83)
% 7.14/7.07 [426]P25(a84)
% 7.14/7.07 [427]P27(a82)
% 7.14/7.07 [428]P27(a85)
% 7.14/7.07 [429]P27(a83)
% 7.14/7.07 [430]P27(a84)
% 7.14/7.07 [431]P33(a82)
% 7.14/7.07 [432]P33(a84)
% 7.14/7.07 [433]P66(a82)
% 7.14/7.07 [434]P66(a83)
% 7.14/7.07 [435]P66(a84)
% 7.14/7.07 [436]P67(a82)
% 7.14/7.07 [437]P67(a84)
% 7.14/7.07 [438]P69(a82)
% 7.14/7.07 [439]P69(a83)
% 7.14/7.07 [440]P69(a84)
% 7.14/7.07 [441]P68(a82)
% 7.14/7.07 [442]P68(a83)
% 7.14/7.07 [443]P68(a84)
% 7.14/7.07 [444]P56(a82)
% 7.14/7.07 [445]P56(a84)
% 7.14/7.07 [446]P57(a82)
% 7.14/7.07 [447]P57(a84)
% 7.14/7.07 [448]P52(a82)
% 7.14/7.07 [449]P52(a83)
% 7.14/7.07 [450]P52(a84)
% 7.14/7.07 [451]P64(a82)
% 7.14/7.07 [452]P64(a83)
% 7.14/7.07 [453]P64(a84)
% 7.14/7.07 [454]P60(a82)
% 7.14/7.07 [455]P60(a83)
% 7.14/7.07 [456]P60(a84)
% 7.14/7.07 [457]P70(a82)
% 7.14/7.07 [458]P70(a84)
% 7.14/7.07 [459]P61(a82)
% 7.14/7.07 [460]P61(a84)
% 7.14/7.07 [461]P42(a82)
% 7.14/7.07 [462]P42(a85)
% 7.14/7.07 [463]P71(a82)
% 7.14/7.07 [464]P71(a85)
% 7.14/7.07 [465]P71(a84)
% 7.14/7.07 [466]P43(a82)
% 7.14/7.07 [467]P43(a85)
% 7.14/7.07 [468]P43(a83)
% 7.14/7.07 [469]P43(a84)
% 7.14/7.07 [470]P75(a82)
% 7.14/7.07 [471]P75(a85)
% 7.14/7.07 [472]P75(a83)
% 7.14/7.07 [473]P75(a84)
% 7.14/7.07 [474]P28(a82)
% 7.14/7.07 [475]P28(a84)
% 7.14/7.07 [476]P26(a82)
% 7.14/7.07 [477]P26(a85)
% 7.14/7.07 [478]P26(a84)
% 7.14/7.07 [479]P72(a82)
% 7.14/7.07 [480]P72(a85)
% 7.14/7.07 [481]P72(a84)
% 7.14/7.07 [482]P13(a82)
% 7.14/7.07 [483]P13(a85)
% 7.14/7.07 [484]P13(a84)
% 7.14/7.07 [485]P73(a82)
% 7.14/7.07 [486]P73(a85)
% 7.14/7.07 [487]P73(a84)
% 7.14/7.07 [488]P49(a82)
% 7.14/7.07 [489]P49(a85)
% 7.14/7.07 [490]P49(a84)
% 7.14/7.07 [491]P14(a83)
% 7.14/7.07 [492]P14(a84)
% 7.14/7.07 [493]P46(a82)
% 7.14/7.07 [494]P46(a85)
% 7.14/7.07 [495]P53(a82)
% 7.14/7.07 [496]P53(a85)
% 7.14/7.07 [497]P54(a82)
% 7.14/7.07 [498]P54(a85)
% 7.14/7.07 [499]P15(a82)
% 7.14/7.07 [500]P15(a85)
% 7.14/7.07 [501]P16(a82)
% 7.14/7.07 [502]P16(a85)
% 7.14/7.07 [503]P44(a82)
% 7.14/7.07 [504]P44(a85)
% 7.14/7.07 [505]P17(a82)
% 7.14/7.07 [506]P18(a82)
% 7.14/7.07 [507]P55(a82)
% 7.14/7.07 [508]P55(a85)
% 7.14/7.07 [509]P55(a84)
% 7.14/7.07 [510]P20(a82)
% 7.14/7.07 [511]P20(a85)
% 7.14/7.07 [512]P20(a83)
% 7.14/7.07 [513]P20(a84)
% 7.14/7.07 [514]P51(a82)
% 7.14/7.07 [515]P51(a85)
% 7.14/7.07 [516]P51(a83)
% 7.14/7.07 [517]P51(a84)
% 7.14/7.07 [518]P50(a82)
% 7.14/7.07 [519]P50(a85)
% 7.14/7.07 [520]P50(a84)
% 7.14/7.07 [527]E(f86(a5,a17),f16(a82))
% 7.14/7.07 [528]E(f86(a10,a17),f3(a82))
% 7.14/7.07 [722]~E(f3(a85),a17)
% 7.14/7.07 [723]~E(f16(a85),a17)
% 7.14/7.07 [724]~E(f16(a82),f3(a82))
% 7.14/7.07 [725]~E(f16(a84),f3(a84))
% 7.14/7.07 [521]E(f4(f3(a85)),f16(a85))
% 7.14/7.07 [522]E(f26(f3(a82)),f3(a83))
% 7.14/7.07 [523]E(f26(f16(a82)),f16(a83))
% 7.14/7.07 [524]E(f33(f3(a82)),f3(a83))
% 7.14/7.07 [525]E(f33(f16(a82)),f16(a83))
% 7.14/7.07 [526]E(f34(f16(a82)),f3(a82))
% 7.14/7.07 [529]E(f86(a5,f3(a85)),f3(a82))
% 7.14/7.07 [530]E(f86(a5,f16(a85)),f3(a82))
% 7.14/7.07 [531]E(f86(a10,f3(a85)),f3(a82))
% 7.14/7.07 [532]E(f86(a10,f16(a85)),f16(a82))
% 7.14/7.07 [533]E(f35(a83,f3(a83)),f3(a82))
% 7.14/7.07 [534]E(f35(a83,f16(a83)),f16(a82))
% 7.14/7.07 [536]E(f11(f3(a82),f16(a82)),a17)
% 7.14/7.07 [537]E(f11(f3(a82),f3(a82)),f3(a85))
% 7.14/7.07 [538]E(f11(f16(a82),f3(a82)),f16(a85))
% 7.14/7.07 [539]E(f18(f16(a82),f3(a82)),f16(a85))
% 7.14/7.07 [585]P77(f86(f28(a84,f3(a84)),f16(a84)))
% 7.14/7.07 [586]P77(f86(f29(a84,f3(a84)),f16(a84)))
% 7.14/7.07 [717]P2(a82,f7(a85,a82,a83,a10,f7(a83,a85,a83,a124,a1)))
% 7.14/7.07 [718]P3(a82,f7(a85,a82,a83,a10,f7(a83,a85,a83,a124,a1)))
% 7.14/7.07 [559]E(f86(a5,f18(f16(a82),f3(a82))),f3(a82))
% 7.14/7.07 [560]E(f86(a10,f18(f16(a82),f3(a82))),f16(a82))
% 7.14/7.07 [572]P77(f86(f28(a82,f3(a82)),a123))
% 7.14/7.07 [573]P77(f86(f28(a82,f3(a82)),a39))
% 7.14/7.07 [574]P77(f86(f28(a82,f3(a82)),a44))
% 7.14/7.07 [575]P77(f86(f29(a82,f3(a82)),a40))
% 7.14/7.07 [576]P77(f86(f29(a82,f3(a82)),a43))
% 7.14/7.07 [594]E(f35(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f16(a82))
% 7.14/7.07 [720]P2(a82,f7(a85,a82,a83,a5,f7(a83,a85,a83,a124,f7(a83,a83,a83,a1,a122))))
% 7.14/7.07 [721]P2(a82,f7(a85,a82,a83,a5,f7(a83,a85,a83,a124,f7(a83,a83,a83,a1,a2))))
% 7.14/7.07 [540]E(f19(a82,x5401),f36(a82,x5401))
% 7.14/7.07 [562]E(f22(a83,x5621,x5621),f3(a83))
% 7.14/7.07 [535]E(f18(f3(a82),x5351),f3(a85))
% 7.14/7.07 [541]E(f26(f35(a83,x5411)),x5411)
% 7.14/7.07 [542]E(f33(f35(a83,x5421)),x5421)
% 7.14/7.07 [547]E(f19(a82,f35(a83,x5471)),f35(a83,x5471))
% 7.14/7.07 [548]E(f86(f86(f23(a83),x5481),f3(a83)),x5481)
% 7.14/7.07 [549]E(f86(f86(f23(a84),x5491),f3(a84)),x5491)
% 7.14/7.07 [550]E(f86(f86(f24(a83),x5501),f16(a83)),x5501)
% 7.14/7.07 [551]E(f86(f86(f24(a84),x5511),f16(a84)),x5511)
% 7.14/7.07 [553]E(f86(f86(f24(a83),x5531),f3(a83)),f3(a83))
% 7.14/7.07 [563]E(f22(a83,x5631,f3(a83)),x5631)
% 7.14/7.07 [565]E(f22(a83,f3(a83),x5651),f3(a83))
% 7.14/7.07 [566]E(f20(a84,f3(a84),x5661),f3(a84))
% 7.14/7.07 [567]E(f11(f86(a10,x5671),f86(a5,x5671)),x5671)
% 7.14/7.07 [568]P77(f86(f28(a82,x5681),x5681))
% 7.14/7.07 [569]P77(f86(f28(a83,x5691),x5691))
% 7.14/7.07 [570]P77(f86(f28(a84,x5701),x5701))
% 7.14/7.07 [571]E(f86(f86(f37(a82),x5711),f19(a82,x5711)),f25(a82,x5711))
% 7.14/7.07 [595]P77(f86(f28(a82,f3(a82)),f35(a83,x5951)))
% 7.14/7.07 [600]E(f86(f86(f37(a82),f86(a5,x6001)),f36(a85,x6001)),f86(a5,f25(a85,x6001)))
% 7.14/7.07 [601]E(f86(f86(f37(a82),f86(a10,x6011)),f36(a85,x6011)),f86(a10,f25(a85,x6011)))
% 7.14/7.07 [611]P77(f86(f28(a82,f86(a10,x6111)),f36(a85,x6111)))
% 7.14/7.07 [657]P77(f86(f28(a82,f19(a82,f86(a5,x6571))),f36(a85,x6571)))
% 7.14/7.07 [658]P77(f86(f28(a82,f19(a82,f86(a10,x6581))),f36(a85,x6581)))
% 7.14/7.07 [660]P77(f86(f28(a82,f86(a5,f18(f16(a82),x6601))),f16(a82)))
% 7.14/7.07 [661]P77(f86(f28(a82,f86(a10,f18(f16(a82),x6611))),f16(a82)))
% 7.14/7.07 [691]P77(f86(f28(a82,f19(a82,f86(a5,f18(f16(a82),x6911)))),f16(a82)))
% 7.14/7.07 [692]P77(f86(f28(a82,f19(a82,f86(a10,f18(f16(a82),x6921)))),f16(a82)))
% 7.14/7.07 [727]~E(f86(f86(f23(a83),x7271),f16(a83)),x7271)
% 7.14/7.07 [733]~E(f86(f86(f23(a83),x7331),f16(a83)),f3(a83))
% 7.14/7.07 [735]~P77(f86(f29(a83,x7351),x7351))
% 7.14/7.07 [738]~P77(f86(f29(a83,x7381),f3(a83)))
% 7.14/7.07 [739]~P77(f86(f29(a82,f35(a83,x7391)),f3(a82)))
% 7.14/7.07 [554]E(f86(f86(f23(a83),f3(a83)),x5541),x5541)
% 7.14/7.07 [555]E(f86(f86(f23(a84),f3(a84)),x5551),x5551)
% 7.14/7.07 [556]E(f86(f86(f24(a82),f16(a82)),x5561),x5561)
% 7.14/7.07 [557]E(f86(f86(f24(a83),f16(a83)),x5571),x5571)
% 7.14/7.07 [558]E(f86(f86(f24(a84),f16(a84)),x5581),x5581)
% 7.14/7.07 [561]E(f86(f86(f24(a83),f3(a83)),x5611),f3(a83))
% 7.14/7.07 [578]P77(f86(f28(a83,f3(a83)),x5781))
% 7.14/7.07 [592]E(f28(a83,f86(f86(f23(a83),x5921),f16(a83))),f29(a83,x5921))
% 7.14/7.07 [599]P77(f86(f28(a82,x5991),f35(a83,f26(x5991))))
% 7.14/7.07 [604]E(f20(a83,x6041,f86(f86(f23(a83),f3(a83)),f16(a83))),x6041)
% 7.14/7.07 [609]E(f86(f86(f23(a82),f35(a83,x6091)),f16(a82)),f35(a83,f86(f86(f23(a83),x6091),f16(a83))))
% 7.14/7.07 [624]P77(f86(f29(a83,x6241),f86(f86(f23(a83),x6241),f16(a83))))
% 7.14/7.07 [628]P77(f86(f29(a83,f3(a83)),f86(f86(f23(a83),x6281),f16(a83))))
% 7.14/7.07 [655]P77(f86(f29(a82,f3(a82)),f86(f86(f23(a82),f16(a82)),f19(a82,x6551))))
% 7.14/7.07 [676]P77(f86(f29(a82,x6761),f86(f86(f23(a82),f35(a83,f33(x6761))),f16(a82))))
% 7.14/7.07 [677]P77(f86(f29(a82,f22(a82,x6771,f16(a82))),f35(a83,f33(x6771))))
% 7.14/7.07 [694]P77(f86(f28(a82,f19(a82,f86(a5,f86(a124,x6941)))),f86(f86(f23(a82),a123),f16(a82))))
% 7.14/7.07 [621]P77(f86(f28(a83,x6211),f86(f86(f24(a83),x6211),x6211)))
% 7.14/7.07 [639]E(f86(f86(f31(a83),f86(f86(f23(a83),f3(a83)),f16(a83))),x6391),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.07 [641]P77(f86(f28(a82,f36(a85,f86(a124,x6411))),a123))
% 7.14/7.07 [672]P77(f86(f29(a82,f3(a82)),f35(a83,f86(f86(f23(a83),x6721),f16(a83)))))
% 7.14/7.07 [684]P77(f86(f28(a82,f36(a82,f86(a5,x6841))),f86(f86(f24(a82),f36(a85,x6841)),a40)))
% 7.14/7.07 [685]P77(f86(f28(a82,f36(a82,f86(a5,x6851))),f86(f86(f24(a82),f36(a85,x6851)),a39)))
% 7.14/7.07 [686]P77(f86(f28(a82,f36(a82,f86(a5,x6861))),f86(f86(f24(a82),f36(a85,x6861)),a45)))
% 7.14/7.07 [687]P77(f86(f28(a82,f36(a82,f86(a10,x6871))),f86(f86(f24(a82),f36(a85,x6871)),a43)))
% 7.14/7.07 [688]P77(f86(f28(a82,f36(a82,f86(a10,x6881))),f86(f86(f24(a82),f36(a85,x6881)),a44)))
% 7.14/7.07 [689]P77(f86(f28(a82,f36(a82,f86(a10,x6891))),f86(f86(f24(a82),f36(a85,x6891)),a49)))
% 7.14/7.07 [743]~P77(f86(f28(a83,f86(f86(f23(a83),x7431),f16(a83))),x7431))
% 7.14/7.07 [744]~P77(f86(f29(a82,f86(f86(f23(a82),f19(a82,x7441)),f16(a82))),x7441))
% 7.14/7.07 [656]E(f36(a85,f11(f86(a10,f18(f16(a82),x6561)),f86(a5,f18(f16(a82),x6561)))),f16(a82))
% 7.14/7.07 [680]P77(f86(f28(a83,x6801),f86(f86(f24(a83),x6801),f86(f86(f24(a83),x6801),x6801))))
% 7.14/7.07 [704]E(f86(f86(f23(a82),f86(f86(f24(a82),f86(a10,f18(f16(a82),x7041))),f86(a10,f18(f16(a82),x7041)))),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7041))),f86(a5,f18(f16(a82),x7041)))),f16(a82))
% 7.14/7.07 [740]~E(f86(f86(f23(a84),f86(f86(f23(a84),f16(a84)),x7401)),x7401),f3(a84))
% 7.14/7.07 [543]E(f13(f11(x5431,x5432)),f3(a83))
% 7.14/7.07 [544]E(f86(a5,f11(x5441,x5442)),x5442)
% 7.14/7.07 [545]E(f86(a10,f11(x5451,x5452)),x5451)
% 7.14/7.07 [546]E(f27(a85,f11(x5461,x5462)),f3(a83))
% 7.14/7.07 [552]E(f36(a85,f18(x5521,x5522)),f19(a82,x5521))
% 7.14/7.07 [612]E(f22(a82,f86(a5,x6121),f86(a5,x6122)),f86(a5,f22(a85,x6121,x6122)))
% 7.14/7.07 [613]E(f22(a82,f86(a10,x6131),f86(a10,x6132)),f86(a10,f22(a85,x6131,x6132)))
% 7.14/7.07 [710]P77(f86(f28(a82,f22(a82,f36(a85,f86(f86(f23(a85),x7101),x7102)),f36(a85,x7101))),f36(a85,x7102)))
% 7.14/7.07 [715]P77(f86(f28(a82,f22(a82,f86(f86(f37(a82),f35(a83,x7151)),f35(a83,x7152)),f35(a83,f20(a83,x7151,x7152)))),f16(a82)))
% 7.14/7.07 [579]E(f86(f86(f23(a83),x5791),x5792),f86(f86(f23(a83),x5792),x5791))
% 7.14/7.07 [580]E(f86(f86(f23(a84),x5801),x5802),f86(f86(f23(a84),x5802),x5801))
% 7.14/7.07 [581]E(f86(f86(f24(a82),x5811),x5812),f86(f86(f24(a82),x5812),x5811))
% 7.14/7.07 [582]E(f86(f86(f24(a83),x5821),x5822),f86(f86(f24(a83),x5822),x5821))
% 7.14/7.07 [583]E(f86(f86(f24(a84),x5831),x5832),f86(f86(f24(a84),x5832),x5831))
% 7.14/7.07 [623]E(f86(f86(f37(a85),f18(f16(a82),x6231)),f18(f16(a82),x6232)),f18(f16(a82),f22(a82,x6231,x6232)))
% 7.14/7.07 [635]E(f22(a83,x6351,f86(f86(f23(a83),x6352),f16(a83))),f22(a83,f22(a83,x6351,f16(a83)),x6352))
% 7.14/7.07 [669]P77(f86(f28(a83,f22(a83,x6691,x6692)),x6691))
% 7.14/7.07 [670]P77(f86(f28(a83,f20(a83,x6701,x6702)),x6701))
% 7.14/7.07 [671]E(f11(f86(f86(f23(a82),f86(a10,x6711)),f86(a10,x6712)),f86(f86(f23(a82),f86(a5,x6711)),f86(a5,x6712))),f86(f86(f23(a85),x6711),x6712))
% 7.14/7.07 [683]P77(f86(f29(a83,f22(a83,x6831,x6832)),f86(f86(f23(a83),x6831),f16(a83))))
% 7.14/7.07 [695]P77(f86(f29(a83,x6951),f86(f86(f23(a83),f86(f86(f23(a83),x6952),x6951)),f16(a83))))
% 7.14/7.07 [696]P77(f86(f29(a83,x6961),f86(f86(f23(a83),f86(f86(f23(a83),x6961),x6962)),f16(a83))))
% 7.14/7.07 [698]P77(f86(f28(a82,f35(a83,f20(a83,x6981,x6982))),f86(f86(f37(a82),f35(a83,x6981)),f35(a83,x6982))))
% 7.14/7.07 [705]P77(f86(f28(a82,f36(a85,x7051)),f86(f86(f23(a82),f36(a85,f86(f86(f23(a85),x7051),x7052))),f36(a85,x7052))))
% 7.14/7.07 [596]E(f22(a83,f86(f86(f23(a83),x5961),x5962),x5962),x5961)
% 7.14/7.07 [597]E(f22(a83,f86(f86(f23(a83),x5971),x5972),x5971),x5972)
% 7.14/7.07 [598]E(f22(a83,x5981,f86(f86(f23(a83),x5981),x5982)),f3(a83))
% 7.14/7.07 [603]E(f86(f86(f24(a85),f4(x6031)),f4(x6032)),f4(f86(f86(f23(a85),x6031),x6032)))
% 7.14/7.07 [605]E(f86(f86(f24(a82),x6051),f86(a5,f18(f16(a82),x6052))),f86(a5,f18(x6051,x6052)))
% 7.14/7.07 [606]E(f86(f86(f24(a82),x6061),f86(a10,f18(f16(a82),x6062))),f86(a10,f18(x6061,x6062)))
% 7.14/7.07 [608]E(f86(f86(f31(a82),f35(a83,x6081)),x6082),f35(a83,f86(f86(f31(a83),x6081),x6082)))
% 7.14/7.07 [614]E(f86(f86(f23(a82),f86(a5,x6141)),f86(a5,x6142)),f86(a5,f86(f86(f23(a85),x6141),x6142)))
% 7.14/7.07 [615]E(f86(f86(f23(a82),f86(a10,x6151)),f86(a10,x6152)),f86(a10,f86(f86(f23(a85),x6151),x6152)))
% 7.14/7.07 [616]E(f86(f86(f23(a82),f35(a83,x6161)),f35(a83,x6162)),f35(a83,f86(f86(f23(a83),x6161),x6162)))
% 7.14/7.07 [617]E(f86(f86(f24(a82),f35(a83,x6171)),f35(a83,x6172)),f35(a83,f86(f86(f24(a83),x6171),x6172)))
% 7.14/7.07 [618]E(f86(f86(f24(a85),f18(f16(a82),x6181)),f18(f16(a82),x6182)),f18(f16(a82),f86(f86(f23(a82),x6181),x6182)))
% 7.14/7.07 [619]P77(f86(f28(a83,x6191),f86(f86(f23(a83),x6192),x6191)))
% 7.14/7.07 [620]P77(f86(f28(a83,x6201),f86(f86(f23(a83),x6201),x6202)))
% 7.14/7.07 [627]E(f86(f86(f24(a83),x6271),f86(f86(f23(a83),x6272),f16(a83))),f86(f86(f23(a83),x6271),f86(f86(f24(a83),x6271),x6272)))
% 7.14/7.07 [634]E(f18(f16(a82),f86(f86(f24(a82),f35(a83,x6341)),x6342)),f86(f86(f31(a85),f18(f16(a82),x6342)),x6341))
% 7.14/7.07 [648]E(f86(f86(f37(a82),f86(f86(f24(a82),x6481),x6482)),f86(f86(f24(a82),x6481),x6481)),f86(f86(f37(a82),x6482),x6481))
% 7.14/7.07 [650]E(f86(f86(f24(a83),f86(f86(f23(a83),x6501),f16(a83))),x6502),f86(f86(f23(a83),x6502),f86(f86(f24(a83),x6501),x6502)))
% 7.14/7.07 [651]E(f86(f86(f23(a83),f86(f86(f23(a83),x6511),f16(a83))),x6512),f86(f86(f23(a83),x6511),f86(f86(f23(a83),x6512),f16(a83))))
% 7.14/7.07 [662]P77(f86(f28(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x6621)),x6622)))
% 7.14/7.07 [666]E(f86(f86(f23(a83),f86(f86(f23(a83),x6661),f16(a83))),x6662),f86(f86(f23(a83),f86(f86(f23(a83),x6661),x6662)),f16(a83)))
% 7.14/7.07 [679]E(f22(a82,f86(f86(f24(a82),f86(a10,x6791)),f86(a10,x6792)),f86(f86(f24(a82),f86(a5,x6791)),f86(a5,x6792))),f86(a10,f86(f86(f24(a85),x6791),x6792)))
% 7.14/7.07 [690]E(f86(f86(f23(a82),f86(f86(f24(a82),f86(a10,x6901)),f86(a5,x6902))),f86(f86(f24(a82),f86(a5,x6901)),f86(a10,x6902))),f86(a5,f86(f86(f24(a85),x6901),x6902)))
% 7.14/7.07 [707]P77(f86(f28(a82,f3(a82)),f22(a82,f86(f86(f37(a82),f35(a83,x7071)),f35(a83,x7072)),f35(a83,f20(a83,x7071,x7072)))))
% 7.14/7.07 [714]E(f11(f22(a82,f86(f86(f24(a82),f86(a10,x7141)),f86(a10,x7142)),f86(f86(f24(a82),f86(a5,x7141)),f86(a5,x7142))),f86(f86(f23(a82),f86(f86(f24(a82),f86(a10,x7141)),f86(a5,x7142))),f86(f86(f24(a82),f86(a5,x7141)),f86(a10,x7142)))),f86(f86(f24(a85),x7141),x7142))
% 7.14/7.07 [681]E(f86(a5,f18(f16(a82),f86(f86(f24(a82),f35(a83,x6811)),x6812))),f86(a5,f86(f86(f31(a85),f18(f16(a82),x6812)),x6811)))
% 7.14/7.07 [682]E(f86(a10,f18(f16(a82),f86(f86(f24(a82),f35(a83,x6821)),x6822))),f86(a10,f86(f86(f31(a85),f18(f16(a82),x6822)),x6821)))
% 7.14/7.07 [700]E(f22(a82,f86(f86(f24(a82),f86(a10,f18(f16(a82),x7001))),f86(a10,f18(f16(a82),x7002))),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7001))),f86(a5,f18(f16(a82),x7002)))),f86(a10,f18(f16(a82),f86(f86(f23(a82),x7001),x7002))))
% 7.14/7.07 [701]E(f22(a82,f86(f86(f24(a82),f86(a5,f18(f16(a82),x7011))),f86(a10,f18(f16(a82),x7012))),f86(f86(f24(a82),f86(a10,f18(f16(a82),x7011))),f86(a5,f18(f16(a82),x7012)))),f86(a5,f18(f16(a82),f22(a82,x7011,x7012))))
% 7.14/7.07 [702]E(f22(a82,f86(f86(f24(a82),f86(a10,f18(f16(a82),x7021))),f86(a5,f18(f16(a82),x7022))),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7021))),f86(a10,f18(f16(a82),x7022)))),f86(a5,f18(f16(a82),f22(a82,x7022,x7021))))
% 7.14/7.07 [706]E(f86(f86(f23(a82),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7061))),f86(a10,f18(f16(a82),x7062)))),f86(f86(f24(a82),f86(a10,f18(f16(a82),x7061))),f86(a5,f18(f16(a82),x7062)))),f86(a5,f18(f16(a82),f86(f86(f23(a82),x7061),x7062))))
% 7.14/7.07 [708]E(f86(f86(f23(a82),f86(f86(f24(a82),f86(a10,f18(f16(a82),x7081))),f86(a10,f18(f16(a82),x7082)))),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7081))),f86(a5,f18(f16(a82),x7082)))),f86(a10,f18(f16(a82),f22(a82,x7082,x7081))))
% 7.14/7.07 [709]E(f86(f86(f23(a82),f86(f86(f24(a82),f86(a10,f18(f16(a82),x7091))),f86(a10,f18(f16(a82),x7092)))),f86(f86(f24(a82),f86(a5,f18(f16(a82),x7091))),f86(a5,f18(f16(a82),x7092)))),f86(a10,f18(f16(a82),f22(a82,x7091,x7092))))
% 7.14/7.07 [716]P77(f86(f28(a82,f36(a85,f22(a85,x7161,x7162))),f86(f86(f23(a82),f19(a82,f22(a82,f86(a10,x7161),f86(a10,x7162)))),f19(a82,f22(a82,f86(a5,x7161),f86(a5,x7162))))))
% 7.14/7.07 [741]~P77(f86(f29(a83,f86(f86(f23(a83),x7411),x7412)),x7412))
% 7.14/7.07 [742]~P77(f86(f29(a83,f86(f86(f23(a83),x7421),x7422)),x7421))
% 7.14/7.07 [699]E(f86(f86(f24(a85),f18(f16(a82),x6991)),f18(f16(a82),f86(f86(f24(a82),f35(a83,x6992)),x6991))),f18(f16(a82),f86(f86(f24(a82),f35(a83,f86(f86(f23(a83),x6992),f16(a83)))),x6991)))
% 7.14/7.07 [636]E(f22(a83,f22(a83,x6361,x6362),x6363),f22(a83,f22(a83,x6361,x6363),x6362))
% 7.14/7.07 [678]E(f22(a83,f22(a83,f86(f86(f23(a83),x6781),f16(a83)),x6782),f86(f86(f23(a83),x6783),f16(a83))),f22(a83,f22(a83,x6781,x6782),x6783))
% 7.14/7.07 [625]E(f86(f86(f23(a83),x6251),f86(f86(f23(a83),x6252),x6253)),f86(f86(f23(a83),x6252),f86(f86(f23(a83),x6251),x6253)))
% 7.14/7.07 [626]E(f86(f86(f23(a84),x6261),f86(f86(f23(a84),x6262),x6263)),f86(f86(f23(a84),x6262),f86(f86(f23(a84),x6261),x6263)))
% 7.14/7.07 [629]E(f22(a83,f86(f86(f23(a83),x6291),x6292),f86(f86(f23(a83),x6293),x6292)),f22(a83,x6291,x6293))
% 7.14/7.07 [630]E(f22(a83,f86(f86(f23(a83),x6301),x6302),f86(f86(f23(a83),x6301),x6303)),f22(a83,x6302,x6303))
% 7.14/7.07 [632]E(f22(a83,x6321,f86(f86(f23(a83),x6322),x6323)),f22(a83,f22(a83,x6321,x6322),x6323))
% 7.14/7.07 [633]E(f20(a83,x6331,f86(f86(f24(a83),x6332),x6333)),f20(a83,f20(a83,x6331,x6332),x6333))
% 7.14/7.07 [652]E(f22(a83,f86(f86(f24(a83),x6521),x6522),f86(f86(f24(a83),x6521),x6523)),f86(f86(f24(a83),x6521),f22(a83,x6522,x6523)))
% 7.14/7.07 [653]E(f22(a84,f86(f86(f24(a84),x6531),x6532),f86(f86(f24(a84),x6531),x6533)),f86(f86(f24(a84),x6531),f22(a84,x6532,x6533)))
% 7.14/7.07 [654]E(f18(f86(f86(f31(a82),x6541),x6542),f86(f86(f24(a82),f35(a83,x6542)),x6543)),f86(f86(f31(a85),f18(x6541,x6543)),x6542))
% 7.14/7.07 [663]E(f86(f86(f23(a83),f86(f86(f24(a83),x6631),x6632)),f86(f86(f24(a83),x6631),x6633)),f86(f86(f24(a83),x6631),f86(f86(f23(a83),x6632),x6633)))
% 7.14/7.07 [664]E(f86(f86(f23(a84),f86(f86(f24(a84),x6641),x6642)),f86(f86(f24(a84),x6641),x6643)),f86(f86(f24(a84),x6641),f86(f86(f23(a84),x6642),x6643)))
% 7.14/7.07 [665]E(f86(f86(f24(a84),f86(f86(f31(a84),x6651),x6652)),f86(f86(f31(a84),x6651),x6653)),f86(f86(f31(a84),x6651),f86(f86(f23(a83),x6652),x6653)))
% 7.14/7.07 [667]E(f22(a83,f86(f86(f24(a83),x6671),x6672),f86(f86(f24(a83),x6673),x6672)),f86(f86(f24(a83),f22(a83,x6671,x6673)),x6672))
% 7.14/7.07 [668]E(f22(a84,f86(f86(f24(a84),x6681),x6682),f86(f86(f24(a84),x6683),x6682)),f86(f86(f24(a84),f22(a84,x6681,x6683)),x6682))
% 7.14/7.07 [642]E(f86(f86(f23(a83),f86(f86(f23(a83),x6421),x6422)),x6423),f86(f86(f23(a83),x6421),f86(f86(f23(a83),x6422),x6423)))
% 7.14/7.07 [643]E(f86(f86(f23(a84),f86(f86(f23(a84),x6431),x6432)),x6433),f86(f86(f23(a84),x6431),f86(f86(f23(a84),x6432),x6433)))
% 7.14/7.07 [644]E(f86(f86(f24(a82),f86(f86(f24(a82),x6441),x6442)),x6443),f86(f86(f24(a82),x6441),f86(f86(f24(a82),x6442),x6443)))
% 7.14/7.07 [645]E(f86(f86(f24(a83),f86(f86(f24(a83),x6451),x6452)),x6453),f86(f86(f24(a83),x6451),f86(f86(f24(a83),x6452),x6453)))
% 7.14/7.07 [646]E(f86(f86(f24(a84),f86(f86(f24(a84),x6461),x6462)),x6463),f86(f86(f24(a84),x6461),f86(f86(f24(a84),x6462),x6463)))
% 7.14/7.07 [647]E(f86(f86(f31(a84),f86(f86(f31(a84),x6471),x6472)),x6473),f86(f86(f31(a84),x6471),f86(f86(f24(a83),x6472),x6473)))
% 7.14/7.07 [673]E(f86(f86(f23(a82),f86(f86(f24(a82),x6731),x6732)),f86(f86(f24(a82),x6733),x6732)),f86(f86(f24(a82),f86(f86(f23(a82),x6731),x6733)),x6732))
% 7.14/7.07 [674]E(f86(f86(f23(a83),f86(f86(f24(a83),x6741),x6742)),f86(f86(f24(a83),x6743),x6742)),f86(f86(f24(a83),f86(f86(f23(a83),x6741),x6743)),x6742))
% 7.14/7.07 [675]E(f86(f86(f23(a84),f86(f86(f24(a84),x6751),x6752)),f86(f86(f24(a84),x6753),x6752)),f86(f86(f24(a84),f86(f86(f23(a84),x6751),x6753)),x6752))
% 7.14/7.07 [719]E(f22(a82,f86(x7191,x7192),f86(f86(f24(a82),f86(f86(f37(a82),f22(a82,f86(x7191,x7193),f86(x7191,x7192))),f22(a82,x7193,x7192))),x7192)),f22(a82,f86(x7191,x7193),f86(f86(f24(a82),f86(f86(f37(a82),f22(a82,f86(x7191,x7193),f86(x7191,x7192))),f22(a82,x7193,x7192))),x7193)))
% 7.14/7.07 [590]E(f14(x5901,x5902,f11(x5903,x5904)),f86(f86(x5902,x5903),x5904))
% 7.14/7.07 [591]E(f15(x5911,x5912,f11(x5913,x5914)),f86(f86(x5912,x5913),x5914))
% 7.14/7.07 [593]E(f86(f6(x5931,x5932,x5933),x5934),x5933)
% 7.14/7.07 [622]E(f86(f86(f32(x6221,x6222,x6223),x6224),f3(a83)),x6222)
% 7.14/7.07 [640]E(f11(f22(a82,x6401,x6402),f22(a82,x6403,x6404)),f22(a85,f11(x6401,x6403),f11(x6402,x6404)))
% 7.14/7.07 [637]E(f11(f86(f86(f23(a82),x6371),x6372),f86(f86(f23(a82),x6373),x6374)),f86(f86(f23(a85),f11(x6371,x6373)),f11(x6372,x6374)))
% 7.14/7.07 [638]E(f18(f86(f86(f24(a82),x6381),x6382),f86(f86(f23(a82),x6383),x6384)),f86(f86(f24(a85),f18(x6381,x6383)),f18(x6382,x6384)))
% 7.14/7.07 [697]E(f11(f22(a82,f86(f86(f24(a82),x6971),x6972),f86(f86(f24(a82),x6973),x6974)),f86(f86(f23(a82),f86(f86(f24(a82),x6971),x6974)),f86(f86(f24(a82),x6973),x6972))),f86(f86(f24(a85),f11(x6971,x6973)),f11(x6972,x6974)))
% 7.14/7.07 [703]E(f86(f86(f23(a83),f86(f86(f24(a83),x7031),x7032)),f86(f86(f23(a83),f86(f86(f24(a83),x7033),x7032)),x7034)),f86(f86(f23(a83),f86(f86(f24(a83),f86(f86(f23(a83),x7031),x7033)),x7032)),x7034))
% 7.14/7.07 [693]E(f86(f86(f32(x6931,x6932,x6933),x6934),f86(f86(f23(a83),x6935),f16(a83))),f86(f86(x6933,x6934),f86(f86(f32(x6931,x6932,x6933),x6934),x6935)))
% 7.14/7.07 [711]E(f86(f7(x7111,x7112,x7113,x7114,x7115),x7116),f86(x7114,f86(x7115,x7116)))
% 7.14/7.07 [712]E(f86(f8(x7121,x7122,x7123,x7124,x7125),x7126),f86(f86(x7124,x7126),x7125))
% 7.14/7.07 [713]E(f86(f9(x7131,x7132,x7133,x7134,x7135),x7136),f86(f86(x7134,x7136),f86(x7135,x7136)))
% 7.14/7.07 [1942]~P77(f86(f29(a82,f3(a82)),f86(f86(f23(a82),a123),f16(a82))))+~P77(f86(f28(a82,f19(a82,f86(a5,f86(a124,f86(a1,f86(a122,a116)))))),f86(f86(f23(a82),a123),f16(a82))))
% 7.14/7.07 [745]~P34(x7451)+P7(f120(x7451))
% 7.14/7.07 [746]~P34(x7461)+P8(f120(x7461))
% 7.14/7.07 [747]~P34(x7471)+P9(f120(x7471))
% 7.14/7.07 [748]~P32(x7481)+P32(f120(x7481))
% 7.14/7.07 [749]~P34(x7491)+P34(f120(x7491))
% 7.14/7.07 [750]~P20(x7501)+P10(f120(x7501))
% 7.14/7.07 [751]~P20(x7511)+P11(f120(x7511))
% 7.14/7.07 [752]~P22(x7521)+P12(f120(x7521))
% 7.14/7.07 [753]~P47(x7531)+P21(f120(x7531))
% 7.14/7.07 [754]~P22(x7541)+P22(f120(x7541))
% 7.14/7.07 [755]~P22(x7551)+P23(f120(x7551))
% 7.14/7.07 [756]~P34(x7561)+P24(f120(x7561))
% 7.14/7.07 [757]~P34(x7571)+P29(f120(x7571))
% 7.14/7.07 [758]~P34(x7581)+P30(f120(x7581))
% 7.14/7.07 [759]~P34(x7591)+P31(f120(x7591))
% 7.14/7.07 [760]~P47(x7601)+P58(f120(x7601))
% 7.14/7.07 [761]~P34(x7611)+P37(f120(x7611))
% 7.14/7.07 [762]~P34(x7621)+P38(f120(x7621))
% 7.14/7.07 [763]~P34(x7631)+P39(f120(x7631))
% 7.14/7.07 [764]~P34(x7641)+P40(f120(x7641))
% 7.14/7.07 [765]~P47(x7651)+P47(f120(x7651))
% 7.14/7.07 [766]~P55(x7661)+P76(f120(x7661))
% 7.14/7.07 [767]~P34(x7671)+P59(f120(x7671))
% 7.14/7.07 [768]~P51(x7681)+P19(f120(x7681))
% 7.14/7.07 [769]~P55(x7691)+P62(f120(x7691))
% 7.14/7.07 [770]~P55(x7701)+P65(f120(x7701))
% 7.14/7.07 [771]~P51(x7711)+P63(f120(x7711))
% 7.14/7.07 [772]~P51(x7721)+P74(f120(x7721))
% 7.14/7.07 [773]~P51(x7731)+P48(f120(x7731))
% 7.14/7.07 [774]~P47(x7741)+P25(f120(x7741))
% 7.14/7.07 [775]~P47(x7751)+P27(f120(x7751))
% 7.14/7.07 [776]~P34(x7761)+P33(f120(x7761))
% 7.14/7.07 [777]~P34(x7771)+P66(f120(x7771))
% 7.14/7.07 [778]~P34(x7781)+P67(f120(x7781))
% 7.14/7.07 [779]~P34(x7791)+P69(f120(x7791))
% 7.14/7.07 [780]~P34(x7801)+P68(f120(x7801))
% 7.14/7.07 [781]~P34(x7811)+P56(f120(x7811))
% 7.14/7.07 [782]~P34(x7821)+P57(f120(x7821))
% 7.14/7.07 [783]~P34(x7831)+P52(f120(x7831))
% 7.14/7.07 [784]~P34(x7841)+P64(f120(x7841))
% 7.14/7.07 [785]~P34(x7851)+P60(f120(x7851))
% 7.14/7.07 [786]~P34(x7861)+P70(f120(x7861))
% 7.14/7.07 [787]~P34(x7871)+P61(f120(x7871))
% 7.14/7.07 [788]~P55(x7881)+P71(f120(x7881))
% 7.14/7.07 [789]~P47(x7891)+P43(f120(x7891))
% 7.14/7.07 [790]~P51(x7901)+P75(f120(x7901))
% 7.14/7.07 [791]~P34(x7911)+P28(f120(x7911))
% 7.14/7.07 [792]~P13(x7921)+P26(f120(x7921))
% 7.14/7.07 [793]~P50(x7931)+P72(f120(x7931))
% 7.14/7.07 [794]~P13(x7941)+P13(f120(x7941))
% 7.14/7.07 [795]~P49(x7951)+P73(f120(x7951))
% 7.14/7.07 [796]~P49(x7961)+P49(f120(x7961))
% 7.14/7.07 [797]~P15(x7971)+P14(f120(x7971))
% 7.14/7.07 [798]~P55(x7981)+P55(f120(x7981))
% 7.14/7.07 [799]~P20(x7991)+P20(f120(x7991))
% 7.14/7.07 [800]~P51(x8001)+P51(f120(x8001))
% 7.14/7.07 [801]~P50(x8011)+P50(f120(x8011))
% 7.14/7.07 [803]~P58(x8031)+~E(f16(x8031),f3(x8031))
% 7.14/7.07 [804]~E(x8041,f3(a83))+E(f35(a83,x8041),f3(a82))
% 7.14/7.07 [808]E(x8081,f3(a83))+~E(f35(a83,x8081),f3(a82))
% 7.14/7.07 [848]E(x8481,f3(a84))+E(f20(a84,x8481,x8481),f16(a84))
% 7.14/7.07 [1899]~P3(a85,x18991)+P3(a82,f7(a85,a82,a83,a5,x18991))
% 7.14/7.07 [1900]~P3(a85,x19001)+P3(a82,f7(a85,a82,a83,a10,x19001))
% 7.14/7.07 [811]~P35(x8111)+E(f36(x8111,f3(x8111)),f3(a82))
% 7.14/7.07 [812]~P36(x8121)+E(f36(x8121,f16(x8121)),f16(a82))
% 7.14/7.07 [817]~P9(x8171)+E(f19(x8171,f3(x8171)),f3(x8171))
% 7.14/7.07 [818]~P34(x8181)+E(f19(x8181,f16(x8181)),f16(x8181))
% 7.14/7.07 [819]~P35(x8191)+E(f25(x8191,f3(x8191)),f3(x8191))
% 7.14/7.07 [820]~P33(x8201)+E(f25(x8201,f3(x8201)),f3(x8201))
% 7.14/7.07 [821]~P36(x8211)+E(f25(x8211,f16(x8211)),f16(x8211))
% 7.14/7.07 [904]~P43(x9041)+E(f32(x9041,f16(x9041),f24(x9041)),f31(x9041))
% 7.14/7.07 [946]~P41(x9461)+P77(f86(f28(a82,f3(a82)),f51(x9461)))
% 7.14/7.07 [947]~P41(x9471)+P77(f86(f29(a82,f3(a82)),f46(x9471)))
% 7.14/7.07 [950]P1(x9501)+P77(f86(f29(a83,f41(x9501)),f42(x9501)))
% 7.14/7.07 [963]~P7(x9631)+P77(f86(f28(x9631,f3(x9631)),f16(x9631)))
% 7.14/7.07 [964]~P7(x9641)+P77(f86(f29(x9641,f3(x9641)),f16(x9641)))
% 7.14/7.07 [967]E(x9671,f3(a83))+~P77(f86(f28(a83,x9671),f3(a83)))
% 7.14/7.07 [969]E(f26(x9691),f3(a83))+~P77(f86(f28(a82,x9691),f3(a82)))
% 7.14/7.07 [970]E(f33(x9701),f3(a83))+~P77(f86(f28(a82,x9701),f3(a82)))
% 7.14/7.07 [1053]~E(x10531,f3(a83))+P77(f86(f28(a82,f35(a83,x10531)),f3(a82)))
% 7.14/7.07 [1054]~E(x10541,f3(a84))+P77(f86(f29(a84,f19(a84,x10541)),f16(a84)))
% 7.14/7.07 [1070]~P7(x10701)+~P77(f86(f28(x10701,f16(x10701)),f3(x10701)))
% 7.14/7.07 [1071]~P7(x10711)+~P77(f86(f29(x10711,f16(x10711)),f3(x10711)))
% 7.14/7.07 [1125]~P77(f86(f28(a82,x11251),f16(a82)))+P77(f86(f28(a83,f26(x11251)),f16(a83)))
% 7.14/7.07 [1142]~P77(f86(f28(a83,f26(x11421)),f16(a83)))+P77(f86(f28(a82,x11421),f16(a82)))
% 7.14/7.07 [1183]E(x11831,f3(a83))+~P77(f86(f28(a82,f35(a83,x11831)),f3(a82)))
% 7.14/7.07 [1184]E(x11841,f3(a84))+~P77(f86(f29(a84,f19(a84,x11841)),f16(a84)))
% 7.14/7.07 [1887]~P77(f86(f29(a84,x18871),f3(a84)))+P77(f86(f29(a84,f86(f86(f23(a84),f86(f86(f23(a84),f16(a84)),x18871)),x18871)),f3(a84)))
% 7.14/7.07 [1918]P77(f86(f29(a84,x19181),f3(a84)))+~P77(f86(f29(a84,f86(f86(f23(a84),f86(f86(f23(a84),f16(a84)),x19181)),x19181)),f3(a84)))
% 7.14/7.07 [924]E(x9241,f3(a83))+P77(f86(f29(a83,f3(a83)),x9241))
% 7.14/7.07 [951]~E(f86(a10,f18(f16(a82),x9511)),f16(a82))+E(f86(a5,f18(f16(a82),x9511)),f3(a82))
% 7.14/7.07 [1010]E(f25(a82,x10101),f16(a82))+~P77(f86(f29(a82,f3(a82)),x10101))
% 7.14/7.07 [1091]E(f86(f86(f23(a83),f72(x10911)),f16(a83)),x10911)+~P77(f86(f29(a83,f3(a83)),x10911))
% 7.14/7.07 [1118]~P77(f86(f29(a84,f3(a84)),x11181))+P77(f86(f28(a84,f16(a84)),x11181))
% 7.14/7.07 [1119]P77(f86(f29(a84,f3(a84)),x11191))+~P77(f86(f28(a84,f16(a84)),x11191))
% 7.14/7.07 [1127]~P77(f86(f29(a82,f3(a82)),x11271))+P77(f86(f29(a82,f34(x11271)),x11271))
% 7.14/7.07 [1128]P77(f86(f28(a82,f3(a82)),f34(x11281)))+~P77(f86(f28(a82,f16(a82)),x11281))
% 7.14/7.07 [1129]P77(f86(f28(a83,f16(a83)),f33(x11291)))+~P77(f86(f28(a82,f16(a82)),x11291))
% 7.14/7.07 [1130]P77(f86(f29(a82,f3(a82)),f34(x11301)))+~P77(f86(f29(a82,f16(a82)),x11301))
% 7.14/7.07 [1136]~P77(f86(f28(a83,f16(a83)),f33(x11361)))+P77(f86(f28(a82,f16(a82)),x11361))
% 7.14/7.07 [1178]P77(f86(f29(a82,f3(a82)),f35(a83,x11781)))+~P77(f86(f29(a83,f3(a83)),x11781))
% 7.14/7.07 [1192]~P77(f86(f28(a82,f3(a82)),x11921))+P77(f86(f29(a82,x11921),f35(a83,f101(x11921))))
% 7.14/7.07 [1198]~P77(f86(f29(a82,f3(a82)),f35(a83,x11981)))+P77(f86(f29(a83,f3(a83)),x11981))
% 7.14/7.07 [1200]E(f26(f86(f86(f23(a82),x12001),f16(a82))),f86(f86(f23(a83),f26(x12001)),f16(a83)))+~P77(f86(f28(a82,f3(a82)),x12001))
% 7.14/7.07 [1201]E(f33(f86(f86(f23(a82),x12011),f16(a82))),f86(f86(f23(a83),f33(x12011)),f16(a83)))+~P77(f86(f28(a82,f3(a82)),x12011))
% 7.14/7.07 [1233]E(f86(a10,f18(f16(a82),f38(x12331))),x12331)+~P77(f86(f28(a82,f19(a82,x12331)),f16(a82)))
% 7.14/7.07 [1299]~P7(x12991)+P77(f86(f29(x12991,f3(x12991)),f86(f86(f23(x12991),f16(x12991)),f16(x12991))))
% 7.14/7.07 [1312]E(f86(f86(f23(a83),f22(a83,x13121,f16(a83))),f16(a83)),x13121)+~P77(f86(f29(a83,f3(a83)),x13121))
% 7.14/7.07 [1364]E(x13641,f3(a83))+~P77(f86(f29(a83,x13641),f86(f86(f23(a83),f3(a83)),f16(a83))))
% 7.14/7.07 [1376]P1(x13761)+~P77(f86(f29(a83,f86(x13761,f41(x13761))),f86(x13761,f42(x13761))))
% 7.14/7.07 [1626]E(f86(f86(f23(a83),f22(a83,x16261,f86(f86(f23(a83),f3(a83)),f16(a83)))),f16(a83)),x16261)+~P77(f86(f29(a83,f3(a83)),x16261))
% 7.14/7.07 [1050]~E(f86(a5,f18(f16(a82),x10501)),f3(a82))+E(f19(a82,f86(a10,f18(f16(a82),x10501))),f16(a82))
% 7.14/7.07 [1175]E(x11751,f3(a82))+P77(f86(f29(a82,f3(a82)),f86(f86(f24(a82),x11751),x11751)))
% 7.14/7.07 [1258]~P77(f86(f28(a82,f3(a82)),x12581))+P77(f86(f28(a82,f35(a83,f33(x12581))),x12581))
% 7.14/7.07 [1259]~P77(f86(f28(a82,f3(a82)),x12591))+P77(f86(f28(a82,f35(a83,f89(x12591))),x12591))
% 7.14/7.07 [1341]~E(x13411,f3(a82))+~P77(f86(f29(a82,f3(a82)),f86(f86(f24(a82),x13411),x13411)))
% 7.14/7.07 [1345]~P77(f86(f28(a84,f3(a84)),x13451))+P77(f86(f29(a84,f3(a84)),f86(f86(f23(a84),f16(a84)),x13451)))
% 7.14/7.07 [1569]~P77(f86(f28(a82,f3(a82)),x15691))+P77(f86(f29(a82,x15691),f35(a83,f86(f86(f23(a83),f89(x15691)),f16(a83)))))
% 7.14/7.07 [1788]P1(x17881)+~P77(f86(f29(a83,f86(x17881,f79(x17881))),f86(x17881,f86(f86(f23(a83),f79(x17881)),f16(a83)))))
% 7.14/7.07 [1065]E(x10651,f3(a82))+E(f86(a10,f18(f16(a82),f12(f11(f3(a82),x10651)))),f3(a82))
% 7.14/7.07 [1222]~P77(f86(f29(a82,x12221),f3(a82)))+E(f86(a10,f18(f16(a82),f12(f11(f3(a82),x12221)))),f3(a82))
% 7.14/7.07 [1231]E(f86(a10,f18(f16(a82),f12(f11(f3(a82),x12311)))),f3(a82))+~P77(f86(f29(a82,f3(a82)),x12311))
% 7.14/7.07 [1801]~P77(f86(f28(a82,f3(a82)),x18011))+P77(f86(f28(a82,f35(a83,f22(a83,f101(x18011),f16(a83)))),x18011))
% 7.14/7.07 [1749]~P77(f86(f28(a82,f3(a82)),x17491))+P77(f86(f28(a82,f34(f86(f86(f23(a82),f16(a82)),x17491))),x17491))
% 7.14/7.07 [806]E(x8061,f3(a82))+~E(f11(x8061,x8062),a17)
% 7.14/7.07 [807]E(x8071,f16(a82))+~E(f11(x8072,x8071),a17)
% 7.14/7.07 [813]E(x8131,f3(a82))+~E(f11(x8132,x8131),f3(a85))
% 7.14/7.07 [814]E(x8141,f3(a82))+~E(f11(x8142,x8141),f16(a85))
% 7.14/7.07 [815]E(x8151,f3(a82))+~E(f11(x8151,x8152),f3(a85))
% 7.14/7.07 [816]E(x8161,f16(a82))+~E(f11(x8161,x8162),f16(a85))
% 7.14/7.07 [826]~P37(x8262)+P37(f121(x8261,x8262))
% 7.14/7.07 [827]~P38(x8272)+P38(f121(x8271,x8272))
% 7.14/7.07 [828]~P40(x8282)+P40(f121(x8281,x8282))
% 7.14/7.07 [833]E(x8331,x8332)+~E(f35(a83,x8331),f35(a83,x8332))
% 7.14/7.07 [855]~E(x8552,f3(a84))+E(f20(a84,x8551,x8552),f3(a84))
% 7.14/7.07 [858]~P26(x8581)+E(f22(x8581,x8582,x8582),f3(x8581))
% 7.14/7.07 [961]~P42(x9611)+P3(x9611,f6(x9611,a83,x9612))
% 7.14/7.07 [849]~P35(x8491)+E(f19(a82,f36(x8491,x8492)),f36(x8491,x8492))
% 7.14/7.07 [853]~P9(x8531)+E(f19(x8531,f19(x8531,x8532)),f19(x8531,x8532))
% 7.14/7.07 [854]~P34(x8541)+E(f25(x8541,f25(x8541,x8542)),f25(x8541,x8542))
% 7.14/7.07 [856]~P47(x8561)+E(f86(f86(f31(x8561),x8562),f16(a83)),x8562)
% 7.14/7.07 [857]~P27(x8571)+E(f86(f86(f31(x8571),x8572),f16(a83)),x8572)
% 7.14/7.07 [859]~P22(x8591)+E(f86(f86(f23(x8591),x8592),f3(x8591)),x8592)
% 7.14/7.07 [860]~P23(x8601)+E(f86(f86(f23(x8601),x8602),f3(x8601)),x8602)
% 7.14/7.07 [861]~P47(x8611)+E(f86(f86(f23(x8611),x8612),f3(x8611)),x8612)
% 7.14/7.07 [862]~P47(x8621)+E(f86(f86(f24(x8621),x8622),f16(x8621)),x8622)
% 7.14/7.07 [863]~P25(x8631)+E(f86(f86(f24(x8631),x8632),f16(x8631)),x8632)
% 7.14/7.07 [864]~P27(x8641)+E(f86(f86(f24(x8641),x8642),f16(x8641)),x8642)
% 7.14/7.07 [865]~P53(x8651)+E(f86(f86(f37(x8651),x8652),f16(x8651)),x8652)
% 7.14/7.07 [866]~P47(x8661)+E(f86(f86(f31(x8661),x8662),f3(a83)),f16(x8661))
% 7.14/7.07 [867]~P43(x8671)+E(f86(f86(f31(x8671),x8672),f3(a83)),f16(x8671))
% 7.14/7.07 [868]~P26(x8681)+E(f22(x8681,x8682,f3(x8681)),x8682)
% 7.14/7.07 [869]~P14(x8691)+E(f20(x8691,x8692,f16(x8691)),x8692)
% 7.14/7.07 [876]~P47(x8761)+E(f86(f86(f24(x8761),x8762),f3(x8761)),f3(x8761))
% 7.14/7.07 [878]~P41(x8781)+E(f86(f86(f24(x8781),x8782),f3(x8781)),f3(x8781))
% 7.14/7.07 [879]~P63(x8791)+E(f86(f86(f24(x8791),x8792),f3(x8791)),f3(x8791))
% 7.14/7.07 [880]~P54(x8801)+E(f86(f86(f37(x8801),x8802),f3(x8801)),f3(x8801))
% 7.14/7.07 [882]~P14(x8821)+E(f20(x8821,x8822,f3(x8821)),f3(x8821))
% 7.14/7.07 [883]~P14(x8831)+E(f20(x8831,f3(x8831),x8832),f3(x8831))
% 7.14/7.07 [905]~E(x9051,x9052)+P77(f86(f28(a82,x9051),x9052))
% 7.14/7.07 [908]~E(x9081,x9082)+P77(f86(f28(a83,x9081),x9082))
% 7.14/7.07 [922]~P37(x9221)+P77(f86(f28(x9221,x9222),x9222))
% 7.14/7.07 [925]E(f30(x9251,x9252),f3(a84))+P77(f86(f28(a84,x9252),x9251))
% 7.14/7.07 [935]~P34(x9351)+E(f86(f86(f24(x9351),x9352),f25(x9351,x9352)),f19(x9351,x9352))
% 7.14/7.07 [953]~E(x9531,x9532)+~P77(f86(f29(a82,x9531),x9532))
% 7.14/7.07 [958]~E(x9581,x9582)+~P77(f86(f29(a83,x9581),x9582))
% 7.14/7.07 [959]~E(x9591,x9592)+~P77(f86(f29(a84,x9591),x9592))
% 7.14/7.07 [962]~E(x9621,f3(a83))+~P77(f86(f29(a83,x9622),x9621))
% 7.14/7.07 [965]E(x9651,x9652)+~E(f86(x9651,f50(x9652,x9651)),f86(x9652,f50(x9652,x9651)))
% 7.14/7.07 [968]~P1(x9682)+P77(f86(f28(a83,x9681),f86(x9682,x9681)))
% 7.14/7.07 [971]~P37(x9711)+~P77(f86(f29(x9711,x9712),x9712))
% 7.14/7.07 [972]~P34(x9721)+E(f86(f86(f24(x9721),f25(x9721,x9722)),f19(x9721,x9722)),x9722)
% 7.14/7.07 [980]~P9(x9801)+P77(f86(f28(x9801,x9802),f19(x9801,x9802)))
% 7.14/7.07 [986]~P35(x9861)+P77(f86(f28(a82,f3(a82)),f36(x9861,x9862)))
% 7.14/7.07 [987]~P41(x9872)+P77(f86(f28(a82,f3(a82)),f56(x9871,x9872)))
% 7.14/7.07 [988]~P41(x9882)+P77(f86(f28(a82,f3(a82)),f57(x9881,x9882)))
% 7.14/7.07 [989]~P41(x9892)+P77(f86(f29(a82,f3(a82)),f47(x9891,x9892)))
% 7.14/7.07 [990]~P41(x9902)+P77(f86(f29(a82,f3(a82)),f48(x9901,x9902)))
% 7.14/7.07 [1005]P77(f86(f28(a82,x10052),x10051))+P77(f86(f28(a82,x10051),x10052))
% 7.14/7.07 [1006]P77(f86(f28(a83,x10062),x10061))+P77(f86(f28(a83,x10061),x10062))
% 7.14/7.07 [1007]P77(f86(f28(a84,x10072),x10071))+P77(f86(f28(a84,x10071),x10072))
% 7.14/7.07 [1016]~E(f22(a83,x10161,x10162),f3(a83))+P77(f86(f28(a83,x10161),x10162))
% 7.14/7.07 [1018]~P9(x10181)+P77(f86(f28(x10181,f3(x10181)),f19(x10181,x10182)))
% 7.14/7.07 [1047]E(f22(a83,x10471,x10472),f3(a83))+~P77(f86(f28(a83,x10471),x10472))
% 7.14/7.07 [1048]E(f20(a83,x10481,x10482),f3(a83))+~P77(f86(f29(a83,x10481),x10482))
% 7.14/7.07 [1060]E(f22(a84,x10601,x10602),f30(x10601,x10602))+~P77(f86(f28(a84,x10602),x10601))
% 7.14/7.07 [1066]E(f86(f86(f23(a83),x10661),f66(x10662,x10661)),x10662)+~P77(f86(f28(a83,x10661),x10662))
% 7.14/7.07 [1067]E(f86(f86(f23(a83),x10671),f87(x10672,x10671)),x10672)+~P77(f86(f28(a83,x10671),x10672))
% 7.14/7.07 [1073]~P77(f86(f29(a82,x10731),x10732))+P77(f86(f28(a82,x10731),x10732))
% 7.14/7.07 [1078]~P77(f86(f29(a83,x10781),x10782))+P77(f86(f28(a83,x10781),x10782))
% 7.14/7.07 [1079]~P77(f86(f29(a84,x10791),x10792))+P77(f86(f28(a84,x10791),x10792))
% 7.14/7.07 [1117]E(f86(f86(f23(a83),x11171),f22(a83,x11172,x11171)),x11172)+P77(f86(f29(a83,x11172),x11171))
% 7.14/7.07 [1122]~P77(f86(f28(a82,x11221),x11222))+P77(f86(f28(a83,f26(x11221)),f26(x11222)))
% 7.14/7.07 [1123]~P77(f86(f28(a82,x11231),x11232))+P77(f86(f28(a83,f33(x11231)),f33(x11232)))
% 7.14/7.07 [1172]E(f86(f86(f23(a83),x11721),f22(a83,x11722,x11721)),x11722)+~P77(f86(f28(a83,x11721),x11722))
% 7.14/7.07 [1185]E(f22(a83,x11851,f22(a83,x11851,x11852)),x11852)+~P77(f86(f28(a83,x11852),x11851))
% 7.14/7.07 [1199]~P35(x11991)+~P77(f86(f29(a82,f36(x11991,x11992)),f3(a82)))
% 7.14/7.07 [1225]~P9(x12251)+~P77(f86(f29(x12251,f19(x12251,x12252)),f3(x12251)))
% 7.14/7.07 [1235]~P77(f86(f28(a83,x12351),x12352))+P77(f86(f28(a82,f35(a83,x12351)),f35(a83,x12352)))
% 7.14/7.07 [1236]~P77(f86(f29(a83,x12361),x12362))+P77(f86(f29(a82,f35(a83,x12361)),f35(a83,x12362)))
% 7.14/7.07 [1240]E(f22(a82,f35(a83,x12401),f35(a83,x12402)),f35(a83,f22(a83,x12401,x12402)))+~P77(f86(f28(a83,x12402),x12401))
% 7.14/7.07 [1314]P77(f86(f28(a83,x13141),x13142))+~P77(f86(f28(a82,f35(a83,x13141)),f35(a83,x13142)))
% 7.14/7.07 [1315]P77(f86(f29(a83,x13151),x13152))+~P77(f86(f29(a82,f35(a83,x13151)),f35(a83,x13152)))
% 7.14/7.07 [1322]P77(f86(f29(a83,f3(a83)),f22(a83,x13221,x13222)))+~P77(f86(f29(a83,x13222),x13221))
% 7.14/7.07 [1361]E(f86(f86(f23(a83),f86(f86(f23(a83),x13611),f77(x13612,x13611))),f16(a83)),x13612)+~P77(f86(f29(a83,x13611),x13612))
% 7.14/7.07 [1437]~P77(f86(f29(a83,f3(a83)),f22(a83,x14372,x14371)))+P77(f86(f29(a83,x14371),x14372))
% 7.14/7.07 [1487]~P77(f86(f28(a82,x14871),x14872))+P77(f86(f28(a82,f22(a82,x14871,x14872)),f3(a82)))
% 7.14/7.07 [1488]~P77(f86(f29(a84,x14881),x14882))+P77(f86(f29(a84,f22(a84,x14881,x14882)),f3(a84)))
% 7.14/7.07 [1597]~P57(x15971)+~P77(f86(f29(x15971,f86(f86(f24(x15971),x15972),x15972)),f3(x15971)))
% 7.14/7.07 [1642]P77(f86(f28(a82,x16421),x16422))+~P77(f86(f28(a82,f22(a82,x16421,x16422)),f3(a82)))
% 7.14/7.07 [1643]P77(f86(f29(a84,x16431),x16432))+~P77(f86(f29(a84,f22(a84,x16431,x16432)),f3(a84)))
% 7.14/7.07 [1717]~P77(f86(f29(a83,x17171),x17172))+P77(f86(f28(a82,f86(f86(f23(a82),f35(a83,x17171)),f16(a82))),f35(a83,x17172)))
% 7.14/7.07 [1839]P77(f86(f29(a83,x18391),x18392))+~P77(f86(f28(a82,f86(f86(f23(a82),f35(a83,x18391)),f16(a82))),f35(a83,x18392)))
% 7.14/7.07 [840]~E(x8401,f3(a83))+E(f86(f86(f23(a83),x8401),x8402),x8402)
% 7.14/7.07 [842]~E(x8422,f3(a83))+E(f86(f86(f24(a83),x8421),x8422),f3(a83))
% 7.14/7.07 [844]~E(x8441,f3(a83))+E(f86(f86(f24(a83),x8441),x8442),f3(a83))
% 7.14/7.07 [845]~E(x8452,f3(a83))+E(f86(f86(f31(a83),x8451),x8452),f16(a83))
% 7.14/7.07 [890]~P22(x8901)+E(f86(f86(f23(x8901),f3(x8901)),x8902),x8902)
% 7.14/7.07 [891]~P23(x8911)+E(f86(f86(f23(x8911),f3(x8911)),x8912),x8912)
% 7.14/7.07 [892]~P47(x8921)+E(f86(f86(f23(x8921),f3(x8921)),x8922),x8922)
% 7.14/7.07 [893]~P47(x8931)+E(f86(f86(f24(x8931),f16(x8931)),x8932),x8932)
% 7.14/7.07 [894]~P25(x8941)+E(f86(f86(f24(x8941),f16(x8941)),x8942),x8942)
% 7.14/7.07 [895]~P27(x8951)+E(f86(f86(f24(x8951),f16(x8951)),x8952),x8952)
% 7.14/7.07 [896]~P47(x8961)+E(f86(f86(f24(x8961),f3(x8961)),x8962),f3(x8961))
% 7.14/7.07 [898]~P41(x8981)+E(f86(f86(f24(x8981),f3(x8981)),x8982),f3(x8981))
% 7.14/7.07 [899]~P63(x8991)+E(f86(f86(f24(x8991),f3(x8991)),x8992),f3(x8991))
% 7.14/7.07 [900]~P27(x9001)+E(f86(f86(f31(x9001),f16(x9001)),x9002),f16(x9001))
% 7.14/7.07 [901]~P46(x9011)+E(f86(f86(f37(x9011),f3(x9011)),x9012),f3(x9011))
% 7.14/7.07 [902]~P53(x9021)+E(f86(f86(f37(x9021),f3(x9021)),x9022),f3(x9021))
% 7.14/7.07 [903]E(x9031,f3(a83))+~E(f86(f86(f23(a83),x9032),x9031),x9032)
% 7.14/7.07 [911]E(x9111,f3(a83))+~E(f86(f86(f23(a83),x9112),x9111),f3(a83))
% 7.14/7.07 [912]E(x9121,f3(a83))+~E(f86(f86(f23(a83),x9121),x9122),f3(a83))
% 7.14/7.07 [913]E(x9131,f16(a83))+~E(f86(f86(f24(a83),x9132),x9131),f16(a83))
% 7.14/7.07 [914]E(x9141,f16(a83))+~E(f86(f86(f24(a83),x9141),x9142),f16(a83))
% 7.14/7.07 [945]~E(x9452,f3(a83))+E(f86(f86(f31(a83),x9451),x9452),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.07 [1021]~E(x10211,f86(f86(f23(a83),x10212),f16(a83)))+P77(f86(f29(a83,f3(a83)),x10211))
% 7.14/7.07 [1061]~P34(x10611)+E(f86(f86(f24(x10611),f19(x10611,x10612)),f19(x10611,x10612)),f86(f86(f24(x10611),x10612),x10612))
% 7.14/7.07 [1062]~E(x10621,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f31(a83),x10621),x10622),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.07 [1094]E(x10941,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f24(a83),x10942),x10941),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.07 [1095]E(x10951,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f24(a83),x10951),x10952),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.07 [1173]~E(x11731,x11732)+P77(f86(f29(a83,x11731),f86(f86(f23(a83),x11732),f16(a83))))
% 7.14/7.07 [1174]~E(x11741,x11742)+P77(f86(f29(a84,x11741),f86(f86(f23(a84),x11742),f16(a84))))
% 7.14/7.07 [1180]~E(x11801,f3(a83))+P77(f86(f29(a83,x11801),f86(f86(f23(a83),x11802),f16(a83))))
% 7.14/7.07 [1188]P77(f86(f29(a82,f3(a82)),f100(x11881,x11882)))+~P77(f86(f29(a82,f3(a82)),x11882))
% 7.14/7.07 [1195]~P77(f86(f28(a82,x11951),f35(a83,x11952)))+P77(f86(f28(a83,f26(x11951)),x11952))
% 7.14/7.07 [1223]~P7(x12231)+P77(f86(f29(x12231,x12232),f86(f86(f23(x12231),x12232),f16(x12231))))
% 7.14/7.07 [1239]E(f86(f86(f31(a82),f100(x12391,x12392)),f86(f86(f23(a83),x12391),f16(a83))),x12392)+~P77(f86(f29(a82,f3(a82)),x12392))
% 7.14/7.07 [1241]E(f26(f86(f86(f23(a82),x12411),f35(a83,x12412))),f86(f86(f23(a83),f26(x12411)),x12412))+~P77(f86(f28(a82,f3(a82)),x12411))
% 7.14/7.07 [1242]E(f33(f86(f86(f23(a82),x12421),f35(a83,x12422))),f86(f86(f23(a83),f33(x12421)),x12422))+~P77(f86(f28(a82,f3(a82)),x12421))
% 7.14/7.07 [1245]P77(f86(f29(a83,x12451),x12452))+P77(f86(f29(a83,x12452),f86(f86(f23(a83),x12451),f16(a83))))
% 7.14/7.07 [1256]P77(f86(f28(a83,x12561),f33(x12562)))+~P77(f86(f28(a82,f35(a83,x12561)),x12562))
% 7.14/7.07 [1262]E(f86(f86(f23(a83),f22(a83,x12621,x12622)),x12622),x12621)+~P77(f86(f28(a83,x12622),x12621))
% 7.14/7.07 [1288]~P77(f86(f28(a83,x12881),x12882))+P77(f86(f29(a83,x12881),f86(f86(f23(a83),x12882),f16(a83))))
% 7.14/7.07 [1291]~P77(f86(f28(a84,x12911),x12912))+P77(f86(f29(a84,x12911),f86(f86(f23(a84),x12912),f16(a84))))
% 7.14/7.07 [1292]~P77(f86(f29(a84,x12921),x12922))+P77(f86(f29(a84,x12921),f86(f86(f23(a84),x12922),f16(a84))))
% 7.14/7.07 [1321]~P77(f86(f29(a84,x13211),x13212))+P77(f86(f28(a84,x13211),f22(a84,x13212,f16(a84))))
% 7.14/7.07 [1370]E(f26(f22(a82,x13701,f35(a83,x13702))),f22(a83,f26(x13701),x13702))+~P77(f86(f28(a82,f35(a83,x13702)),x13701))
% 7.14/7.07 [1371]E(f33(f22(a82,x13711,f35(a83,x13712))),f22(a83,f33(x13711),x13712))+~P77(f86(f28(a82,f35(a83,x13712)),x13711))
% 7.14/7.07 [1386]P77(f86(f28(a83,x13861),x13862))+~P77(f86(f29(a83,x13861),f86(f86(f23(a83),x13862),f16(a83))))
% 7.14/7.07 [1387]P77(f86(f28(a84,x13871),x13872))+~P77(f86(f29(a84,x13871),f86(f86(f23(a84),x13872),f16(a84))))
% 7.14/7.07 [1436]P77(f86(f29(a84,x14361),x14362))+~P77(f86(f28(a84,x14361),f22(a84,x14362,f16(a84))))
% 7.14/7.07 [1439]~P77(f86(f29(a83,x14391),x14392))+~P77(f86(f29(a83,x14392),f86(f86(f23(a83),x14391),f16(a83))))
% 7.14/7.07 [1456]~P73(x14561)+E(f86(f86(f24(x14561),f86(f86(f23(x14561),x14562),f16(x14561))),f22(x14561,x14562,f16(x14561))),f22(x14561,f86(f86(f24(x14561),x14562),x14562),f16(x14561)))
% 7.14/7.07 [1528]~P77(f86(f28(a83,x15281),x15282))+P77(f86(f29(a82,f35(a83,x15281)),f86(f86(f23(a82),f35(a83,x15282)),f16(a82))))
% 7.14/7.07 [1683]P77(f86(f28(a83,x16831),x16832))+~P77(f86(f29(a82,f35(a83,x16831)),f86(f86(f23(a82),f35(a83,x16832)),f16(a82))))
% 7.14/7.07 [1757]P77(f86(f28(a83,x17571),x17572))+~P77(f86(f28(a83,f86(f86(f23(a83),x17571),f16(a83))),f86(f86(f23(a83),x17572),f16(a83))))
% 7.14/7.07 [1759]P77(f86(f29(a83,x17591),x17592))+~P77(f86(f29(a83,f86(f86(f23(a83),x17591),f16(a83))),f86(f86(f23(a83),x17592),f16(a83))))
% 7.14/7.07 [1769]E(x17691,f3(a83))+E(f86(f86(f23(a83),f86(f86(f23(a83),f22(a83,x17691,f16(a83))),x17692)),f16(a83)),f86(f86(f23(a83),x17691),x17692))
% 7.14/7.07 [1055]E(f19(a84,x10551),f16(a84))+~E(f19(a84,f86(f86(f24(a84),x10551),x10552)),f16(a84))
% 7.14/7.07 [1056]~E(f35(a83,f33(x10561)),x10561)+E(f33(f86(f86(f31(a82),x10561),x10562)),f86(f86(f31(a83),f33(x10561)),x10562))
% 7.14/7.07 [1182]~E(x11822,f3(a83))+P77(f86(f29(a83,f3(a83)),f86(f86(f31(a83),x11821),x11822)))
% 7.14/7.07 [1189]E(f20(a83,f86(f86(f24(a83),x11891),x11892),x11892),x11891)+~P77(f86(f29(a83,f3(a83)),x11892))
% 7.14/7.07 [1190]E(f20(a83,f86(f86(f24(a83),x11901),x11902),x11901),x11902)+~P77(f86(f29(a83,f3(a83)),x11901))
% 7.14/7.07 [1224]~P57(x12241)+P77(f86(f28(x12241,f3(x12241)),f86(f86(f24(x12241),x12242),x12242)))
% 7.14/7.07 [1234]E(f86(f86(f24(a82),f35(a83,x12341)),f34(x12342)),f34(f86(f86(f31(a82),x12342),x12341)))+~P77(f86(f29(a82,f3(a82)),x12342))
% 7.14/7.07 [1294]~P47(x12941)+E(f86(f86(f23(x12941),x12942),x12942),f86(f86(f24(x12941),f86(f86(f23(x12941),f16(x12941)),f16(x12941))),x12942))
% 7.14/7.07 [1302]E(x13021,f3(a83))+E(f86(f86(f24(a83),x13022),f86(f86(f31(a83),x13022),f22(a83,x13021,f16(a83)))),f86(f86(f31(a83),x13022),x13021))
% 7.14/7.07 [1305]~P77(f86(f28(a84,f3(a84)),x13051))+P77(f86(f28(a84,f3(a84)),f86(f86(f31(a84),x13051),x13052)))
% 7.14/7.07 [1309]~P77(f86(f29(a83,f3(a83)),x13091))+P77(f86(f29(a83,f3(a83)),f86(f86(f31(a83),x13091),x13092)))
% 7.14/7.07 [1362]E(x13621,f3(a84))+P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x13621)),x13622)))
% 7.14/7.07 [1363]~E(x13632,f3(a83))+P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x13631)),x13632)))
% 7.14/7.07 [1394]E(x13941,f3(a82))+~E(f86(f86(f23(a82),f86(f86(f24(a82),x13942),x13942)),f86(f86(f24(a82),x13941),x13941)),f3(a82))
% 7.14/7.07 [1395]E(x13951,f3(a82))+~E(f86(f86(f23(a82),f86(f86(f24(a82),x13951),x13951)),f86(f86(f24(a82),x13952),x13952)),f3(a82))
% 7.14/7.07 [1399]P77(f86(f29(a83,f3(a83)),x13991))+~P77(f86(f29(a83,f3(a83)),f86(f86(f24(a83),x13992),x13991)))
% 7.14/7.07 [1400]P77(f86(f29(a83,f3(a83)),x14001))+~P77(f86(f29(a83,f3(a83)),f86(f86(f24(a83),x14001),x14002)))
% 7.14/7.07 [1430]P77(f86(f28(a83,x14301),x14302))+P77(f86(f28(a83,f86(f86(f23(a83),x14302),f16(a83))),x14301))
% 7.14/7.07 [1463]~P77(f86(f29(a83,x14631),x14632))+P77(f86(f28(a83,f86(f86(f23(a83),x14631),f16(a83))),x14632))
% 7.14/7.07 [1465]~P77(f86(f29(a84,x14651),x14652))+P77(f86(f28(a84,f86(f86(f23(a84),x14651),f16(a84))),x14652))
% 7.14/7.07 [1500]~P1(x15001)+P77(f86(f29(a83,f86(x15001,x15002)),f86(x15001,f86(f86(f23(a83),x15002),f16(a83)))))
% 7.14/7.07 [1602]P77(f86(f29(a83,x16021),x16022))+~P77(f86(f28(a83,f86(f86(f23(a83),x16021),f16(a83))),x16022))
% 7.14/7.07 [1604]P77(f86(f29(a84,x16041),x16042))+~P77(f86(f28(a84,f86(f86(f23(a84),x16041),f16(a84))),x16042))
% 7.14/7.07 [1635]~P77(f86(f28(a83,x16351),x16352))+~P77(f86(f28(a83,f86(f86(f23(a83),x16352),f16(a83))),x16351))
% 7.14/7.07 [1719]P77(f86(f29(a82,x17191),f35(a83,x17192)))+~P77(f86(f28(a83,f86(f86(f23(a83),f33(x17191)),f16(a83))),x17192))
% 7.14/7.07 [1843]~P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18431))+P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f31(a83),x18431),x18432)))
% 7.14/7.07 [1860]P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18601))+~P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f24(a83),x18602),x18601)))
% 7.14/7.07 [1861]P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18611))+~P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f24(a83),x18611),x18612)))
% 7.14/7.07 [1503]E(x15031,f3(a83))+E(f86(f86(f23(a83),x15032),f86(f86(f24(a83),f22(a83,x15031,f16(a83))),x15032)),f86(f86(f24(a83),x15031),x15032))
% 7.14/7.07 [1718]~P77(f86(f29(a82,f3(a82)),x17182))+P77(f86(f29(a82,x17181),f86(f86(f24(a82),f35(a83,f97(x17182,x17181))),x17182)))
% 7.14/7.07 [1834]~P77(f86(f29(a83,f3(a83)),x18341))+P77(f86(f29(a83,f22(a83,x18341,f86(f86(f23(a83),x18342),f16(a83)))),x18341))
% 7.14/7.07 [1932]~P77(f86(f28(a82,f3(a82)),x19322))+P77(f86(f28(a82,f86(f86(f23(a82),f86(f86(f24(a82),f35(a83,x19321)),x19322)),f16(a82))),f86(f86(f31(a82),f86(f86(f23(a82),x19322),f16(a82))),x19321)))
% 7.14/7.07 [1139]~P9(x11391)+E(f19(x11391,f22(x11391,x11392,x11393)),f19(x11391,f22(x11391,x11393,x11392)))
% 7.14/7.07 [1140]~P35(x11401)+E(f36(x11401,f22(x11401,x11402,x11403)),f36(x11401,f22(x11401,x11403,x11402)))
% 7.14/7.07 [1227]~P78(x12271,x12273,x12272)+P77(f86(x12271,f20(a84,x12272,x12273)))
% 7.14/7.07 [1342]P78(x13421,x13422,x13423)+~P77(f86(x13421,f20(a84,x13423,x13422)))
% 7.14/7.07 [1352]~E(x13522,f86(f86(f23(a83),f86(f86(f23(a83),x13521),x13523)),f16(a83)))+P77(f86(f29(a83,x13521),x13522))
% 7.14/7.07 [1611]~P77(f86(f28(a83,x16113),x16112))+P77(f86(f28(a83,f22(a83,x16111,x16112)),f22(a83,x16111,x16113)))
% 7.14/7.07 [1612]~P77(f86(f28(a83,x16121),x16123))+P77(f86(f28(a83,f22(a83,x16121,x16122)),f22(a83,x16123,x16122)))
% 7.14/7.07 [1613]~P77(f86(f28(a83,x16131),x16133))+P77(f86(f28(a83,f20(a83,x16131,x16132)),f20(a83,x16133,x16132)))
% 7.14/7.07 [1933]~P57(x19331)+~P77(f86(f29(x19331,f86(f86(f23(x19331),f86(f86(f24(x19331),x19332),x19332)),f86(f86(f24(x19331),x19333),x19333))),f3(x19331)))
% 7.14/7.07 [932]~E(x9322,f3(a83))+E(f86(f86(f24(a83),x9321),x9322),f86(f86(f24(a83),x9323),x9322))
% 7.14/7.07 [934]~E(x9341,f3(a83))+E(f86(f86(f24(a83),x9341),x9342),f86(f86(f24(a83),x9341),x9343))
% 7.14/7.07 [948]~P47(x9481)+E(f86(f86(f23(x9481),x9482),x9483),f86(f86(f23(x9481),x9483),x9482))
% 7.14/7.07 [949]~P47(x9491)+E(f86(f86(f24(x9491),x9492),x9493),f86(f86(f24(x9491),x9493),x9492))
% 7.14/7.07 [984]E(x9841,x9842)+~E(f86(f86(f23(a83),x9843),x9841),f86(f86(f23(a83),x9843),x9842))
% 7.14/7.07 [985]E(x9851,x9852)+~E(f86(f86(f23(a83),x9851),x9853),f86(f86(f23(a83),x9852),x9853))
% 7.14/7.07 [998]~E(x9982,f86(f86(f23(a83),x9981),x9983))+P77(f86(f28(a83,x9981),x9982))
% 7.14/7.07 [1179]~P26(x11791)+E(f86(f86(f23(x11791),f22(x11791,x11792,x11793)),x11793),x11792)
% 7.14/7.07 [1313]~P9(x13131)+E(f19(x13131,f86(f86(f23(x13131),f19(x13131,x13132)),f19(x13131,x13133))),f86(f86(f23(x13131),f19(x13131,x13132)),f19(x13131,x13133)))
% 7.14/7.07 [1482]~P77(f86(f29(a83,x14821),x14823))+P77(f86(f29(a83,f22(a83,x14821,x14822)),x14823))
% 7.14/7.07 [1678]E(f22(a83,f86(f86(f23(a83),x16781),x16782),f86(f86(f23(a83),x16783),f16(a83))),f22(a83,x16781,f86(f86(f23(a83),f22(a83,x16783,x16782)),f16(a83))))+~P77(f86(f28(a83,x16782),x16783))
% 7.14/7.07 [1832]~P35(x18321)+P77(f86(f28(a82,f22(a82,f36(x18321,x18322),f36(x18321,x18323))),f36(x18321,f22(x18321,x18322,x18323))))
% 7.14/7.07 [1835]~P9(x18351)+P77(f86(f28(x18351,f22(x18351,f19(x18351,x18352),f19(x18351,x18353))),f19(x18351,f22(x18351,x18353,x18352))))
% 7.14/7.07 [1836]~P9(x18361)+P77(f86(f28(x18361,f22(x18361,f19(x18361,x18362),f19(x18361,x18363))),f19(x18361,f22(x18361,x18362,x18363))))
% 7.14/7.07 [1844]~P35(x18441)+P77(f86(f28(a82,f36(x18441,f86(f86(f23(x18441),x18442),x18443))),f86(f86(f23(a82),f36(x18441,x18442)),f36(x18441,x18443))))
% 7.14/7.07 [1845]~P41(x18451)+P77(f86(f28(a82,f36(x18451,f86(f86(f24(x18451),x18452),x18453))),f86(f86(f24(a82),f36(x18451,x18453)),f48(x18452,x18451))))
% 7.14/7.07 [1846]~P41(x18461)+P77(f86(f28(a82,f36(x18461,f86(f86(f24(x18461),x18462),x18463))),f86(f86(f24(a82),f36(x18461,x18463)),f57(x18462,x18461))))
% 7.14/7.07 [1847]~P41(x18471)+P77(f86(f28(a82,f36(x18471,f86(f86(f24(x18471),x18472),x18473))),f86(f86(f24(a82),f36(x18471,x18473)),f103(x18472,x18471))))
% 7.14/7.07 [1848]~P41(x18481)+P77(f86(f28(a82,f36(x18481,f86(f86(f24(x18481),x18482),x18483))),f86(f86(f24(a82),f36(x18481,x18482)),f36(x18481,x18483))))
% 7.14/7.07 [1849]~P41(x18491)+P77(f86(f28(a82,f36(x18491,f86(f86(f24(x18491),x18492),x18493))),f86(f86(f24(a82),f36(x18491,x18492)),f47(x18493,x18491))))
% 7.14/7.07 [1850]~P41(x18501)+P77(f86(f28(a82,f36(x18501,f86(f86(f24(x18501),x18502),x18503))),f86(f86(f24(a82),f36(x18501,x18502)),f56(x18503,x18501))))
% 7.14/7.07 [1851]~P41(x18511)+P77(f86(f28(a82,f36(x18511,f86(f86(f24(x18511),x18512),x18513))),f86(f86(f24(a82),f36(x18511,x18512)),f104(x18513,x18511))))
% 7.14/7.07 [1852]~P9(x18521)+P77(f86(f28(x18521,f19(x18521,f86(f86(f23(x18521),x18522),x18523))),f86(f86(f23(x18521),f19(x18521,x18522)),f19(x18521,x18523))))
% 7.14/7.07 [1853]~P35(x18531)+P77(f86(f28(a82,f36(x18531,f22(x18531,x18532,x18533))),f86(f86(f23(a82),f36(x18531,x18532)),f36(x18531,x18533))))
% 7.14/7.07 [1857]~P9(x18571)+P77(f86(f28(x18571,f19(x18571,f22(x18571,x18572,x18573))),f86(f86(f23(x18571),f19(x18571,x18572)),f19(x18571,x18573))))
% 7.14/7.07 [1897]~P35(x18971)+P77(f86(f28(a82,f19(a82,f22(a82,f36(x18971,x18972),f36(x18971,x18973)))),f36(x18971,f22(x18971,x18972,x18973))))
% 7.14/7.07 [1898]~P9(x18981)+P77(f86(f28(x18981,f19(x18981,f22(x18981,f19(x18981,x18982),f19(x18981,x18983)))),f19(x18981,f22(x18981,x18982,x18983))))
% 7.14/7.07 [1912]~P41(x19121)+P77(f86(f28(a82,f36(x19121,f86(f86(f24(x19121),x19122),x19123))),f86(f86(f24(a82),f86(f86(f24(a82),f36(x19121,x19122)),f36(x19121,x19123))),f46(x19121))))
% 7.14/7.07 [1913]~P41(x19131)+P77(f86(f28(a82,f36(x19131,f86(f86(f24(x19131),x19132),x19133))),f86(f86(f24(a82),f86(f86(f24(a82),f36(x19131,x19132)),f36(x19131,x19133))),f51(x19131))))
% 7.14/7.07 [1914]~P41(x19141)+P77(f86(f28(a82,f36(x19141,f86(f86(f24(x19141),x19142),x19143))),f86(f86(f24(a82),f86(f86(f24(a82),f36(x19141,x19142)),f36(x19141,x19143))),f105(x19141))))
% 7.14/7.07 [1017]~P26(x10171)+E(f22(x10171,f86(f86(f23(x10171),x10172),x10173),x10173),x10172)
% 7.14/7.07 [1116]~P45(x11161)+E(f36(x11161,f86(f86(f31(x11161),x11162),x11163)),f86(f86(f31(a82),f36(x11161,x11162)),x11163))
% 7.14/7.07 [1120]~P34(x11201)+E(f19(x11201,f86(f86(f31(x11201),x11202),x11203)),f86(f86(f31(x11201),f19(x11201,x11202)),x11203))
% 7.14/7.07 [1131]~E(x11311,f3(a83))+E(f20(a83,f86(f86(f24(a83),x11311),x11312),f86(f86(f24(a83),x11311),x11313)),f3(a83))
% 7.14/7.07 [1137]~P45(x11371)+E(f86(f86(f24(a82),f36(x11371,x11372)),f36(x11371,x11373)),f36(x11371,f86(f86(f24(x11371),x11372),x11373)))
% 7.14/7.07 [1145]~P34(x11451)+E(f86(f86(f24(x11451),f19(x11451,x11452)),f19(x11451,x11453)),f19(x11451,f86(f86(f24(x11451),x11452),x11453)))
% 7.14/7.07 [1146]~P34(x11461)+E(f86(f86(f24(x11461),f25(x11461,x11462)),f25(x11461,x11463)),f25(x11461,f86(f86(f24(x11461),x11462),x11463)))
% 7.14/7.07 [1147]~P45(x11471)+E(f86(f86(f24(x11471),f25(x11471,x11472)),f25(x11471,x11473)),f25(x11471,f86(f86(f24(x11471),x11472),x11473)))
% 7.14/7.07 [1194]E(x11941,f3(a83))+E(f20(a83,f86(f86(f24(a83),x11941),x11942),f86(f86(f24(a83),x11941),x11943)),f20(a83,x11942,x11943))
% 7.14/7.07 [1208]~P47(x12081)+E(f86(f86(f24(x12081),x12082),f86(f86(f31(x12081),x12082),x12083)),f86(f86(f31(x12081),x12082),f86(f86(f23(a83),x12083),f16(a83))))
% 7.14/7.07 [1209]~P47(x12091)+E(f86(f86(f31(x12091),x12092),f86(f86(f23(a83),x12093),f16(a83))),f86(f86(f24(x12091),x12092),f86(f86(f31(x12091),x12092),x12093)))
% 7.14/7.07 [1210]~P43(x12101)+E(f86(f86(f31(x12101),x12102),f86(f86(f23(a83),x12103),f16(a83))),f86(f86(f24(x12101),x12102),f86(f86(f31(x12101),x12102),x12103)))
% 7.14/7.07 [1266]~P77(f86(f28(a83,x12661),x12663))+P77(f86(f28(a83,x12661),f86(f86(f23(a83),x12662),x12663)))
% 7.14/7.07 [1268]~P77(f86(f28(a83,x12681),x12682))+P77(f86(f28(a83,x12681),f86(f86(f23(a83),x12682),x12683)))
% 7.14/7.07 [1270]~P77(f86(f29(a83,x12701),x12703))+P77(f86(f29(a83,x12701),f86(f86(f23(a83),x12702),x12703)))
% 7.14/7.07 [1272]~P77(f86(f29(a83,x12721),x12722))+P77(f86(f29(a83,x12721),f86(f86(f23(a83),x12722),x12723)))
% 7.14/7.07 [1319]~P77(f86(f28(a83,x13193),x13192))+E(f22(a83,f86(f86(f23(a83),x13191),x13192),x13193),f86(f86(f23(a83),x13191),f22(a83,x13192,x13193)))
% 7.14/7.07 [1337]~P77(f86(f28(a83,x13372),x13373))+E(f22(a83,f86(f86(f23(a83),x13371),x13372),x13373),f22(a83,x13371,f22(a83,x13373,x13372)))
% 7.14/7.07 [1338]E(f20(a83,f86(f86(f24(a83),x13381),x13382),f86(f86(f24(a83),x13381),x13383)),f20(a83,x13382,x13383))+~P77(f86(f29(a83,f3(a83)),x13381))
% 7.14/7.07 [1353]E(f20(a84,x13531,f86(f86(f24(a84),x13532),x13533)),f20(a84,f20(a84,x13531,x13532),x13533))+~P77(f86(f29(a84,f3(a84)),x13533))
% 7.14/7.07 [1356]~P47(x13561)+E(f86(f86(f23(x13561),x13562),f86(f86(f24(x13561),x13563),x13562)),f86(f86(f24(x13561),f86(f86(f23(x13561),x13563),f16(x13561))),x13562))
% 7.14/7.07 [1408]~P77(f86(f28(a83,x14083),x14081))+E(f22(a83,f86(f86(f23(a83),x14081),x14082),x14083),f86(f86(f23(a83),f22(a83,x14081,x14083)),x14082))
% 7.14/7.07 [1416]~P34(x14161)+P77(f86(f28(x14161,f3(x14161)),f86(f86(f31(x14161),f19(x14161,x14162)),x14163)))
% 7.14/7.07 [1548]P77(f86(f29(a83,f3(a83)),x15481))+P77(f86(f28(a83,f86(f86(f24(a83),x15482),x15481)),f86(f86(f24(a83),x15483),x15481)))
% 7.14/7.07 [1549]P77(f86(f29(a83,f3(a83)),x15491))+P77(f86(f28(a83,f86(f86(f24(a83),x15491),x15492)),f86(f86(f24(a83),x15491),x15493)))
% 7.14/7.07 [1558]~P77(f86(f28(a82,x15582),x15583))+P77(f86(f28(a82,f86(f86(f23(a82),x15581),x15582)),f86(f86(f23(a82),x15581),x15583)))
% 7.14/7.07 [1559]~P77(f86(f28(a83,x15592),x15593))+P77(f86(f28(a83,f86(f86(f23(a83),x15591),x15592)),f86(f86(f23(a83),x15591),x15593)))
% 7.14/7.07 [1560]~P77(f86(f28(a83,x15601),x15603))+P77(f86(f28(a83,f86(f86(f23(a83),x15601),x15602)),f86(f86(f23(a83),x15603),x15602)))
% 7.14/7.07 [1562]~P77(f86(f28(a83,x15622),x15623))+P77(f86(f28(a83,f86(f86(f24(a83),x15621),x15622)),f86(f86(f24(a83),x15621),x15623)))
% 7.14/7.07 [1564]~P77(f86(f28(a83,x15641),x15643))+P77(f86(f28(a83,f86(f86(f24(a83),x15641),x15642)),f86(f86(f24(a83),x15643),x15642)))
% 7.14/7.07 [1565]~P77(f86(f28(a84,x15652),x15653))+P77(f86(f28(a84,f86(f86(f23(a84),x15651),x15652)),f86(f86(f23(a84),x15651),x15653)))
% 7.14/7.07 [1566]~P77(f86(f29(a83,x15662),x15663))+P77(f86(f29(a83,f86(f86(f23(a83),x15661),x15662)),f86(f86(f23(a83),x15661),x15663)))
% 7.14/7.07 [1567]~P77(f86(f29(a83,x15671),x15673))+P77(f86(f29(a83,f86(f86(f23(a83),x15671),x15672)),f86(f86(f23(a83),x15673),x15672)))
% 7.14/7.07 [1568]~P77(f86(f29(a84,x15681),x15683))+P77(f86(f29(a84,f86(f86(f23(a84),x15681),x15682)),f86(f86(f23(a84),x15683),x15682)))
% 7.14/7.07 [1573]E(x15731,x15732)+~E(f86(f86(f24(a83),f86(f86(f23(a83),x15733),f16(a83))),x15731),f86(f86(f24(a83),f86(f86(f23(a83),x15733),f16(a83))),x15732))
% 7.14/7.07 [1670]P77(f86(f28(a83,f22(a83,x16701,x16702)),x16703))+~P77(f86(f28(a83,x16701),f86(f86(f23(a83),x16703),x16702)))
% 7.14/7.07 [1679]~P77(f86(f28(a83,x16792),x16791))+E(f22(a83,f86(f86(f23(a83),x16791),f16(a83)),f86(f86(f23(a83),x16792),x16793)),f22(a83,f86(f86(f23(a83),f22(a83,x16791,x16792)),f16(a83)),x16793))
% 7.14/7.07 [1741]~P77(f86(f28(a83,f22(a83,x17411,x17413)),x17412))+P77(f86(f28(a83,x17411),f86(f86(f23(a83),x17412),x17413)))
% 7.14/7.07 [1742]P77(f86(f28(a83,x17421),x17422))+~P77(f86(f28(a83,f86(f86(f23(a83),x17423),x17421)),f86(f86(f23(a83),x17423),x17422)))
% 7.14/7.07 [1743]P77(f86(f29(a83,x17431),x17432))+~P77(f86(f29(a83,f86(f86(f23(a83),x17433),x17431)),f86(f86(f23(a83),x17433),x17432)))
% 7.14/7.07 [1744]P77(f86(f29(a83,x17441),x17442))+~P77(f86(f29(a83,f86(f86(f24(a83),x17443),x17441)),f86(f86(f24(a83),x17443),x17442)))
% 7.14/7.07 [1745]P77(f86(f29(a83,x17451),x17452))+~P77(f86(f29(a83,f86(f86(f24(a83),x17451),x17453)),f86(f86(f24(a83),x17452),x17453)))
% 7.14/7.07 [1747]P77(f86(f29(a83,f3(a83)),x17471))+~P77(f86(f29(a83,f86(f86(f24(a83),x17472),x17471)),f86(f86(f24(a83),x17473),x17471)))
% 7.14/7.07 [1748]P77(f86(f29(a83,f3(a83)),x17481))+~P77(f86(f29(a83,f86(f86(f24(a83),x17481),x17482)),f86(f86(f24(a83),x17481),x17483)))
% 7.14/7.07 [1833]~P36(x18331)+P77(f86(f28(a82,f36(x18331,f86(f86(f31(x18331),x18332),x18333))),f86(f86(f31(a82),f36(x18331,x18332)),x18333)))
% 7.14/7.07 [1904]~P49(x19041)+E(f22(x19041,f86(f86(f31(x19041),x19042),f86(f86(f23(a83),f86(f86(f23(a83),f3(a83)),f16(a83))),f16(a83))),f86(f86(f31(x19041),x19043),f86(f86(f23(a83),f86(f86(f23(a83),f3(a83)),f16(a83))),f16(a83)))),f86(f86(f24(x19041),f22(x19041,x19042,x19043)),f86(f86(f23(x19041),x19042),x19043)))
% 7.14/7.07 [1316]~P47(x13161)+E(f86(f86(f24(x13161),f86(f86(f31(x13161),x13162),x13163)),x13162),f86(f86(f31(x13161),x13162),f86(f86(f23(a83),x13163),f16(a83))))
% 7.14/7.07 [1317]~P27(x13171)+E(f86(f86(f31(x13171),x13172),f86(f86(f23(a83),x13173),f16(a83))),f86(f86(f24(x13171),f86(f86(f31(x13171),x13172),x13173)),x13172))
% 7.14/7.07 [1332]~P27(x13321)+E(f86(f86(f24(x13321),f86(f86(f31(x13321),x13322),x13323)),x13322),f86(f86(f24(x13321),x13322),f86(f86(f31(x13321),x13322),x13323)))
% 7.14/7.07 [1375]~P16(x13751)+E(f86(f86(f31(x13751),f86(f86(f37(x13751),f16(x13751)),x13752)),x13753),f86(f86(f37(x13751),f16(x13751)),f86(f86(f31(x13751),x13752),x13753)))
% 7.14/7.07 [1441]~P47(x14411)+E(f86(f86(f23(x14411),f86(f86(f24(x14411),x14412),x14413)),x14413),f86(f86(f24(x14411),f86(f86(f23(x14411),x14412),f16(x14411))),x14413))
% 7.14/7.07 [1577]P77(f86(f28(a83,x15771),x15772))+~P77(f86(f28(a83,f86(f86(f23(a83),x15773),x15771)),x15772))
% 7.14/7.07 [1578]P77(f86(f28(a83,x15781),x15782))+~P77(f86(f28(a83,f86(f86(f23(a83),x15781),x15783)),x15782))
% 7.14/7.07 [1579]P77(f86(f29(a83,x15791),x15792))+~P77(f86(f29(a83,f86(f86(f23(a83),x15791),x15793)),x15792))
% 7.14/7.07 [1580]~P77(f86(f28(a83,x15803),x15802))+P77(f86(f28(a83,x15801),f22(a83,f86(f86(f23(a83),x15802),x15801),x15803)))
% 7.14/7.07 [1661]~P77(f86(f29(a83,x16611),f22(a83,x16613,x16612)))+P77(f86(f29(a83,f86(f86(f23(a83),x16611),x16612)),x16613))
% 7.14/7.07 [1699]P77(f86(f29(a83,x16991),f22(a83,x16992,x16993)))+~P77(f86(f29(a83,f86(f86(f23(a83),x16991),x16993)),x16992))
% 7.14/7.07 [1829]~P35(x18291)+P77(f86(f28(a82,f22(a82,f36(x18291,x18292),f36(x18291,x18293))),f36(x18291,f86(f86(f23(x18291),x18292),x18293))))
% 7.14/7.07 [1854]~P57(x18541)+P77(f86(f28(x18541,f3(x18541)),f86(f86(f23(x18541),f86(f86(f24(x18541),x18542),x18542)),f86(f86(f24(x18541),x18543),x18543))))
% 7.14/7.07 [1909]~P77(f86(f29(a83,x19092),x19093))+P77(f86(f29(a83,f86(f86(f24(a83),f86(f86(f23(a83),x19091),f16(a83))),x19092)),f86(f86(f24(a83),f86(f86(f23(a83),x19091),f16(a83))),x19093)))
% 7.14/7.07 [1936]P77(f86(f28(a83,x19361),x19362))+~P77(f86(f28(a83,f86(f86(f24(a83),f86(f86(f23(a83),x19363),f16(a83))),x19361)),f86(f86(f24(a83),f86(f86(f23(a83),x19363),f16(a83))),x19362)))
% 7.14/7.07 [1970]~P77(f86(f29(a84,f3(a84)),x19703))+P77(f86(f29(a84,x19701),f86(f86(f23(a84),x19702),f86(f86(f24(a84),f86(f86(f23(a84),f19(a84,f22(a84,x19702,x19701))),f16(a84))),x19703))))
% 7.14/7.07 [1974]~P77(f86(f29(a84,f3(a84)),x19743))+P77(f86(f29(a84,f22(a84,x19741,f86(f86(f24(a84),f86(f86(f23(a84),f19(a84,f22(a84,x19741,x19742))),f16(a84))),x19743))),x19742))
% 7.14/7.07 [838]E(x8381,x8382)+~E(f11(x8383,x8381),f11(x8384,x8382))
% 7.14/7.07 [839]E(x8391,x8392)+~E(f11(x8391,x8393),f11(x8392,x8394))
% 7.14/7.07 [1220]~P47(x12201)+E(f86(f86(f23(x12201),x12202),f86(f86(f23(x12201),x12203),x12204)),f86(f86(f23(x12201),x12203),f86(f86(f23(x12201),x12202),x12204)))
% 7.14/7.07 [1221]~P47(x12211)+E(f86(f86(f24(x12211),x12212),f86(f86(f24(x12211),x12213),x12214)),f86(f86(f24(x12211),x12213),f86(f86(f24(x12211),x12212),x12214)))
% 7.14/7.07 [1340]~P41(x13401)+E(f22(x13401,f86(f86(f24(x13401),x13402),x13403),f86(f86(f24(x13401),x13402),x13404)),f86(f86(f24(x13401),x13402),f22(x13401,x13403,x13404)))
% 7.14/7.07 [1397]~P27(x13971)+E(f86(f86(f24(x13971),f86(f86(f31(x13971),x13972),x13973)),f86(f86(f31(x13971),x13972),x13974)),f86(f86(f31(x13971),x13972),f86(f86(f23(a83),x13973),x13974)))
% 7.14/7.07 [1398]~P47(x13981)+E(f86(f86(f24(x13981),f86(f86(f31(x13981),x13982),x13983)),f86(f86(f31(x13981),x13982),x13984)),f86(f86(f31(x13981),x13982),f86(f86(f23(a83),x13983),x13984)))
% 7.14/7.07 [1411]~P47(x14111)+E(f86(f86(f23(x14111),f86(f86(f24(x14111),x14112),x14113)),f86(f86(f24(x14111),x14112),x14114)),f86(f86(f24(x14111),x14112),f86(f86(f23(x14111),x14113),x14114)))
% 7.14/7.07 [1413]~P41(x14131)+E(f86(f86(f23(x14131),f86(f86(f24(x14131),x14132),x14133)),f86(f86(f24(x14131),x14132),x14134)),f86(f86(f24(x14131),x14132),f86(f86(f23(x14131),x14133),x14134)))
% 7.14/7.07 [1425]~P41(x14251)+E(f22(x14251,f86(f86(f24(x14251),x14252),x14253),f86(f86(f24(x14251),x14254),x14253)),f86(f86(f24(x14251),f22(x14251,x14252,x14254)),x14253))
% 7.14/7.07 [1426]~P46(x14261)+E(f22(x14261,f86(f86(f37(x14261),x14262),x14263),f86(f86(f37(x14261),x14264),x14263)),f86(f86(f37(x14261),f22(x14261,x14262,x14264)),x14263))
% 7.14/7.07 [1427]~P53(x14271)+E(f22(x14271,f86(f86(f37(x14271),x14272),x14273),f86(f86(f37(x14271),x14274),x14273)),f86(f86(f37(x14271),f22(x14271,x14272,x14274)),x14273))
% 7.14/7.07 [1303]~P47(x13031)+E(f86(f86(f31(x13031),f86(f86(f31(x13031),x13032),x13033)),x13034),f86(f86(f31(x13031),x13032),f86(f86(f24(a83),x13033),x13034)))
% 7.14/7.07 [1304]~P27(x13041)+E(f86(f86(f31(x13041),f86(f86(f31(x13041),x13042),x13043)),x13044),f86(f86(f31(x13041),x13042),f86(f86(f24(a83),x13043),x13044)))
% 7.14/7.07 [1327]~P53(x13271)+E(f86(f86(f37(x13271),f86(f86(f24(x13271),x13272),x13273)),x13274),f86(f86(f24(x13271),x13272),f86(f86(f37(x13271),x13273),x13274)))
% 7.14/7.07 [1328]~P12(x13281)+E(f86(f86(f23(x13281),f86(f86(f23(x13281),x13282),x13283)),x13284),f86(f86(f23(x13281),x13282),f86(f86(f23(x13281),x13283),x13284)))
% 7.14/7.07 [1329]~P47(x13291)+E(f86(f86(f23(x13291),f86(f86(f23(x13291),x13292),x13293)),x13294),f86(f86(f23(x13291),x13292),f86(f86(f23(x13291),x13293),x13294)))
% 7.14/7.07 [1330]~P47(x13301)+E(f86(f86(f24(x13301),f86(f86(f24(x13301),x13302),x13303)),x13304),f86(f86(f24(x13301),x13302),f86(f86(f24(x13301),x13303),x13304)))
% 7.14/7.07 [1331]~P19(x13311)+E(f86(f86(f24(x13311),f86(f86(f24(x13311),x13312),x13313)),x13314),f86(f86(f24(x13311),x13312),f86(f86(f24(x13311),x13313),x13314)))
% 7.14/7.07 [1409]~P47(x14091)+E(f86(f86(f23(x14091),f86(f86(f23(x14091),x14092),x14093)),x14094),f86(f86(f23(x14091),f86(f86(f23(x14091),x14092),x14094)),x14093))
% 7.14/7.07 [1410]~P47(x14101)+E(f86(f86(f24(x14101),f86(f86(f24(x14101),x14102),x14103)),x14104),f86(f86(f24(x14101),f86(f86(f24(x14101),x14102),x14104)),x14103))
% 7.14/7.07 [1492]~P41(x14921)+E(f86(f86(f23(x14921),f86(f86(f24(x14921),x14922),x14923)),f86(f86(f24(x14921),x14924),x14923)),f86(f86(f24(x14921),f86(f86(f23(x14921),x14922),x14924)),x14923))
% 7.14/7.07 [1493]~P48(x14931)+E(f86(f86(f23(x14931),f86(f86(f24(x14931),x14932),x14933)),f86(f86(f24(x14931),x14934),x14933)),f86(f86(f24(x14931),f86(f86(f23(x14931),x14932),x14934)),x14933))
% 7.14/7.07 [1494]~P47(x14941)+E(f86(f86(f24(x14941),f86(f86(f31(x14941),x14942),x14943)),f86(f86(f31(x14941),x14944),x14943)),f86(f86(f31(x14941),f86(f86(f24(x14941),x14942),x14944)),x14943))
% 7.14/7.07 [1495]~P25(x14951)+E(f86(f86(f24(x14951),f86(f86(f31(x14951),x14952),x14953)),f86(f86(f31(x14951),x14954),x14953)),f86(f86(f31(x14951),f86(f86(f24(x14951),x14952),x14954)),x14953))
% 7.14/7.07 [1496]~P16(x14961)+E(f86(f86(f37(x14961),f86(f86(f31(x14961),x14962),x14963)),f86(f86(f31(x14961),x14964),x14963)),f86(f86(f31(x14961),f86(f86(f37(x14961),x14962),x14964)),x14963))
% 7.14/7.07 [1497]~P46(x14971)+E(f86(f86(f23(x14971),f86(f86(f37(x14971),x14972),x14973)),f86(f86(f37(x14971),x14974),x14973)),f86(f86(f37(x14971),f86(f86(f23(x14971),x14972),x14974)),x14973))
% 7.14/7.07 [1498]~P53(x14981)+E(f86(f86(f23(x14981),f86(f86(f37(x14981),x14982),x14983)),f86(f86(f37(x14981),x14984),x14983)),f86(f86(f37(x14981),f86(f86(f23(x14981),x14982),x14984)),x14983))
% 7.14/7.07 [1499]~P47(x14991)+E(f86(f86(f23(x14991),f86(f86(f24(x14991),x14992),x14993)),f86(f86(f24(x14991),x14994),x14993)),f86(f86(f24(x14991),f86(f86(f23(x14991),x14992),x14994)),x14993))
% 7.14/7.07 [1506]~P13(x15061)+E(f22(x15061,f86(f86(f23(x15061),x15062),x15063),f86(f86(f23(x15061),x15064),x15065)),f86(f86(f23(x15061),f22(x15061,x15062,x15064)),f22(x15061,x15063,x15065)))
% 7.14/7.07 [1553]~P47(x15531)+E(f86(f86(f23(x15531),f86(f86(f23(x15531),x15532),x15533)),f86(f86(f23(x15531),x15534),x15535)),f86(f86(f23(x15531),f86(f86(f23(x15531),x15532),x15534)),f86(f86(f23(x15531),x15533),x15535)))
% 7.14/7.07 [1554]~P47(x15541)+E(f86(f86(f24(x15541),f86(f86(f24(x15541),x15542),x15543)),f86(f86(f24(x15541),x15544),x15545)),f86(f86(f24(x15541),f86(f86(f24(x15541),x15542),x15544)),f86(f86(f24(x15541),x15543),x15545)))
% 7.14/7.07 [1841]~P72(x18411)+E(f86(f86(f23(x18411),f86(f86(f24(x18411),x18412),f22(x18411,x18413,x18414))),f86(f86(f24(x18411),f22(x18411,x18412,x18415)),x18414)),f22(x18411,f86(f86(f24(x18411),x18412),x18413),f86(f86(f24(x18411),x18415),x18414)))
% 7.14/7.07 [1945]~P35(x19451)+P77(f86(f28(a82,f36(x19451,f22(x19451,f86(f86(f23(x19451),x19452),x19453),f86(f86(f23(x19451),x19454),x19455)))),f86(f86(f23(a82),f36(x19451,f22(x19451,x19452,x19454))),f36(x19451,f22(x19451,x19453,x19455)))))
% 7.14/7.07 [1948]~P9(x19481)+P77(f86(f28(x19481,f19(x19481,f22(x19481,f86(f86(f23(x19481),x19482),x19483),f86(f86(f23(x19481),x19484),x19485)))),f86(f86(f23(x19481),f19(x19481,f22(x19481,x19482,x19484))),f19(x19481,f22(x19481,x19483,x19485)))))
% 7.14/7.07 [1954]~P41(x19541)+E(f86(f86(f23(x19541),f86(f86(f23(x19541),f86(f86(f24(x19541),f22(x19541,x19542,x19543)),f22(x19541,x19544,x19545))),f86(f86(f24(x19541),f22(x19541,x19542,x19543)),x19545))),f86(f86(f24(x19541),x19543),f22(x19541,x19544,x19545))),f22(x19541,f86(f86(f24(x19541),x19542),x19544),f86(f86(f24(x19541),x19543),x19545)))
% 7.14/7.07 [1915]~P77(f86(f28(a83,x19151),x19154))+E(f22(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19151),x19152)),x19153),f86(f86(f23(a83),f86(f86(f24(a83),x19154),x19152)),x19155)),f22(a83,x19153,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19154,x19151)),x19152)),x19155)))
% 7.14/7.07 [1916]~P77(f86(f28(a83,x19164),x19161))+E(f22(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19161),x19162)),x19163),f86(f86(f23(a83),f86(f86(f24(a83),x19164),x19162)),x19165)),f22(a83,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19161,x19164)),x19162)),x19163),x19165))
% 7.14/7.07 [1871]~P74(x18711)+E(f86(f86(f23(x18711),f86(f86(f24(x18711),x18712),x18713)),f86(f86(f23(x18711),f86(f86(f24(x18711),x18714),x18713)),x18715)),f86(f86(f23(x18711),f86(f86(f24(x18711),f86(f86(f23(x18711),x18712),x18714)),x18713)),x18715))
% 7.14/7.07 [1943]~P44(x19431)+E(f86(f86(f23(x19431),f86(f86(f24(x19431),x19432),f86(f86(f37(x19431),f22(x19431,x19433,x19434)),x19435))),f86(f86(f24(x19431),f86(f86(f37(x19431),f22(x19431,x19432,x19436)),x19435)),x19434)),f86(f86(f37(x19431),f22(x19431,f86(f86(f24(x19431),x19432),x19433),f86(f86(f24(x19431),x19436),x19434))),x19435))
% 7.14/7.07 [841]~P2(a82,x8411)+~P4(a82,x8411)+P3(a82,x8411)
% 7.14/7.07 [983]~P4(a82,x9831)+P3(a82,x9831)+P77(f86(f28(a83,f55(x9831)),f65(x9831)))
% 7.14/7.07 [1004]~E(x10041,f16(a82))+E(f34(x10041),f3(a82))+~P77(f86(f29(a82,f3(a82)),x10041))
% 7.14/7.07 [1009]~E(f34(x10091),f3(a82))+E(x10091,f16(a82))+~P77(f86(f29(a82,f3(a82)),x10091))
% 7.14/7.07 [1211]P2(a82,f86(f31(a82),x12111))+~P77(f86(f28(a82,x12111),f16(a82)))+~P77(f86(f28(a82,f3(a82)),x12111))
% 7.14/7.07 [1212]P3(a82,f86(f31(a82),x12121))+~P77(f86(f28(a82,x12121),f16(a82)))+~P77(f86(f28(a82,f3(a82)),x12121))
% 7.14/7.07 [1213]P4(a82,f86(f31(a82),x12131))+~P77(f86(f28(a82,x12131),f16(a82)))+~P77(f86(f28(a82,f3(a82)),x12131))
% 7.14/7.07 [1264]~P77(f86(f29(a82,x12641),f16(a82)))+P77(f86(f29(a82,f34(x12641)),f3(a82)))+~P77(f86(f29(a82,f3(a82)),x12641))
% 7.14/7.07 [1279]~P77(f86(f28(a82,f3(a82)),f34(x12791)))+~P77(f86(f29(a82,f3(a82)),x12791))+P77(f86(f28(a82,f16(a82)),x12791))
% 7.14/7.07 [1281]~P77(f86(f29(a82,f3(a82)),f34(x12811)))+~P77(f86(f29(a82,f3(a82)),x12811))+P77(f86(f29(a82,f16(a82)),x12811))
% 7.14/7.07 [1293]~P77(f86(f29(a82,f34(x12931)),f3(a82)))+P77(f86(f29(a82,x12931),f16(a82)))+~P77(f86(f29(a82,f3(a82)),x12931))
% 7.14/7.07 [1403]~P4(a82,x14031)+P3(a82,x14031)+~P77(f86(f28(a82,f86(x14031,f55(x14031))),f86(x14031,f65(x14031))))
% 7.14/7.07 [1870]E(x18701,f3(a83))+E(x18701,f86(f86(f23(a83),f3(a83)),f16(a83)))+~P77(f86(f29(a83,x18701),f86(f86(f23(a83),f86(f86(f23(a83),f3(a83)),f16(a83))),f16(a83))))
% 7.14/7.07 [835]~P40(x8351)+~P5(x8351,x8352)+P2(x8351,x8352)
% 7.14/7.07 [836]~P40(x8361)+~P6(x8361,x8362)+P2(x8361,x8362)
% 7.14/7.07 [805]~E(x8052,f16(a82))+~E(x8051,f3(a82))+E(f11(x8051,x8052),a17)
% 7.14/7.07 [809]~E(x8092,f3(a82))+~E(x8091,f3(a82))+E(f11(x8091,x8092),f3(a85))
% 7.14/7.08 [810]~E(x8102,f3(a82))+~E(x8101,f16(a82))+E(f11(x8101,x8102),f16(a85))
% 7.14/7.08 [822]~P35(x8221)+~E(x8222,f3(x8221))+E(f36(x8221,x8222),f3(a82))
% 7.14/7.08 [823]~P9(x8231)+~E(x8232,f3(x8231))+E(f19(x8231,x8232),f3(x8231))
% 7.14/7.08 [824]~P34(x8241)+~E(x8242,f3(x8241))+E(f25(x8241,x8242),f3(x8241))
% 7.14/7.08 [825]~P35(x8251)+~E(x8252,f3(x8251))+E(f25(x8251,x8252),f3(x8251))
% 7.14/7.08 [829]~P35(x8292)+E(x8291,f3(x8292))+~E(f36(x8292,x8291),f3(a82))
% 7.14/7.08 [830]~P9(x8302)+~E(f19(x8302,x8301),f3(x8302))+E(x8301,f3(x8302))
% 7.14/7.08 [831]~P34(x8312)+~E(f25(x8312,x8311),f3(x8312))+E(x8311,f3(x8312))
% 7.14/7.08 [832]~P35(x8322)+~E(f25(x8322,x8321),f3(x8322))+E(x8321,f3(x8322))
% 7.14/7.08 [881]~P14(x8812)+E(f20(x8812,x8811,x8811),f16(x8812))+E(x8811,f3(x8812))
% 7.14/7.08 [916]E(x9161,x9162)+~E(f86(a5,x9161),f86(a5,x9162))+~E(f86(a10,x9161),f86(a10,x9162))
% 7.14/7.08 [1051]E(x10511,x10512)+~E(f22(a83,x10512,x10511),f3(a83))+~E(f22(a83,x10511,x10512),f3(a83))
% 7.14/7.08 [834]~P32(x8341)+E(f21(x8341,x8342),f3(a83))+~E(x8342,f3(f120(x8341)))
% 7.14/7.08 [837]~P32(x8372)+~E(f21(x8372,x8371),f3(a83))+E(x8371,f3(f120(x8372)))
% 7.14/7.08 [846]~P35(x8462)+E(x8461,f3(x8462))+E(f36(x8462,f25(x8462,x8461)),f16(a82))
% 7.14/7.08 [847]~P35(x8471)+~E(x8472,f3(x8471))+E(f36(x8471,f25(x8471,x8472)),f3(a82))
% 7.14/7.08 [1008]~P35(x10082)+E(x10081,f3(x10082))+P77(f86(f29(a82,f3(a82)),f36(x10082,x10081)))
% 7.14/7.08 [1012]E(x10121,x10122)+P77(f86(f29(a83,x10122),x10121))+P77(f86(f29(a83,x10121),x10122))
% 7.14/7.08 [1013]E(x10131,x10132)+P77(f86(f29(a84,x10132),x10131))+P77(f86(f29(a84,x10131),x10132))
% 7.14/7.08 [1022]~P35(x10222)+~P4(x10222,x10221)+P77(f86(f29(a82,f3(a82)),f58(x10221,x10222)))
% 7.14/7.08 [1023]~P35(x10232)+~P4(x10232,x10231)+P77(f86(f29(a82,f3(a82)),f59(x10231,x10232)))
% 7.14/7.08 [1026]~P9(x10262)+E(x10261,f3(x10262))+P77(f86(f29(x10262,f3(x10262)),f19(x10262,x10261)))
% 7.14/7.08 [1085]E(x10851,x10852)+P77(f86(f29(a82,x10851),x10852))+~P77(f86(f28(a82,x10851),x10852))
% 7.14/7.08 [1088]E(x10881,x10882)+P77(f86(f29(a83,x10881),x10882))+~P77(f86(f28(a83,x10881),x10882))
% 7.14/7.08 [1089]E(x10891,x10892)+P77(f86(f29(a84,x10891),x10892))+~P77(f86(f28(a84,x10891),x10892))
% 7.14/7.08 [1092]~P35(x10921)+~E(x10922,f3(x10921))+P77(f86(f28(a82,f36(x10921,x10922)),f3(a82)))
% 7.14/7.08 [1093]~P9(x10931)+~E(x10932,f3(x10931))+P77(f86(f28(x10931,f19(x10931,x10932)),f3(x10931)))
% 7.14/7.08 [1124]~P35(x11242)+~E(x11241,f3(x11242))+~P77(f86(f29(a82,f3(a82)),f36(x11242,x11241)))
% 7.14/7.08 [1132]E(x11321,x11322)+~P77(f86(f28(a82,x11322),x11321))+~P77(f86(f28(a82,x11321),x11322))
% 7.14/7.08 [1133]E(x11331,x11332)+~P77(f86(f28(a83,x11332),x11331))+~P77(f86(f28(a83,x11331),x11332))
% 7.14/7.08 [1134]E(x11341,x11342)+~P77(f86(f28(a84,x11342),x11341))+~P77(f86(f28(a84,x11341),x11342))
% 7.14/7.08 [1148]~P40(x11481)+P2(x11481,x11482)+P77(f86(f28(a83,f88(x11482,x11481)),f99(x11482,x11481)))
% 7.14/7.08 [1149]~P40(x11491)+P2(x11491,x11492)+P77(f86(f28(a83,f110(x11492,x11491)),f118(x11492,x11491)))
% 7.14/7.08 [1150]~P40(x11501)+P5(x11501,x11502)+P77(f86(f28(a83,f52(x11502,x11501)),f53(x11502,x11501)))
% 7.14/7.08 [1151]~P40(x11511)+P6(x11511,x11512)+P77(f86(f28(a83,f60(x11512,x11511)),f62(x11512,x11511)))
% 7.14/7.08 [1156]~P9(x11562)+~E(x11561,f3(x11562))+~P77(f86(f29(x11562,f3(x11562)),f19(x11562,x11561)))
% 7.14/7.08 [1205]~P35(x12052)+E(x12051,f3(x12052))+~P77(f86(f28(a82,f36(x12052,x12051)),f3(a82)))
% 7.14/7.08 [1207]E(f20(a84,x12071,x12072),f3(a84))+~P77(f86(f29(a84,x12072),x12071))+~P77(f86(f28(a84,x12071),f3(a84)))
% 7.14/7.08 [1226]~P9(x12262)+E(x12261,f3(x12262))+~P77(f86(f28(x12262,f19(x12262,x12261)),f3(x12262)))
% 7.14/7.08 [1257]~P34(x12571)+~P77(f86(f29(x12571,x12572),f3(x12571)))+P77(f86(f29(x12571,f25(x12571,x12572)),f3(x12571)))
% 7.14/7.08 [1320]~P34(x13201)+~P77(f86(f29(x13201,f25(x13201,x13202)),f3(x13201)))+P77(f86(f29(x13201,x13202),f3(x13201)))
% 7.14/7.08 [1452]P77(f86(f28(a84,f3(a84)),f20(a84,x14521,x14522)))+~P77(f86(f28(a84,x14521),f3(a84)))+~P77(f86(f29(a84,x14522),f3(a84)))
% 7.14/7.08 [1524]~P24(x15241)+~P77(f86(f28(x15241,x15242),f3(x15241)))+P77(f86(f28(x15241,f86(f86(f23(x15241),x15242),x15242)),f3(x15241)))
% 7.14/7.08 [1525]~P34(x15251)+~P77(f86(f29(x15251,x15252),f3(x15251)))+P77(f86(f29(x15251,f86(f86(f23(x15251),x15252),x15252)),f3(x15251)))
% 7.14/7.08 [1526]~P24(x15261)+~P77(f86(f29(x15261,x15262),f3(x15261)))+P77(f86(f29(x15261,f86(f86(f23(x15261),x15262),x15262)),f3(x15261)))
% 7.14/7.08 [1530]~P77(f86(f28(a84,f3(a84)),f20(a84,x15301,x15302)))+P77(f86(f28(a84,x15301),f3(a84)))+~P77(f86(f29(a84,x15302),f3(a84)))
% 7.14/7.08 [1667]~P24(x16671)+~P77(f86(f28(x16671,f86(f86(f23(x16671),x16672),x16672)),f3(x16671)))+P77(f86(f28(x16671,x16672),f3(x16671)))
% 7.14/7.08 [1668]~P34(x16681)+~P77(f86(f29(x16681,f86(f86(f23(x16681),x16682),x16682)),f3(x16681)))+P77(f86(f29(x16681,x16682),f3(x16681)))
% 7.14/7.08 [1669]~P24(x16691)+~P77(f86(f29(x16691,f86(f86(f23(x16691),x16692),x16692)),f3(x16691)))+P77(f86(f29(x16691,x16692),f3(x16691)))
% 7.14/7.08 [1951]E(x19511,f3(a83))+E(x19512,f3(a85))+P77(f86(f29(a82,f36(a85,f86(f86(f23(a85),f16(a85)),f86(f86(f24(a85),x19512),f86(f86(f31(a85),f94(x19511,x19512)),x19511))))),f16(a82)))
% 7.14/7.08 [851]~E(x8512,f3(a83))+~E(x8511,f3(a83))+E(f86(f86(f23(a83),x8511),x8512),f3(a83))
% 7.14/7.08 [852]~E(x8522,f16(a83))+~E(x8521,f16(a83))+E(f86(f86(f24(a83),x8521),x8522),f16(a83))
% 7.14/7.08 [870]~P53(x8702)+E(x8701,f3(x8702))+E(f86(f86(f37(x8702),x8701),x8701),f16(x8702))
% 7.14/7.08 [871]~P54(x8712)+E(x8711,f3(x8712))+E(f86(f86(f37(x8712),x8711),x8711),f16(x8712))
% 7.14/7.08 [885]~P24(x8851)+~E(x8852,f3(x8851))+E(f86(f86(f23(x8851),x8852),x8852),f3(x8851))
% 7.14/7.08 [888]~P54(x8881)+~E(x8882,f3(x8881))+E(f86(f86(f37(x8881),x8882),x8882),f3(x8881))
% 7.14/7.08 [917]E(x9171,f16(a83))+E(x9172,f3(a83))+~E(f86(f86(f24(a83),x9172),x9171),x9172)
% 7.14/7.08 [918]E(x9181,f3(a83))+E(x9182,f3(a83))+~E(f86(f86(f24(a83),x9182),x9181),f3(a83))
% 7.14/7.08 [937]~P24(x9372)+E(x9371,f3(x9372))+~E(f86(f86(f23(x9372),x9371),x9371),f3(x9372))
% 7.14/7.08 [981]~P34(x9811)+~E(f25(x9811,x9812),f16(x9811))+P77(f86(f29(x9811,f3(x9811)),x9812))
% 7.14/7.08 [1019]E(x10191,f3(a83))+E(x10192,f3(a83))+~E(f86(f86(f23(a83),x10192),x10191),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1020]E(x10201,f3(a83))+E(x10202,f3(a83))+~E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x10202),x10201))
% 7.14/7.08 [1052]~P43(x10521)+~P75(x10521)+E(f86(f86(f31(x10521),f3(x10521)),f86(f86(f23(a83),x10522),f16(a83))),f3(x10521))
% 7.14/7.08 [1063]~P9(x10631)+E(f19(x10631,x10632),x10632)+~P77(f86(f28(x10631,f3(x10631)),x10632))
% 7.14/7.08 [1064]~P9(x10641)+E(f19(x10641,x10642),x10642)+~P77(f86(f29(x10641,f3(x10641)),x10642))
% 7.14/7.08 [1069]~P34(x10691)+E(f25(x10691,x10692),f16(x10691))+~P77(f86(f29(x10691,f3(x10691)),x10692))
% 7.14/7.08 [1080]~E(x10802,f3(a83))+~E(x10801,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f23(a83),x10801),x10802),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1081]~E(x10811,f3(a83))+~E(x10812,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f23(a83),x10811),x10812),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1082]~E(x10822,f3(a83))+~E(x10821,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x10821),x10822))
% 7.14/7.08 [1083]~E(x10831,f3(a83))+~E(x10832,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x10831),x10832))
% 7.14/7.08 [1100]E(x11001,f16(a84))+~E(f86(f86(f24(a84),x11002),x11001),f16(a84))+~P77(f86(f29(a84,f3(a84)),x11002))
% 7.14/7.08 [1101]E(x11011,f16(a84))+~E(f86(f86(f24(a84),x11011),x11012),f16(a84))+~P77(f86(f29(a84,f3(a84)),x11011))
% 7.14/7.08 [1102]E(x11021,f3(a83))+E(x11022,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f31(a83),x11022),x11021),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1103]E(x11031,f3(a83))+E(x11031,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),x11032),x11031),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1104]E(x11041,f3(a83))+E(x11041,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),x11041),x11042),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1105]E(x11051,f3(a83))+E(x11051,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x11052),x11051))
% 7.14/7.08 [1106]E(x11061,f3(a83))+E(x11061,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x11061),x11062))
% 7.14/7.08 [1155]~P77(f86(x11551,x11552))+P77(f86(x11551,f3(a83)))+P77(f86(f29(a83,f54(x11552,x11551)),x11552))
% 7.14/7.08 [1176]E(x11761,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(x11762,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),x11761),x11762),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1177]E(x11771,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(x11772,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),x11771),x11772))
% 7.14/7.08 [1187]~E(x11872,f86(f86(f23(a83),f3(a83)),f16(a83)))+~E(x11871,f86(f86(f23(a83),f3(a83)),f16(a83)))+E(f86(f86(f24(a83),x11871),x11872),f86(f86(f23(a83),f3(a83)),f16(a83)))
% 7.14/7.08 [1216]E(f20(a84,x12161,x12162),f3(a84))+~P77(f86(f29(a84,x12161),x12162))+~P77(f86(f28(a84,f3(a84)),x12161))
% 7.14/7.08 [1237]~P34(x12371)+P77(f86(f29(x12371,f3(x12371)),f25(x12371,x12372)))+~P77(f86(f29(x12371,f3(x12371)),x12372))
% 7.14/7.08 [1261]~P34(x12611)+~P77(f86(f29(x12611,f3(x12611)),f25(x12611,x12612)))+P77(f86(f29(x12611,f3(x12611)),x12612))
% 7.14/7.08 [1273]E(f86(f86(f31(a82),f95(x12731,x12732)),x12732),x12731)+~P77(f86(f29(a82,f3(a82)),x12731))+~P77(f86(f29(a83,f3(a83)),x12732))
% 7.14/7.08 [1274]E(f86(f86(f31(a82),f96(x12741,x12742)),x12742),x12741)+~P77(f86(f29(a82,f3(a82)),x12741))+~P77(f86(f29(a83,f3(a83)),x12742))
% 7.14/7.08 [1333]P77(f86(f28(a84,f3(a84)),f30(x13331,x13332)))+~P77(f86(f28(a84,f3(a84)),x13331))+~P77(f86(f28(a84,f3(a84)),x13332))
% 7.14/7.08 [1334]P77(f86(f29(a82,f3(a82)),f95(x13341,x13342)))+~P77(f86(f29(a82,f3(a82)),x13341))+~P77(f86(f29(a83,f3(a83)),x13342))
% 7.14/7.08 [1335]P77(f86(f29(a82,f3(a82)),f96(x13351,x13352)))+~P77(f86(f29(a82,f3(a82)),x13351))+~P77(f86(f29(a83,f3(a83)),x13352))
% 7.14/7.08 [1336]P77(f86(f28(a82,x13361),f35(a83,x13362)))+~P77(f86(f28(a82,f3(a82)),x13361))+~P77(f86(f28(a83,f26(x13361)),x13362))
% 7.14/7.08 [1344]~P77(f86(f29(a82,x13441),f35(a83,x13442)))+~P77(f86(f28(a82,f3(a82)),x13441))+P77(f86(f29(a83,f33(x13441)),x13442))
% 7.14/7.08 [1358]~P77(f86(f28(a83,x13581),f33(x13582)))+~P77(f86(f28(a82,f3(a82)),x13582))+P77(f86(f28(a82,f35(a83,x13581)),x13582))
% 7.14/7.08 [1372]E(f33(f86(f86(f37(a82),x13721),f35(a83,x13722))),f20(a83,f33(x13721),x13722))+~P77(f86(f29(a83,f3(a83)),x13722))+~P77(f86(f28(a82,f16(a82)),x13721))
% 7.14/7.08 [1391]E(x13911,x13912)+P77(f86(f29(a83,x13911),x13912))+~P77(f86(f29(a83,x13911),f86(f86(f23(a83),x13912),f16(a83))))
% 7.14/7.08 [1392]E(x13921,x13922)+P77(f86(f29(a84,x13921),x13922))+~P77(f86(f29(a84,x13921),f86(f86(f23(a84),x13922),f16(a84))))
% 7.14/7.08 [1406]~P77(f86(x14061,x14062))+P77(f86(x14061,f3(a83)))+P77(f86(x14061,f86(f86(f23(a83),f54(x14062,x14061)),f16(a83))))
% 7.14/7.08 [1418]E(x14181,f3(a83))+E(f86(f86(f23(a83),f78(x14182,x14181)),f16(a83)),x14181)+~P77(f86(f29(a83,x14181),f86(f86(f23(a83),x14182),f16(a83))))
% 7.14/7.08 [1440]E(x14401,x14402)+~P77(f86(f28(a83,x14402),x14401))+~P77(f86(f29(a83,x14401),f86(f86(f23(a83),x14402),f16(a83))))
% 7.14/7.08 [1448]E(x14481,f86(f86(f23(a83),x14482),f16(a83)))+P77(f86(f28(a83,x14481),x14482))+~P77(f86(f28(a83,x14481),f86(f86(f23(a83),x14482),f16(a83))))
% 7.14/7.08 [1451]P77(f86(f29(a84,f3(a84)),f20(a84,x14511,x14512)))+~P77(f86(f28(a84,x14512),x14511))+~P77(f86(f29(a84,f3(a84)),x14512))
% 7.14/7.08 [1457]P77(f86(f28(a84,f3(a84)),f20(a84,x14571,x14572)))+~P77(f86(f28(a84,f3(a84)),x14572))+~P77(f86(f28(a84,f3(a84)),x14571))
% 7.14/7.08 [1458]P77(f86(f28(a84,f3(a84)),f20(a84,x14581,x14582)))+~P77(f86(f28(a84,f3(a84)),x14581))+~P77(f86(f29(a84,f3(a84)),x14582))
% 7.14/7.08 [1481]E(x14811,f3(a83))+P77(f86(f29(a83,f78(x14812,x14811)),x14812))+~P77(f86(f29(a83,x14811),f86(f86(f23(a83),x14812),f16(a83))))
% 7.14/7.08 [1534]~P77(f86(f29(a84,f3(a84)),f20(a84,x15342,x15341)))+P77(f86(f28(a84,x15341),x15342))+~P77(f86(f29(a84,f3(a84)),x15341))
% 7.14/7.08 [1535]~P77(f86(f29(a84,f3(a84)),f20(a84,x15352,x15351)))+P77(f86(f28(a84,x15351),x15352))+~P77(f86(f28(a84,f3(a84)),x15352))
% 7.14/7.08 [1536]~P77(f86(f28(a84,f3(a84)),f20(a84,x15361,x15362)))+P77(f86(f28(a84,f3(a84)),x15361))+~P77(f86(f29(a84,f3(a84)),x15362))
% 7.14/7.08 [1537]~P77(f86(f29(a84,f3(a84)),f20(a84,x15372,x15371)))+P77(f86(f29(a84,f3(a84)),x15371))+~P77(f86(f28(a84,f3(a84)),x15372))
% 7.14/7.08 [1581]~P77(f86(f28(a84,x15811),f3(a84)))+P77(f86(f28(a84,f20(a84,x15811,x15812)),f3(a84)))+~P77(f86(f29(a84,f3(a84)),x15812))
% 7.14/7.08 [1582]~P77(f86(f29(a84,x15822),f3(a84)))+P77(f86(f28(a84,f20(a84,x15821,x15822)),f3(a84)))+~P77(f86(f28(a84,f3(a84)),x15821))
% 7.14/7.08 [1583]~P77(f86(f29(a84,x15832),f3(a84)))+P77(f86(f29(a84,f20(a84,x15831,x15832)),f3(a84)))+~P77(f86(f29(a84,f3(a84)),x15831))
% 7.14/7.08 [1585]~P77(f86(f29(a84,x15851),f3(a84)))+P77(f86(f29(a84,f20(a84,x15851,x15852)),f3(a84)))+~P77(f86(f29(a84,f3(a84)),x15852))
% 7.14/7.08 [1586]~P77(f86(f29(a83,f3(a83)),x15861))+~P77(f86(f29(a83,f3(a83)),x15862))+P77(f86(f29(a83,f22(a83,x15861,x15862)),x15861))
% 7.14/7.08 [1587]~P77(f86(f29(a83,f3(a83)),x15871))+P77(f86(f29(a83,f20(a83,x15871,x15872)),x15871))+~P77(f86(f29(a83,f16(a83)),x15872))
% 7.14/7.08 [1588]~P77(f86(f29(a84,f3(a84)),x15881))+P77(f86(f29(a84,f20(a84,x15881,x15882)),x15881))+~P77(f86(f29(a84,f16(a84)),x15882))
% 7.14/7.08 [1662]~P40(x16621)+P2(x16621,x16622)+~P77(f86(f28(x16621,f86(x16622,f88(x16622,x16621))),f86(x16622,f99(x16622,x16621))))
% 7.14/7.08 [1663]~P40(x16631)+P2(x16631,x16632)+~P77(f86(f28(x16631,f86(x16632,f118(x16632,x16631))),f86(x16632,f110(x16632,x16631))))
% 7.14/7.08 [1664]~P40(x16641)+P5(x16641,x16642)+~P77(f86(f28(x16641,f86(x16642,f53(x16642,x16641))),f86(x16642,f52(x16642,x16641))))
% 7.14/7.08 [1665]~P40(x16651)+P6(x16651,x16652)+~P77(f86(f28(x16651,f86(x16652,f60(x16652,x16651))),f86(x16652,f62(x16652,x16651))))
% 7.14/7.08 [1687]E(f86(f86(f23(a83),f20(a83,f22(a83,x16871,x16872),x16872)),f16(a83)),f20(a83,x16871,x16872))+P77(f86(f29(a83,x16871),x16872))+~P77(f86(f29(a83,f3(a83)),x16872))
% 7.14/7.08 [1700]E(f33(x17001),x17002)+~P77(f86(f28(a82,f35(a83,x17002)),x17001))+~P77(f86(f29(a82,x17001),f86(f86(f23(a82),f35(a83,x17002)),f16(a82))))
% 7.14/7.08 [1711]E(f86(f86(f23(a83),f20(a83,f22(a83,x17111,x17112),x17112)),f16(a83)),f20(a83,x17111,x17112))+~P77(f86(f28(a83,x17112),x17111))+~P77(f86(f29(a83,f3(a83)),x17112))
% 7.14/7.08 [1720]~P77(f86(f29(a84,x17202),f3(a84)))+~P77(f86(f29(a84,f20(a84,x17201,x17202)),f3(a84)))+P77(f86(f29(a84,f3(a84)),x17201))
% 7.14/7.08 [1736]P77(f86(f29(a84,x17361),f3(a84)))+~P77(f86(f29(a84,f20(a84,x17361,x17362)),f3(a84)))+~P77(f86(f29(a84,f3(a84)),x17362))
% 7.14/7.08 [1740]E(f26(x17401),f86(f86(f23(a83),x17402),f16(a83)))+~P77(f86(f29(a82,f35(a83,x17402)),x17401))+~P77(f86(f28(a82,x17401),f86(f86(f23(a82),f35(a83,x17402)),f16(a82))))
% 7.14/7.08 [1910]~P40(x19101)+P2(x19101,x19102)+~P77(f86(f28(x19101,f86(x19102,f86(f86(f23(a83),f81(x19102,x19101)),f16(a83)))),f86(x19102,f81(x19102,x19101))))
% 7.14/7.08 [1232]~E(x12322,f3(a82))+~E(x12321,f3(a82))+E(f86(f86(f23(a82),f86(f86(f24(a82),x12321),x12321)),f86(f86(f24(a82),x12322),x12322)),f3(a82))
% 7.14/7.08 [1346]E(f86(f86(f23(a82),f34(x13461)),f34(x13462)),f34(f86(f86(f24(a82),x13461),x13462)))+~P77(f86(f29(a82,f3(a82)),x13462))+~P77(f86(f29(a82,f3(a82)),x13461))
% 7.14/7.08 [1351]E(f34(f86(f86(f37(a82),x13511),x13512)),f22(a82,f34(x13511),f34(x13512)))+~P77(f86(f29(a82,f3(a82)),x13512))+~P77(f86(f29(a82,f3(a82)),x13511))
% 7.14/7.08 [1378]~P24(x13781)+~P77(f86(f28(x13781,f3(x13781)),x13782))+P77(f86(f28(x13781,f3(x13781)),f86(f86(f23(x13781),x13782),x13782)))
% 7.14/7.08 [1381]~P24(x13811)+~P77(f86(f29(x13811,f3(x13811)),x13812))+P77(f86(f29(x13811,f3(x13811)),f86(f86(f23(x13811),x13812),x13812)))
% 7.14/7.08 [1405]E(x14051,f3(a83))+P77(f86(f29(a83,f3(a83)),x14052))+~P77(f86(f29(a83,f3(a83)),f86(f86(f31(a83),x14052),x14051)))
% 7.14/7.08 [1417]~P77(f86(f28(a82,x14171),f3(a82)))+~P77(f86(f28(a82,x14172),f3(a82)))+P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14171),x14172)))
% 7.14/7.08 [1431]~P77(f86(f28(a82,x14312),f3(a82)))+~P77(f86(f28(a82,f3(a82)),x14312))+P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14311),x14312)))
% 7.14/7.08 [1432]~P77(f86(f28(a82,x14321),f3(a82)))+~P77(f86(f28(a82,f3(a82)),x14321))+P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14321),x14322)))
% 7.14/7.08 [1442]~P77(f86(f28(a82,f3(a82)),x14422))+~P77(f86(f28(a82,f3(a82)),x14421))+P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14421),x14422)))
% 7.14/7.08 [1443]~P77(f86(f28(a84,f3(a84)),x14431))+~P77(f86(f28(a84,f3(a84)),x14432))+P77(f86(f28(a84,f3(a84)),f86(f86(f23(a84),x14431),x14432)))
% 7.14/7.08 [1444]~P77(f86(f28(a84,f3(a84)),x14441))+~P77(f86(f28(a84,f3(a84)),x14442))+P77(f86(f28(a84,f3(a84)),f86(f86(f24(a84),x14441),x14442)))
% 7.14/7.08 [1445]~P77(f86(f29(a82,f3(a82)),x14452))+~P77(f86(f29(a82,f3(a82)),x14451))+P77(f86(f29(a82,f3(a82)),f86(f86(f24(a82),x14451),x14452)))
% 7.14/7.08 [1446]~P77(f86(f29(a83,f3(a83)),x14462))+~P77(f86(f29(a83,f3(a83)),x14461))+P77(f86(f29(a83,f3(a83)),f86(f86(f24(a83),x14461),x14462)))
% 7.14/7.08 [1476]P77(f86(f28(a82,x14761),f3(a82)))+P77(f86(f28(a82,f3(a82)),x14762))+~P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14762),x14761)))
% 7.14/7.08 [1477]P77(f86(f28(a82,x14771),f3(a82)))+P77(f86(f28(a82,f3(a82)),x14772))+~P77(f86(f28(a82,f3(a82)),f86(f86(f37(a82),x14771),x14772)))
% 7.14/7.08 [1478]P77(f86(f29(a83,f3(a83)),x14781))+P77(f86(f29(a83,f3(a83)),x14782))+~P77(f86(f29(a83,f3(a83)),f86(f86(f23(a83),x14782),x14781)))
% 7.14/7.08 [1479]~P24(x14791)+P77(f86(f28(x14791,f3(x14791)),x14792))+~P77(f86(f28(x14791,f3(x14791)),f86(f86(f23(x14791),x14792),x14792)))
% 7.14/7.08 [1480]~P24(x14801)+P77(f86(f29(x14801,f3(x14801)),x14802))+~P77(f86(f29(x14801,f3(x14801)),f86(f86(f23(x14801),x14802),x14802)))
% 7.14/7.08 [1505]E(f86(f86(f23(a83),x15051),f16(a83)),x15052)+~P77(f86(f29(a83,x15051),x15052))+P77(f86(f29(a83,f86(f86(f23(a83),x15051),f16(a83))),x15052))
% 7.14/7.08 [1551]E(x15511,f3(a83))+~E(x15512,f3(a84))+~P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x15512)),x15511)))
% 7.14/7.08 [1595]E(f20(a84,f86(f86(f31(a84),x15951),x15952),x15951),f86(f86(f31(a84),x15951),f22(a83,x15952,f86(f86(f23(a83),f3(a83)),f16(a83)))))+~P77(f86(f29(a83,f3(a83)),x15952))+~P77(f86(f29(a84,f3(a84)),x15951))
% 7.14/7.08 [1872]~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18721))+~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18722))+P77(f86(f29(a83,x18721),f86(f86(f24(a83),x18722),x18721)))
% 7.14/7.08 [1873]~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18731))+~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18732))+P77(f86(f29(a83,x18731),f86(f86(f24(a83),x18731),x18732)))
% 7.14/7.08 [1883]~P40(x18831)+P2(x18831,x18832)+~P77(f86(f28(x18831,f86(x18832,f80(x18832,x18831))),f86(x18832,f86(f86(f23(a83),f80(x18832,x18831)),f16(a83)))))
% 7.14/7.08 [1894]~P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18941))+~P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18942))+P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f24(a83),x18941),x18942)))
% 7.14/7.08 [1895]~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18952))+~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),x18951))+P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f24(a83),x18951),x18952)))
% 7.14/7.08 [1791]~P77(f86(f28(a82,f3(a82)),x17912))+~P77(f86(f28(a82,f3(a82)),x17911))+P77(f86(f28(a83,f86(f86(f24(a83),f33(x17911)),f33(x17912))),f33(f86(f86(f24(a82),x17911),x17912))))
% 7.14/7.08 [1879]~P77(f86(f28(a82,f3(a82)),x18791))+~P77(f86(f29(a82,f3(a82)),x18792))+P77(f86(f28(a82,f86(f86(f24(a82),f35(a83,f98(x18791,x18792))),x18792)),x18791))
% 7.14/7.08 [1924]~P77(f86(f28(a82,f3(a82)),x19241))+~P77(f86(f29(a82,f3(a82)),x19242))+P77(f86(f29(a82,x19241),f86(f86(f24(a82),f35(a83,f86(f86(f23(a83),f98(x19241,x19242)),f16(a83)))),x19242)))
% 7.14/7.08 [873]~E(x8732,x8733)+~P26(x8731)+E(f22(x8731,x8732,x8733),f3(x8731))
% 7.14/7.08 [874]~E(x8742,x8743)+~P13(x8741)+E(f22(x8741,x8742,x8743),f3(x8741))
% 7.14/7.08 [939]~P26(x9393)+E(x9391,x9392)+~E(f22(x9393,x9391,x9392),f3(x9393))
% 7.14/7.08 [940]~P13(x9403)+E(x9401,x9402)+~E(f22(x9403,x9401,x9402),f3(x9403))
% 7.14/7.08 [927]~E(x9272,x9273)+~P37(x9271)+P77(f86(f28(x9271,x9272),x9273))
% 7.14/7.08 [929]~E(x9292,x9293)+~P40(x9291)+P77(f86(f28(x9291,x9292),x9293))
% 7.14/7.08 [966]~P78(x9661,x9662,x9663)+~E(x9662,f3(a84))+P77(f86(x9661,f3(a84)))
% 7.14/7.08 [978]~E(x9781,x9782)+~P39(x9783)+~P77(f86(f29(x9783,x9781),x9782))
% 7.14/7.08 [979]~E(x9791,x9792)+~P40(x9793)+~P77(f86(f29(x9793,x9791),x9792))
% 7.14/7.08 [1028]~P39(x10281)+P77(f86(f28(x10281,x10283),x10282))+P77(f86(f28(x10281,x10282),x10283))
% 7.14/7.08 [1033]~P39(x10331)+P77(f86(f29(x10331,x10333),x10332))+P77(f86(f28(x10331,x10332),x10333))
% 7.14/7.08 [1097]~P37(x10971)+~P77(f86(f29(x10971,x10972),x10973))+P77(f86(f28(x10971,x10972),x10973))
% 7.14/7.08 [1099]~P40(x10991)+~P77(f86(f29(x10991,x10992),x10993))+P77(f86(f28(x10991,x10992),x10993))
% 7.14/7.08 [1157]~P37(x11571)+~P77(f86(f29(x11571,x11573),x11572))+~P77(f86(f28(x11571,x11572),x11573))
% 7.14/7.08 [1161]~P37(x11611)+~P77(f86(f29(x11611,x11613),x11612))+~P77(f86(f29(x11611,x11612),x11613))
% 7.14/7.08 [1164]~P39(x11641)+~P77(f86(f29(x11641,x11643),x11642))+~P77(f86(f28(x11641,x11642),x11643))
% 7.14/7.08 [1165]~P39(x11651)+~P77(f86(f29(x11651,x11653),x11652))+~P77(f86(f29(x11651,x11652),x11653))
% 7.14/7.08 [1166]~P40(x11661)+~P77(f86(f29(x11661,x11663),x11662))+~P77(f86(f29(x11661,x11662),x11663))
% 7.14/7.08 [1204]~E(x12043,f3(a83))+P77(f86(x12041,f20(a83,x12042,x12043)))+~P77(f86(x12041,f3(a83)))
% 7.14/7.08 [1217]~P77(f86(f28(a82,x12171),x12173))+P77(f86(f28(a82,x12171),x12172))+~P77(f86(f28(a82,x12173),x12172))
% 7.14/7.08 [1218]~P77(f86(f28(a83,x12181),x12183))+P77(f86(f28(a83,x12181),x12182))+~P77(f86(f28(a83,x12183),x12182))
% 7.14/7.08 [1219]~P77(f86(f28(a84,x12191),x12193))+P77(f86(f28(a84,x12191),x12192))+~P77(f86(f28(a84,x12193),x12192))
% 7.14/7.08 [1260]~P1(x12601)+~P77(f86(f29(a83,x12602),x12603))+P77(f86(f29(a83,f86(x12601,x12602)),f86(x12601,x12603)))
% 7.14/7.08 [1324]~E(x13242,f3(a83))+~P77(f86(x13241,f20(a83,x13243,x13242)))+P77(f86(x13241,f3(a83)))
% 7.14/7.08 [1359]E(f86(f86(f23(a83),x13591),f102(x13591,x13592,x13593)),x13592)+P77(f86(x13593,f22(a83,x13592,x13591)))+~P77(f86(x13593,f3(a83)))
% 7.14/7.08 [1360]E(f86(f86(f23(a83),x13601),f106(x13601,x13602,x13603)),x13602)+P77(f86(x13603,f22(a83,x13602,x13601)))+~P77(f86(x13603,f3(a83)))
% 7.14/7.08 [1366]E(f86(f86(f23(a83),x13661),f102(x13661,x13662,x13663)),x13662)+P77(f86(x13663,f22(a83,x13662,x13661)))+P77(f86(f29(a83,x13662),x13661))
% 7.14/7.08 [1367]E(f86(f86(f23(a83),x13671),f106(x13671,x13672,x13673)),x13672)+P77(f86(x13673,f22(a83,x13672,x13671)))+P77(f86(f29(a83,x13672),x13671))
% 7.14/7.08 [1368]~P35(x13681)+~P4(x13681,x13682)+P77(f86(f28(a82,f36(x13681,f86(x13682,x13683))),f58(x13682,x13681)))
% 7.14/7.08 [1369]~P35(x13691)+~P4(x13691,x13692)+P77(f86(f28(a82,f36(x13691,f86(x13692,x13693))),f59(x13692,x13691)))
% 7.14/7.08 [1420]~P77(f86(x14201,f22(a83,x14202,x14203)))+~P77(f86(f29(a83,x14202),x14203))+P77(f86(x14201,f3(a83)))
% 7.14/7.08 [1438]P77(f86(f29(a82,f3(a82)),f107(x14381,x14382,x14383)))+~P77(f86(f29(a82,x14383),x14382))+~P77(f86(f29(a82,x14382),x14381))
% 7.14/7.08 [1450]E(f22(a83,f22(a83,x14501,x14502),f22(a83,x14503,x14502)),f22(a83,x14501,x14503))+~P77(f86(f28(a83,x14502),x14501))+~P77(f86(f28(a83,x14502),x14503))
% 7.14/7.08 [1489]E(x14891,f3(a83))+P77(f86(x14892,f114(x14891,x14893,x14892)))+~P77(f86(x14892,f20(a83,x14893,x14891)))
% 7.14/7.08 [1502]E(x15021,f3(a83))+~P77(f86(x15022,f109(x15021,x15023,x15022)))+P77(f86(x15022,f20(a83,x15023,x15021)))
% 7.14/7.08 [1520]P77(f86(x15201,f114(x15202,x15203,x15201)))+~P77(f86(x15201,f20(a83,x15203,x15202)))+P77(f86(x15201,f3(a83)))
% 7.14/7.08 [1522]~P28(x15221)+~P77(f86(f28(x15221,x15222),x15223))+P77(f86(f28(x15221,f22(x15221,x15222,x15223)),f3(x15221)))
% 7.14/7.08 [1523]~P28(x15231)+~P77(f86(f29(x15231,x15232),x15233))+P77(f86(f29(x15231,f22(x15231,x15232,x15233)),f3(x15231)))
% 7.14/7.08 [1531]~P77(f86(x15311,f102(x15313,x15312,x15311)))+P77(f86(x15311,f22(a83,x15312,x15313)))+~P77(f86(x15311,f3(a83)))
% 7.14/7.08 [1532]~P77(f86(x15321,f106(x15323,x15322,x15321)))+P77(f86(x15321,f22(a83,x15322,x15323)))+~P77(f86(x15321,f3(a83)))
% 7.14/7.08 [1533]~P77(f86(x15331,f109(x15333,x15332,x15331)))+P77(f86(x15331,f20(a83,x15332,x15333)))+~P77(f86(x15331,f3(a83)))
% 7.14/7.08 [1543]~P77(f86(x15433,f102(x15432,x15431,x15433)))+P77(f86(x15433,f22(a83,x15431,x15432)))+P77(f86(f29(a83,x15431),x15432))
% 7.14/7.08 [1544]~P77(f86(x15443,f106(x15442,x15441,x15443)))+P77(f86(x15443,f22(a83,x15441,x15442)))+P77(f86(f29(a83,x15441),x15442))
% 7.14/7.08 [1676]~P28(x16761)+~P77(f86(f28(x16761,f22(x16761,x16762,x16763)),f3(x16761)))+P77(f86(f28(x16761,x16762),x16763))
% 7.14/7.08 [1677]~P28(x16771)+~P77(f86(f29(x16771,f22(x16771,x16772,x16773)),f3(x16771)))+P77(f86(f29(x16771,x16772),x16773))
% 7.14/7.08 [1684]~P77(f86(f29(a83,x16843),x16842))+~P77(f86(f29(a83,x16843),x16841))+P77(f86(f29(a83,f22(a83,x16841,x16842)),f22(a83,x16841,x16843)))
% 7.14/7.08 [1685]~P77(f86(f28(a83,x16852),x16851))+~P77(f86(f29(a83,x16851),x16853))+P77(f86(f29(a83,f22(a83,x16851,x16852)),f22(a83,x16853,x16852)))
% 7.14/7.08 [1689]~P77(f86(f28(a84,x16893),x16891))+P77(f86(f28(a84,f20(a84,x16891,x16892)),f20(a84,x16893,x16892)))+~P77(f86(f29(a84,x16892),f3(a84)))
% 7.14/7.08 [1737]E(x17371,f3(a83))+E(f86(f86(f23(a83),f86(f86(f24(a83),x17371),f109(x17371,x17372,x17373))),f115(x17371,x17372,x17373)),x17372)+P77(f86(x17373,f20(a83,x17372,x17371)))
% 7.14/7.08 [1746]E(f86(f86(f23(a83),f86(f86(f24(a83),x17461),f109(x17461,x17462,x17463))),f115(x17461,x17462,x17463)),x17462)+P77(f86(x17463,f20(a83,x17462,x17461)))+~P77(f86(x17463,f3(a83)))
% 7.14/7.08 [1934]~P56(x19342)+E(x19341,f3(x19342))+~P77(f86(f28(x19342,f86(f86(f23(x19342),f86(f86(f24(x19342),x19343),x19343)),f86(f86(f24(x19342),x19341),x19341))),f3(x19342)))
% 7.14/7.08 [1935]~P56(x19352)+E(x19351,f3(x19352))+~P77(f86(f28(x19352,f86(f86(f23(x19352),f86(f86(f24(x19352),x19351),x19351)),f86(f86(f24(x19352),x19353),x19353))),f3(x19352)))
% 7.14/7.08 [872]~P76(x8721)+~E(x8723,f3(x8721))+E(f86(f86(f23(x8721),x8722),x8723),x8722)
% 7.14/7.08 [875]~P43(x8751)+~E(x8753,f3(a83))+E(f86(f86(f31(x8751),x8752),x8753),f16(x8751))
% 7.14/7.08 [886]~P65(x8861)+~E(x8863,f3(x8861))+E(f86(f86(f24(x8861),x8862),x8863),f3(x8861))
% 7.14/7.08 [887]~P65(x8871)+~E(x8872,f3(x8871))+E(f86(f86(f24(x8871),x8872),x8873),f3(x8871))
% 7.14/7.08 [930]~P76(x9302)+E(x9301,f3(x9302))+~E(f86(f86(f23(x9302),x9303),x9301),x9303)
% 7.14/7.08 [938]~P71(x9382)+E(x9381,f3(x9382))+~E(f86(f86(f31(x9382),x9381),x9383),f3(x9382))
% 7.14/7.08 [999]E(x9991,x9992)+E(x9993,f3(a82))+~E(f86(f86(f24(a82),x9993),x9991),f86(f86(f24(a82),x9993),x9992))
% 7.14/7.08 [1001]E(x10011,x10012)+E(x10013,f3(a83))+~E(f86(f86(f24(a83),x10013),x10011),f86(f86(f24(a83),x10013),x10012))
% 7.14/7.08 [1002]E(x10021,x10022)+E(x10023,f3(a82))+~E(f86(f86(f24(a82),x10021),x10023),f86(f86(f24(a82),x10022),x10023))
% 7.14/7.08 [1003]E(x10031,x10032)+E(x10033,f3(a83))+~E(f86(f86(f24(a83),x10031),x10033),f86(f86(f24(a83),x10032),x10033))
% 7.14/7.08 [1138]E(f22(a83,x11381,x11382),x11383)+~E(x11381,f86(f86(f23(a83),x11383),x11382))+~P77(f86(f28(a83,x11382),x11381))
% 7.14/7.08 [1143]~E(f22(a83,x11431,x11433),x11432)+E(x11431,f86(f86(f23(a83),x11432),x11433))+~P77(f86(f28(a83,x11433),x11431))
% 7.14/7.08 [1193]E(x11931,x11932)+~E(f86(f86(f24(a83),x11933),x11931),f86(f86(f24(a83),x11933),x11932))+~P77(f86(f29(a83,f3(a83)),x11933))
% 7.14/7.08 [1277]~P9(x12771)+P77(f86(f28(x12771,x12772),x12773))+~P77(f86(f28(x12771,f19(x12771,x12772)),x12773))
% 7.14/7.08 [1365]~E(x13651,f86(f86(f23(a83),x13653),f16(a83)))+~P77(f86(f29(a83,x13653),x13652))+P77(f86(f29(a83,x13651),f86(f86(f23(a83),x13652),f16(a83))))
% 7.14/7.08 [1571]E(x15711,f3(a83))+P77(f86(x15712,f20(a83,x15713,x15711)))+P77(f86(f29(a83,f115(x15711,x15713,x15712)),x15711))
% 7.14/7.08 [1598]P77(f86(x15981,f20(a83,x15982,x15983)))+~P77(f86(x15981,f3(a83)))+P77(f86(f29(a83,f115(x15983,x15982,x15981)),x15983))
% 7.14/7.08 [1614]E(x16141,f3(a82))+~P77(f86(f28(a82,x16142),f3(a82)))+~P77(f86(f28(a82,f19(a82,x16141)),f86(f86(f24(a82),x16142),f19(a82,x16143))))
% 7.14/7.08 [1692]~P77(f86(f28(a83,x16923),x16922))+P77(f86(f28(a83,f20(a83,x16921,x16922)),f20(a83,x16921,x16923)))+~P77(f86(f29(a83,f3(a83)),x16923))
% 7.14/7.08 [1693]~P77(f86(f28(a84,x16931),x16933))+P77(f86(f28(a84,f20(a84,x16931,x16932)),f20(a84,x16933,x16932)))+~P77(f86(f29(a84,f3(a84)),x16932))
% 7.14/7.08 [1902]~P41(x19021)+~P3(x19021,x19023)+P3(x19021,f7(x19021,x19021,a83,f86(f24(x19021),x19022),x19023))
% 7.14/7.08 [1944]~P35(x19441)+~P4(x19441,x19442)+P4(x19441,f7(a83,x19441,a83,x19442,f8(a83,a83,a83,f23(a83),x19443)))
% 7.14/7.08 [1946]~P41(x19461)+~P3(x19461,x19462)+P3(x19461,f8(a83,x19461,x19461,f7(x19461,f121(x19461,x19461),a83,f24(x19461),x19462),x19463))
% 7.14/7.08 [1947]~P46(x19471)+~P3(x19471,x19472)+P3(x19471,f8(a83,x19471,x19471,f7(x19471,f121(x19471,x19471),a83,f37(x19471),x19472),x19473))
% 7.14/7.08 [1962]~P35(x19621)+P4(x19621,x19622)+~P4(x19621,f7(a83,x19621,a83,x19622,f8(a83,a83,a83,f23(a83),x19623)))
% 7.14/7.08 [1024]~P14(x10242)+E(x10241,f3(x10242))+E(f20(x10242,f86(f86(f24(x10242),x10243),x10241),x10241),x10243)
% 7.14/7.08 [1025]~P14(x10252)+E(x10251,f3(x10252))+E(f20(x10252,f86(f86(f24(x10252),x10251),x10253),x10251),x10253)
% 7.14/7.08 [1144]~P46(x11442)+E(x11441,f3(x11442))+E(f86(f86(f37(a82),f36(x11442,x11443)),f36(x11442,x11441)),f36(x11442,f86(f86(f37(x11442),x11443),x11441)))
% 7.14/7.08 [1152]~P46(x11521)+~P16(x11521)+E(f86(f86(f37(a82),f36(x11521,x11522)),f36(x11521,x11523)),f36(x11521,f86(f86(f37(x11521),x11522),x11523)))
% 7.14/7.08 [1301]~P34(x13011)+E(f19(x13011,f86(f86(f24(x13011),x13012),x13013)),f86(f86(f24(x13011),f19(x13011,x13012)),x13013))+~P77(f86(f28(x13011,f3(x13011)),x13013))
% 7.14/7.08 [1350]~P43(x13502)+E(x13501,f3(a83))+E(f86(f86(f24(x13502),x13503),f86(f86(f31(x13502),x13503),f22(a83,x13501,f16(a83)))),f86(f86(f31(x13502),x13503),x13501))
% 7.14/7.08 [1354]~P14(x13542)+E(x13541,f3(x13542))+E(f20(x13542,f86(f86(f23(x13542),x13543),x13541),x13541),f86(f86(f23(x13542),f20(x13542,x13543,x13541)),f16(x13542)))
% 7.14/7.08 [1355]~P14(x13552)+E(x13551,f3(x13552))+E(f20(x13552,f86(f86(f23(x13552),x13551),x13553),x13551),f86(f86(f23(x13552),f20(x13552,x13553,x13551)),f16(x13552)))
% 7.14/7.08 [1379]~P7(x13791)+~P77(f86(f28(x13791,f3(x13791)),x13792))+P77(f86(f28(x13791,f3(x13791)),f86(f86(f31(x13791),x13792),x13793)))
% 7.14/7.08 [1380]~P7(x13801)+~P77(f86(f28(x13801,f16(x13801)),x13802))+P77(f86(f28(x13801,f16(x13801)),f86(f86(f31(x13801),x13802),x13803)))
% 7.14/7.08 [1382]~P7(x13821)+~P77(f86(f29(x13821,f3(x13821)),x13822))+P77(f86(f29(x13821,f3(x13821)),f86(f86(f31(x13821),x13822),x13823)))
% 7.14/7.08 [1466]~P56(x14662)+E(x14661,f3(x14662))+~E(f86(f86(f23(x14662),f86(f86(f24(x14662),x14663),x14663)),f86(f86(f24(x14662),x14661),x14661)),f3(x14662))
% 7.14/7.08 [1467]~P56(x14672)+E(x14671,f3(x14672))+~E(f86(f86(f23(x14672),f86(f86(f24(x14672),x14671),x14671)),f86(f86(f24(x14672),x14673),x14673)),f3(x14672))
% 7.14/7.08 [1546]~P77(f86(f29(a83,x15461),x15463))+~P77(f86(f29(a83,x15463),x15462))+P77(f86(f29(a83,f86(f86(f23(a83),x15461),f16(a83))),x15462))
% 7.14/7.08 [1644]~E(x16443,f20(a83,x16441,x16442))+~P77(f86(f29(a83,f3(a83)),x16442))+P77(f86(f29(a83,x16441),f86(f86(f24(a83),x16442),f86(f86(f23(a83),x16443),f16(a83)))))
% 7.14/7.08 [1646]~P7(x16461)+~P77(f86(f29(x16461,f16(x16461)),x16462))+P77(f86(f29(x16461,f16(x16461)),f86(f86(f31(x16461),x16462),f86(f86(f23(a83),x16463),f16(a83)))))
% 7.14/7.08 [1649]~P77(f86(f28(a82,x16492),x16493))+~P77(f86(f29(a82,f3(a82)),x16491))+P77(f86(f28(a82,f86(f86(f24(a82),x16491),x16492)),f86(f86(f24(a82),x16491),x16493)))
% 7.14/7.08 [1650]~P77(f86(f28(a82,x16501),x16503))+~P77(f86(f29(a82,f3(a82)),x16502))+P77(f86(f28(a82,f86(f86(f24(a82),x16501),x16502)),f86(f86(f24(a82),x16503),x16502)))
% 7.14/7.08 [1652]~P77(f86(f29(a82,x16521),x16523))+~P77(f86(f29(a82,f3(a82)),x16522))+P77(f86(f29(a82,f86(f86(f24(a82),x16521),x16522)),f86(f86(f24(a82),x16523),x16522)))
% 7.14/7.08 [1653]~P77(f86(f29(a82,x16532),x16533))+~P77(f86(f29(a82,f3(a82)),x16531))+P77(f86(f29(a82,f86(f86(f24(a82),x16531),x16532)),f86(f86(f24(a82),x16531),x16533)))
% 7.14/7.08 [1657]~P77(f86(f29(a83,x16571),x16573))+~P77(f86(f29(a83,f3(a83)),x16572))+P77(f86(f29(a83,f86(f86(f24(a83),x16571),x16572)),f86(f86(f24(a83),x16573),x16572)))
% 7.14/7.08 [1658]~P77(f86(f29(a83,x16582),x16583))+~P77(f86(f29(a83,f3(a83)),x16581))+P77(f86(f29(a83,f86(f86(f24(a83),x16581),x16582)),f86(f86(f24(a83),x16581),x16583)))
% 7.14/7.08 [1659]~P77(f86(f29(a84,x16592),x16593))+~P77(f86(f29(a84,f3(a84)),x16591))+P77(f86(f29(a84,f86(f86(f24(a84),x16591),x16592)),f86(f86(f24(a84),x16591),x16593)))
% 7.14/7.08 [1780]P77(f86(f28(a82,x17801),x17802))+~P77(f86(f29(a82,f3(a82)),x17803))+~P77(f86(f28(a82,f86(f86(f24(a82),x17803),x17801)),f86(f86(f24(a82),x17803),x17802)))
% 7.14/7.08 [1781]P77(f86(f28(a82,x17811),x17812))+~P77(f86(f29(a82,f3(a82)),x17813))+~P77(f86(f28(a82,f86(f86(f24(a82),x17811),x17813)),f86(f86(f24(a82),x17812),x17813)))
% 7.14/7.08 [1783]P77(f86(f28(a83,x17831),x17832))+~P77(f86(f29(a83,f3(a83)),x17833))+~P77(f86(f28(a83,f86(f86(f24(a83),x17833),x17831)),f86(f86(f24(a83),x17833),x17832)))
% 7.14/7.08 [1784]P77(f86(f28(a83,x17841),x17842))+~P77(f86(f29(a83,f3(a83)),x17843))+~P77(f86(f28(a83,f86(f86(f24(a83),x17841),x17843)),f86(f86(f24(a83),x17842),x17843)))
% 7.14/7.08 [1785]P77(f86(f29(a82,x17851),x17852))+~P77(f86(f29(a82,f3(a82)),x17853))+~P77(f86(f29(a82,f86(f86(f24(a82),x17851),x17853)),f86(f86(f24(a82),x17852),x17853)))
% 7.14/7.08 [1787]P77(f86(f29(a83,x17871),x17872))+~P77(f86(f29(a83,f3(a83)),x17873))+~P77(f86(f29(a83,f86(f86(f31(a83),x17873),x17871)),f86(f86(f31(a83),x17873),x17872)))
% 7.14/7.08 [1794]~P35(x17941)+~P4(x17941,x17942)+P77(f86(f28(a82,f36(x17941,f86(x17942,x17943))),f35(a83,f86(f86(f23(a83),f90(x17942,x17941)),f16(a83)))))
% 7.14/7.08 [1795]~P35(x17951)+~P4(x17951,x17952)+P77(f86(f29(a82,f36(x17951,f86(x17952,x17953))),f35(a83,f86(f86(f23(a83),f91(x17952,x17951)),f16(a83)))))
% 7.14/7.08 [1865]E(x18651,f3(a83))+~P77(f86(x18653,f20(a83,x18652,x18651)))+P77(f86(f28(a83,f86(f86(f24(a83),x18651),f114(x18651,x18652,x18653))),x18652))
% 7.14/7.08 [1866]~P77(f86(x18661,f20(a83,x18663,x18662)))+P77(f86(x18661,f3(a83)))+P77(f86(f28(a83,f86(f86(f24(a83),x18662),f114(x18662,x18663,x18661))),x18663))
% 7.14/7.08 [1903]E(x19031,f3(a83))+~P77(f86(x19033,f20(a83,x19032,x19031)))+P77(f86(f29(a83,x19032),f86(f86(f24(a83),x19031),f86(f86(f23(a83),f114(x19031,x19032,x19033)),f16(a83)))))
% 7.14/7.08 [1905]~P77(f86(x19051,f20(a83,x19052,x19053)))+P77(f86(x19051,f3(a83)))+P77(f86(f29(a83,x19052),f86(f86(f24(a83),x19053),f86(f86(f23(a83),f114(x19053,x19052,x19051)),f16(a83)))))
% 7.14/7.08 [1925]~P35(x19251)+P4(x19251,x19252)+~P77(f86(f28(a82,f36(x19251,f86(x19252,f92(x19252,x19251,x19253)))),f35(a83,f86(f86(f23(a83),x19253),f16(a83)))))
% 7.14/7.08 [1926]~P35(x19261)+P4(x19261,x19262)+~P77(f86(f29(a82,f36(x19261,f86(x19262,f93(x19262,x19261,x19263)))),f35(a83,f86(f86(f23(a83),x19263),f16(a83)))))
% 7.14/7.08 [1927]~P35(x19272)+P77(f86(f29(a82,f3(a82)),f68(x19271,x19272)))+~P77(f86(f28(a82,f36(x19272,f86(x19271,f69(x19271,x19272,x19273)))),f35(a83,f86(f86(f23(a83),x19273),f16(a83)))))
% 7.14/7.08 [1928]~P35(x19282)+P77(f86(f29(a82,f3(a82)),f73(x19281,x19282)))+~P77(f86(f29(a82,f36(x19282,f86(x19281,f74(x19281,x19282,x19283)))),f35(a83,f86(f86(f23(a83),x19283),f16(a83)))))
% 7.14/7.08 [1527]~E(x15272,f20(a83,x15273,x15271))+~P77(f86(f29(a83,f3(a83)),x15271))+P77(f86(f28(a83,f86(f86(f24(a83),x15271),x15272)),x15273))
% 7.14/7.08 [1671]~P27(x16711)+E(f86(f86(f24(x16711),f86(f86(f31(x16711),x16712),f22(a83,x16713,f16(a83)))),x16712),f86(f86(f31(x16711),x16712),x16713))+~P77(f86(f29(a83,f3(a83)),x16713))
% 7.14/7.08 [1672]~P7(x16721)+~P77(f86(f29(x16721,f16(x16721)),x16722))+P77(f86(f29(x16721,f16(x16721)),f86(f86(f24(x16721),x16722),f86(f86(f31(x16721),x16722),x16723))))
% 7.14/7.08 [1735]~P77(f86(f28(a83,x17352),x17353))+~P77(f86(f28(a83,x17351),f22(a83,x17353,x17352)))+P77(f86(f28(a83,f86(f86(f23(a83),x17351),x17352)),x17353))
% 7.14/7.08 [1755]~P77(f86(f28(a83,x17553),x17552))+P77(f86(f28(a83,x17551),f22(a83,x17552,x17553)))+~P77(f86(f28(a83,f86(f86(f23(a83),x17551),x17553)),x17552))
% 7.14/7.08 [1800]~P7(x18001)+~P77(f86(f29(x18001,f16(x18001)),x18002))+P77(f86(f29(x18001,f86(f86(f31(x18001),x18002),x18003)),f86(f86(f24(x18001),x18002),f86(f86(f31(x18001),x18002),x18003))))
% 7.14/7.08 [1855]~P56(x18552)+E(x18551,f3(x18552))+P77(f86(f29(x18552,f3(x18552)),f86(f86(f23(x18552),f86(f86(f24(x18552),x18553),x18553)),f86(f86(f24(x18552),x18551),x18551))))
% 7.14/7.08 [1856]~P56(x18562)+E(x18561,f3(x18562))+P77(f86(f29(x18562,f3(x18562)),f86(f86(f23(x18562),f86(f86(f24(x18562),x18561),x18561)),f86(f86(f24(x18562),x18563),x18563))))
% 7.14/7.08 [1753]~P35(x17531)+P4(x17531,x17532)+P77(f86(f28(a83,x17533),f67(x17534,x17532,x17533,x17531)))
% 7.14/7.08 [1035]~P10(x10353)+E(x10351,x10352)+~E(f86(f86(f23(x10353),x10354),x10351),f86(f86(f23(x10353),x10354),x10352))
% 7.14/7.08 [1036]~P11(x10363)+E(x10361,x10362)+~E(f86(f86(f23(x10363),x10364),x10361),f86(f86(f23(x10363),x10364),x10362))
% 7.14/7.08 [1038]~P10(x10383)+E(x10381,x10382)+~E(f86(f86(f23(x10383),x10381),x10384),f86(f86(f23(x10383),x10382),x10384))
% 7.14/7.08 [1243]~E(f86(f86(f23(a83),x12433),x12432),f86(f86(f23(a83),x12431),x12434))+~P77(f86(f29(a83,x12433),x12434))+P77(f86(f29(a83,x12431),x12432))
% 7.14/7.08 [1374]P77(f86(x13741,x13742))+~E(x13743,f86(f86(f23(a83),x13744),x13742))+~P77(f86(x13741,f22(a83,x13743,x13744)))
% 7.14/7.08 [1377]~P38(x13772)+~P77(f86(f29(f121(x13771,x13772),x13773),x13774))+P77(f86(f28(f121(x13771,x13772),x13773),x13774))
% 7.14/7.08 [1475]~P38(x14751)+~P77(f86(f29(f121(x14752,x14751),x14754),x14753))+~P77(f86(f28(f121(x14752,x14751),x14753),x14754))
% 7.14/7.08 [1959]~P38(x19592)+~P77(f86(f28(x19592,f86(x19593,f63(x19594,x19593,x19591,x19592))),f86(x19594,f63(x19594,x19593,x19591,x19592))))+P77(f86(f28(f121(x19591,x19592),x19593),x19594))
% 7.14/7.08 [1186]~P14(x11861)+~E(x11862,f3(x11861))+E(f20(x11861,f86(f86(f24(x11861),x11862),x11863),f86(f86(f24(x11861),x11862),x11864)),f3(x11861))
% 7.14/7.08 [1228]~P14(x12282)+E(x12281,f3(x12282))+E(f20(x12282,f86(f86(f24(x12282),x12283),x12281),f86(f86(f24(x12282),x12284),x12281)),f20(x12282,x12283,x12284))
% 7.14/7.08 [1230]~P14(x12302)+E(x12301,f3(x12302))+E(f20(x12302,f86(f86(f24(x12302),x12301),x12303),f86(f86(f24(x12302),x12301),x12304)),f20(x12302,x12303,x12304))
% 7.14/7.08 [1627]~P29(x16271)+~P77(f86(f28(x16271,x16273),x16274))+P77(f86(f28(x16271,f86(f86(f23(x16271),x16272),x16273)),f86(f86(f23(x16271),x16272),x16274)))
% 7.14/7.08 [1628]~P30(x16281)+~P77(f86(f28(x16281,x16283),x16284))+P77(f86(f28(x16281,f86(f86(f23(x16281),x16282),x16283)),f86(f86(f23(x16281),x16282),x16284)))
% 7.14/7.08 [1629]~P29(x16291)+~P77(f86(f28(x16291,x16292),x16294))+P77(f86(f28(x16291,f86(f86(f23(x16291),x16292),x16293)),f86(f86(f23(x16291),x16294),x16293)))
% 7.14/7.08 [1630]~P30(x16301)+~P77(f86(f28(x16301,x16302),x16304))+P77(f86(f28(x16301,f86(f86(f23(x16301),x16302),x16303)),f86(f86(f23(x16301),x16304),x16303)))
% 7.14/7.08 [1631]~P29(x16311)+~P77(f86(f29(x16311,x16313),x16314))+P77(f86(f29(x16311,f86(f86(f23(x16311),x16312),x16313)),f86(f86(f23(x16311),x16312),x16314)))
% 7.14/7.08 [1632]~P31(x16321)+~P77(f86(f29(x16321,x16323),x16324))+P77(f86(f29(x16321,f86(f86(f23(x16321),x16322),x16323)),f86(f86(f23(x16321),x16322),x16324)))
% 7.14/7.08 [1633]~P29(x16331)+~P77(f86(f29(x16331,x16332),x16334))+P77(f86(f29(x16331,f86(f86(f23(x16331),x16332),x16333)),f86(f86(f23(x16331),x16334),x16333)))
% 7.14/7.08 [1634]~P31(x16341)+~P77(f86(f29(x16341,x16342),x16344))+P77(f86(f29(x16341,f86(f86(f23(x16341),x16342),x16343)),f86(f86(f23(x16341),x16344),x16343)))
% 7.14/7.08 [1638]~P77(f86(f28(a83,x16382),x16384))+~P77(f86(f28(a83,x16381),x16383))+P77(f86(f28(a83,f86(f86(f23(a83),x16381),x16382)),f86(f86(f23(a83),x16383),x16384)))
% 7.14/7.08 [1639]~P77(f86(f28(a83,x16392),x16394))+~P77(f86(f28(a83,x16391),x16393))+P77(f86(f28(a83,f86(f86(f24(a83),x16391),x16392)),f86(f86(f24(a83),x16393),x16394)))
% 7.14/7.08 [1640]~P77(f86(f29(a83,x16402),x16404))+~P77(f86(f29(a83,x16401),x16403))+P77(f86(f29(a83,f86(f86(f23(a83),x16401),x16402)),f86(f86(f23(a83),x16403),x16404)))
% 7.14/7.08 [1641]~P77(f86(f28(a84,x16412),x16414))+~P77(f86(f29(a84,x16411),x16413))+P77(f86(f29(a84,f86(f86(f23(a84),x16411),x16412)),f86(f86(f23(a84),x16413),x16414)))
% 7.14/7.08 [1768]~P27(x17681)+E(f86(f86(f31(x17681),x17682),f22(a83,f86(f86(f23(a83),x17683),f16(a83)),x17684)),f86(f86(f24(x17681),f86(f86(f31(x17681),x17682),f22(a83,x17683,x17684))),x17682))+~P77(f86(f28(a83,x17684),x17683))
% 7.14/7.08 [1773]~P29(x17731)+P77(f86(f28(x17731,x17732),x17733))+~P77(f86(f28(x17731,f86(f86(f23(x17731),x17734),x17732)),f86(f86(f23(x17731),x17734),x17733)))
% 7.14/7.08 [1775]~P29(x17751)+P77(f86(f28(x17751,x17752),x17753))+~P77(f86(f28(x17751,f86(f86(f23(x17751),x17752),x17754)),f86(f86(f23(x17751),x17753),x17754)))
% 7.14/7.08 [1777]~P29(x17771)+P77(f86(f29(x17771,x17772),x17773))+~P77(f86(f29(x17771,f86(f86(f23(x17771),x17774),x17772)),f86(f86(f23(x17771),x17774),x17773)))
% 7.14/7.08 [1779]~P29(x17791)+P77(f86(f29(x17791,x17792),x17793))+~P77(f86(f29(x17791,f86(f86(f23(x17791),x17792),x17794)),f86(f86(f23(x17791),x17793),x17794)))
% 7.14/7.08 [1882]~P34(x18821)+~P77(f86(f29(x18821,f19(x18821,f22(x18821,x18822,x18823))),x18824))+P77(f86(f29(x18821,x18822),f86(f86(f23(x18821),x18823),x18824)))
% 7.14/7.08 [1886]~P34(x18861)+P77(f86(f29(x18861,f22(x18861,x18862,x18863)),x18864))+~P77(f86(f29(x18861,f19(x18861,f22(x18861,x18864,x18862))),x18863))
% 7.14/7.08 [1930]~P35(x19301)+P77(f86(f28(a82,f36(x19301,f86(x19302,x19303))),f68(x19302,x19301)))+~P77(f86(f28(a82,f36(x19301,f86(x19302,f69(x19302,x19301,x19304)))),f35(a83,f86(f86(f23(a83),x19304),f16(a83)))))
% 7.14/7.08 [1931]~P35(x19311)+P77(f86(f28(a82,f36(x19311,f86(x19312,x19313))),f73(x19312,x19311)))+~P77(f86(f29(a82,f36(x19311,f86(x19312,f74(x19312,x19311,x19314)))),f35(a83,f86(f86(f23(a83),x19314),f16(a83)))))
% 7.14/7.08 [1428]~P14(x14282)+E(x14281,f3(x14282))+E(f20(x14282,f86(f86(f23(x14282),x14283),f86(f86(f24(x14282),x14284),x14281)),x14281),f86(f86(f23(x14282),x14284),f20(x14282,x14283,x14281)))
% 7.14/7.08 [1429]~P14(x14292)+E(x14291,f3(x14292))+E(f20(x14292,f86(f86(f23(x14292),x14293),f86(f86(f24(x14292),x14291),x14294)),x14291),f86(f86(f23(x14292),x14294),f20(x14292,x14293,x14291)))
% 7.14/7.08 [1504]~P15(x15042)+E(x15041,f3(x15042))+E(f86(f86(f37(x15042),f86(f86(f31(x15042),x15043),x15044)),f86(f86(f31(x15042),x15041),x15044)),f86(f86(f31(x15042),f86(f86(f37(x15042),x15043),x15041)),x15044))
% 7.14/7.08 [1965]~P35(x19651)+P4(x19651,x19652)+~P77(f86(f28(a82,f36(x19651,f86(x19652,f67(x19653,x19652,x19654,x19651)))),x19653))
% 7.14/7.08 [1435]~P38(x14351)+P77(f86(f28(x14351,f86(x14352,x14353)),f86(x14354,x14353)))+~P77(f86(f28(f121(x14355,x14351),x14352),x14354))
% 7.14/7.08 [1556]~E(x15562,x15564)+~P76(x15561)+E(f86(f86(f23(x15561),f86(f86(f24(x15561),x15562),x15563)),f86(f86(f24(x15561),x15564),x15565)),f86(f86(f23(x15561),f86(f86(f24(x15561),x15562),x15565)),f86(f86(f24(x15561),x15564),x15563)))
% 7.14/7.08 [1875]~P77(f86(f28(a83,x18753),x18752))+E(x18751,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x18752,x18753)),x18754)),x18755))+~E(f86(f86(f23(a83),f86(f86(f24(a83),x18753),x18754)),x18751),f86(f86(f23(a83),f86(f86(f24(a83),x18752),x18754)),x18755))
% 7.14/7.08 [1876]~P77(f86(f28(a83,x18762),x18761))+E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x18761,x18762)),x18763)),x18764),x18765)+~E(f86(f86(f23(a83),f86(f86(f24(a83),x18761),x18763)),x18764),f86(f86(f23(a83),f86(f86(f24(a83),x18762),x18763)),x18765))
% 7.14/7.08 [1890]~P77(f86(f28(a83,x18904),x18901))+~E(x18905,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x18901,x18904)),x18902)),x18903))+E(f86(f86(f23(a83),f86(f86(f24(a83),x18901),x18902)),x18903),f86(f86(f23(a83),f86(f86(f24(a83),x18904),x18902)),x18905))
% 7.14/7.08 [1891]~P77(f86(f28(a83,x18914),x18911))+~E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x18911,x18914)),x18912)),x18913),x18915)+E(f86(f86(f23(a83),f86(f86(f24(a83),x18911),x18912)),x18913),f86(f86(f23(a83),f86(f86(f24(a83),x18914),x18912)),x18915))
% 7.14/7.08 [1952]~P77(f86(f28(a83,x19523),x19522))+P77(f86(f28(a83,x19521),f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19522,x19523)),x19524)),x19525)))+~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19523),x19524)),x19521)),f86(f86(f23(a83),f86(f86(f24(a83),x19522),x19524)),x19525)))
% 7.14/7.08 [1953]~P77(f86(f28(a83,x19533),x19532))+P77(f86(f29(a83,x19531),f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19532,x19533)),x19534)),x19535)))+~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19533),x19534)),x19531)),f86(f86(f23(a83),f86(f86(f24(a83),x19532),x19534)),x19535)))
% 7.14/7.08 [1957]~P77(f86(f28(a83,x19571),x19574))+~P77(f86(f28(a83,x19573),f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19574,x19571)),x19572)),x19575)))+P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19571),x19572)),x19573)),f86(f86(f23(a83),f86(f86(f24(a83),x19574),x19572)),x19575)))
% 7.14/7.08 [1958]~P77(f86(f28(a83,x19581),x19584))+~P77(f86(f29(a83,x19583),f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19584,x19581)),x19582)),x19585)))+P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19581),x19582)),x19583)),f86(f86(f23(a83),f86(f86(f24(a83),x19584),x19582)),x19585)))
% 7.14/7.08 [1963]~P77(f86(f28(a83,x19632),x19631))+~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19631),x19633)),x19634)),f86(f86(f23(a83),f86(f86(f24(a83),x19632),x19633)),x19635)))+P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19631,x19632)),x19633)),x19634)),x19635))
% 7.14/7.08 [1964]~P77(f86(f28(a83,x19642),x19641))+~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19641),x19643)),x19644)),f86(f86(f23(a83),f86(f86(f24(a83),x19642),x19643)),x19645)))+P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19641,x19642)),x19643)),x19644)),x19645))
% 7.14/7.08 [1968]~P77(f86(f28(a83,x19684),x19681))+P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19681),x19682)),x19683)),f86(f86(f23(a83),f86(f86(f24(a83),x19684),x19682)),x19685)))+~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19681,x19684)),x19682)),x19683)),x19685))
% 7.14/7.08 [1969]~P77(f86(f28(a83,x19694),x19691))+P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),x19691),x19692)),x19693)),f86(f86(f23(a83),f86(f86(f24(a83),x19694),x19692)),x19695)))+~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x19691,x19694)),x19692)),x19693)),x19695))
% 7.14/7.08 [1880]~P72(x18802)+~E(f86(f86(f23(x18802),f86(f86(f24(x18802),x18804),x18805)),x18801),f86(f86(f23(x18802),f86(f86(f24(x18802),x18803),x18805)),x18806))+E(x18801,f86(f86(f23(x18802),f86(f86(f24(x18802),f22(x18802,x18803,x18804)),x18805)),x18806))
% 7.14/7.08 [1881]~P72(x18811)+~E(f86(f86(f23(x18811),f86(f86(f24(x18811),x18812),x18814)),x18815),f86(f86(f23(x18811),f86(f86(f24(x18811),x18813),x18814)),x18816))+E(f86(f86(f23(x18811),f86(f86(f24(x18811),f22(x18811,x18812,x18813)),x18814)),x18815),x18816)
% 7.14/7.08 [1892]~P72(x18921)+~E(x18926,f86(f86(f23(x18921),f86(f86(f24(x18921),f22(x18921,x18922,x18925)),x18923)),x18924))+E(f86(f86(f23(x18921),f86(f86(f24(x18921),x18922),x18923)),x18924),f86(f86(f23(x18921),f86(f86(f24(x18921),x18925),x18923)),x18926))
% 7.14/7.08 [1893]~P72(x18931)+~E(f86(f86(f23(x18931),f86(f86(f24(x18931),f22(x18931,x18932,x18935)),x18933)),x18934),x18936)+E(f86(f86(f23(x18931),f86(f86(f24(x18931),x18932),x18933)),x18934),f86(f86(f23(x18931),f86(f86(f24(x18931),x18935),x18933)),x18936))
% 7.14/7.08 [1955]~P67(x19551)+~P77(f86(f28(x19551,f86(f86(f23(x19551),f86(f86(f24(x19551),x19554),x19555)),x19552)),f86(f86(f23(x19551),f86(f86(f24(x19551),x19553),x19555)),x19556)))+P77(f86(f28(x19551,x19552),f86(f86(f23(x19551),f86(f86(f24(x19551),f22(x19551,x19553,x19554)),x19555)),x19556)))
% 7.14/7.08 [1956]~P67(x19561)+~P77(f86(f29(x19561,f86(f86(f23(x19561),f86(f86(f24(x19561),x19564),x19565)),x19562)),f86(f86(f23(x19561),f86(f86(f24(x19561),x19563),x19565)),x19566)))+P77(f86(f29(x19561,x19562),f86(f86(f23(x19561),f86(f86(f24(x19561),f22(x19561,x19563,x19564)),x19565)),x19566)))
% 7.14/7.08 [1960]~P67(x19601)+~P77(f86(f28(x19601,x19604),f86(f86(f23(x19601),f86(f86(f24(x19601),f22(x19601,x19605,x19602)),x19603)),x19606)))+P77(f86(f28(x19601,f86(f86(f23(x19601),f86(f86(f24(x19601),x19602),x19603)),x19604)),f86(f86(f23(x19601),f86(f86(f24(x19601),x19605),x19603)),x19606)))
% 7.14/7.08 [1961]~P67(x19611)+~P77(f86(f29(x19611,x19614),f86(f86(f23(x19611),f86(f86(f24(x19611),f22(x19611,x19615,x19612)),x19613)),x19616)))+P77(f86(f29(x19611,f86(f86(f23(x19611),f86(f86(f24(x19611),x19612),x19613)),x19614)),f86(f86(f23(x19611),f86(f86(f24(x19611),x19615),x19613)),x19616)))
% 7.14/7.08 [1966]~P67(x19661)+~P77(f86(f28(x19661,f86(f86(f23(x19661),f86(f86(f24(x19661),x19662),x19664)),x19665)),f86(f86(f23(x19661),f86(f86(f24(x19661),x19663),x19664)),x19666)))+P77(f86(f28(x19661,f86(f86(f23(x19661),f86(f86(f24(x19661),f22(x19661,x19662,x19663)),x19664)),x19665)),x19666))
% 7.14/7.08 [1967]~P67(x19671)+~P77(f86(f29(x19671,f86(f86(f23(x19671),f86(f86(f24(x19671),x19672),x19674)),x19675)),f86(f86(f23(x19671),f86(f86(f24(x19671),x19673),x19674)),x19676)))+P77(f86(f29(x19671,f86(f86(f23(x19671),f86(f86(f24(x19671),f22(x19671,x19672,x19673)),x19674)),x19675)),x19676))
% 7.14/7.08 [1971]~P67(x19711)+P77(f86(f28(x19711,f86(f86(f23(x19711),f86(f86(f24(x19711),x19712),x19713)),x19714)),f86(f86(f23(x19711),f86(f86(f24(x19711),x19715),x19713)),x19716)))+~P77(f86(f28(x19711,f86(f86(f23(x19711),f86(f86(f24(x19711),f22(x19711,x19712,x19715)),x19713)),x19714)),x19716))
% 7.14/7.08 [1972]~P67(x19721)+P77(f86(f29(x19721,f86(f86(f23(x19721),f86(f86(f24(x19721),x19722),x19723)),x19724)),f86(f86(f23(x19721),f86(f86(f24(x19721),x19725),x19723)),x19726)))+~P77(f86(f29(x19721,f86(f86(f23(x19721),f86(f86(f24(x19721),f22(x19721,x19722,x19725)),x19723)),x19724)),x19726))
% 7.14/7.08 [1135]E(x11351,f3(a84))+~E(f20(a84,x11352,x11351),f3(a84))+P77(f86(f29(a84,x11351),x11352))+P77(f86(f29(a84,x11352),x11351))
% 7.14/7.08 [1141]E(x11411,f3(a84))+~E(f20(a84,x11412,x11411),f3(a84))+P77(f86(f29(a84,x11412),x11411))+P77(f86(f28(a84,x11412),f3(a84)))
% 7.14/7.08 [919]~P43(x9192)+~P75(x9192)+E(x9191,f3(a83))+E(f86(f86(f31(x9192),f3(x9192)),x9191),f3(x9192))
% 7.14/7.08 [1090]~E(x10902,f16(a84))+~E(x10901,f16(a84))+E(f86(f86(f24(a84),x10901),x10902),f16(a84))+~P77(f86(f29(a84,f3(a84)),x10901))
% 7.14/7.08 [1153]E(x11531,f3(a84))+~E(f20(a84,x11532,x11531),f3(a84))+P77(f86(f29(a84,x11531),x11532))+P77(f86(f28(a84,f3(a84)),x11532))
% 7.14/7.08 [1196]E(x11961,x11962)+~E(f34(x11961),f34(x11962))+~P77(f86(f29(a82,f3(a82)),x11962))+~P77(f86(f29(a82,f3(a82)),x11961))
% 7.14/7.08 [1401]~P77(f86(f28(a82,x14011),x14012))+P77(f86(f28(a82,f34(x14011)),f34(x14012)))+~P77(f86(f29(a82,f3(a82)),x14012))+~P77(f86(f29(a82,f3(a82)),x14011))
% 7.14/7.08 [1402]~P77(f86(f29(a82,x14021),x14022))+P77(f86(f29(a82,f34(x14021)),f34(x14022)))+~P77(f86(f29(a82,f3(a82)),x14022))+~P77(f86(f29(a82,f3(a82)),x14021))
% 7.14/7.08 [1422]~P77(f86(f28(a82,f34(x14221)),f34(x14222)))+P77(f86(f28(a82,x14221),x14222))+~P77(f86(f29(a82,f3(a82)),x14222))+~P77(f86(f29(a82,f3(a82)),x14221))
% 7.14/7.08 [1423]~P77(f86(f29(a82,f34(x14231)),f34(x14232)))+P77(f86(f29(a82,x14231),x14232))+~P77(f86(f29(a82,f3(a82)),x14232))+~P77(f86(f29(a82,f3(a82)),x14231))
% 7.14/7.08 [1039]~P34(x10393)+E(x10391,x10392)+P77(f86(f29(x10393,x10391),x10392))+P77(f86(f29(x10393,x10392),x10391))
% 7.14/7.08 [1045]~P39(x10453)+E(x10451,x10452)+P77(f86(f29(x10453,x10451),x10452))+P77(f86(f29(x10453,x10452),x10451))
% 7.14/7.08 [1049]~E(x10492,x10493)+~P39(x10491)+P77(f86(f29(x10491,x10492),x10493))+P77(f86(f28(x10491,x10492),x10493))
% 7.14/7.08 [1107]~P40(x11073)+E(x11071,x11072)+~P77(f86(f28(x11073,x11072),x11071))+P77(f86(f29(x11073,x11072),x11071))
% 7.14/7.08 [1109]~P39(x11093)+E(x11091,x11092)+~P77(f86(f28(x11093,x11091),x11092))+P77(f86(f29(x11093,x11091),x11092))
% 7.14/7.08 [1115]~P40(x11153)+E(x11151,x11152)+~P77(f86(f28(x11153,x11151),x11152))+P77(f86(f29(x11153,x11151),x11152))
% 7.14/7.08 [1170]E(x11701,x11702)+~P40(x11703)+~P77(f86(f28(x11703,x11702),x11701))+~P77(f86(f28(x11703,x11701),x11702))
% 7.14/7.08 [1202]~P37(x12021)+P77(f86(f29(x12021,x12023),x12022))+~P77(f86(f28(x12021,x12023),x12022))+P77(f86(f28(x12021,x12022),x12023))
% 7.14/7.08 [1238]~P77(f86(x12381,x12382))+~P77(f86(x12381,x12383))+~P77(f86(f28(a83,x12383),f54(x12382,x12381)))+P77(f86(x12381,f3(a83)))
% 7.14/7.08 [1310]E(x13101,x13102)+~E(f22(a83,x13101,x13103),f22(a83,x13102,x13103))+~P77(f86(f28(a83,x13103),x13101))+~P77(f86(f28(a83,x13103),x13102))
% 7.14/7.08 [1357]P78(x13572,x13571,x13573)+E(x13571,f3(a84))+P77(f86(f28(a84,f3(a84)),f112(x13573,x13571,x13572)))+P77(f86(f29(a84,x13571),f3(a84)))
% 7.14/7.08 [1385]P78(x13851,x13852,x13853)+P77(f86(f28(a84,f3(a84)),f112(x13853,x13852,x13851)))+~P77(f86(x13851,f3(a84)))+P77(f86(f29(a84,x13852),f3(a84)))
% 7.14/7.08 [1414]P78(x14142,x14141,x14143)+E(x14141,f3(a84))+~P77(f86(x14142,f113(x14143,x14141,x14142)))+P77(f86(f29(a84,x14141),f3(a84)))
% 7.14/7.08 [1460]P78(x14601,x14602,x14603)+~P77(f86(x14601,f113(x14603,x14602,x14601)))+~P77(f86(x14601,f3(a84)))+P77(f86(f29(a84,x14602),f3(a84)))
% 7.14/7.08 [1510]P78(x15102,x15101,x15103)+E(x15101,f3(a84))+P77(f86(f28(a84,f3(a84)),f112(x15103,x15101,x15102)))+P77(f86(f29(a84,x15101),f111(x15103,x15101,x15102)))
% 7.14/7.08 [1547]P78(x15471,x15472,x15473)+P77(f86(f28(a84,f3(a84)),f112(x15473,x15472,x15471)))+P77(f86(f29(a84,x15472),f111(x15473,x15472,x15471)))+~P77(f86(x15471,f3(a84)))
% 7.14/7.08 [1557]P78(x15572,x15571,x15573)+E(x15571,f3(a84))+~P77(f86(x15572,f113(x15573,x15571,x15572)))+P77(f86(f29(a84,x15571),f111(x15573,x15571,x15572)))
% 7.14/7.08 [1570]P78(x15702,x15701,x15703)+E(x15701,f3(a84))+P77(f86(f28(a84,f3(a84)),f112(x15703,x15701,x15702)))+~P77(f86(x15702,f117(x15703,x15701,x15702)))
% 7.14/7.08 [1594]P78(x15941,x15942,x15943)+~P77(f86(x15941,f113(x15943,x15942,x15941)))+P77(f86(f29(a84,x15942),f111(x15943,x15942,x15941)))+~P77(f86(x15941,f3(a84)))
% 7.14/7.08 [1596]P78(x15961,x15962,x15963)+P77(f86(f28(a84,f3(a84)),f112(x15963,x15962,x15961)))+~P77(f86(x15961,f117(x15963,x15962,x15961)))+~P77(f86(x15961,f3(a84)))
% 7.14/7.08 [1605]~P8(x16051)+~P77(f86(f28(x16051,x16053),f3(x16051)))+~P77(f86(f28(x16051,x16052),f3(x16051)))+P77(f86(f28(x16051,f86(f86(f23(x16051),x16052),x16053)),f3(x16051)))
% 7.14/7.08 [1606]~P8(x16061)+~P77(f86(f28(x16061,x16063),f3(x16061)))+~P77(f86(f29(x16061,x16062),f3(x16061)))+P77(f86(f29(x16061,f86(f86(f23(x16061),x16062),x16063)),f3(x16061)))
% 7.14/7.08 [1607]~P8(x16071)+~P77(f86(f28(x16071,x16072),f3(x16071)))+~P77(f86(f29(x16071,x16073),f3(x16071)))+P77(f86(f29(x16071,f86(f86(f23(x16071),x16072),x16073)),f3(x16071)))
% 7.14/7.08 [1608]~P8(x16081)+~P77(f86(f29(x16081,x16083),f3(x16081)))+~P77(f86(f29(x16081,x16082),f3(x16081)))+P77(f86(f29(x16081,f86(f86(f23(x16081),x16082),x16083)),f3(x16081)))
% 7.14/7.08 [1615]P78(x16152,x16151,x16153)+E(x16151,f3(a84))+~P77(f86(x16152,f113(x16153,x16151,x16152)))+~P77(f86(x16152,f117(x16153,x16151,x16152)))
% 7.14/7.08 [1645]P78(x16452,x16451,x16453)+E(x16451,f3(a84))+P77(f86(f28(a84,f3(a84)),f112(x16453,x16451,x16452)))+P77(f86(f28(a84,f111(x16453,x16451,x16452)),f3(a84)))
% 7.14/7.08 [1660]P78(x16601,x16602,x16603)+~P77(f86(x16601,f113(x16603,x16602,x16601)))+~P77(f86(x16601,f117(x16603,x16602,x16601)))+~P77(f86(x16601,f3(a84)))
% 7.14/7.08 [1673]P78(x16733,x16731,x16732)+E(x16731,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x16731),f113(x16732,x16731,x16733))),f112(x16732,x16731,x16733)),x16732)+P77(f86(f29(a84,x16731),f3(a84)))
% 7.14/7.08 [1681]P78(x16811,x16812,x16813)+P77(f86(f28(a84,f3(a84)),f112(x16813,x16812,x16811)))+~P77(f86(x16811,f3(a84)))+P77(f86(f28(a84,f111(x16813,x16812,x16811)),f3(a84)))
% 7.14/7.08 [1690]P78(x16902,x16901,x16903)+E(x16901,f3(a84))+~P77(f86(x16902,f113(x16903,x16901,x16902)))+P77(f86(f28(a84,f111(x16903,x16901,x16902)),f3(a84)))
% 7.14/7.08 [1691]P78(x16913,x16911,x16912)+E(f86(f86(f23(a84),f86(f86(f24(a84),x16911),f113(x16912,x16911,x16913))),f112(x16912,x16911,x16913)),x16912)+~P77(f86(x16913,f3(a84)))+P77(f86(f29(a84,x16911),f3(a84)))
% 7.14/7.08 [1712]~P56(x17121)+~P77(f86(f28(x17121,f86(f86(f24(x17121),x17123),x17122)),f3(x17121)))+P77(f86(f28(x17121,x17122),f3(x17121)))+P77(f86(f28(x17121,x17123),f3(x17121)))
% 7.14/7.08 [1738]P78(x17381,x17382,x17383)+~P77(f86(x17381,f113(x17383,x17382,x17381)))+~P77(f86(x17381,f3(a84)))+P77(f86(f28(a84,f111(x17383,x17382,x17381)),f3(a84)))
% 7.14/7.08 [1760]P78(x17603,x17601,x17602)+E(x17601,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x17601),f113(x17602,x17601,x17603))),f112(x17602,x17601,x17603)),x17602)+P77(f86(f29(a84,x17601),f111(x17602,x17601,x17603)))
% 7.14/7.08 [1761]P78(x17613,x17611,x17612)+E(x17611,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x17611),f117(x17612,x17611,x17613))),f111(x17612,x17611,x17613)),x17612)+P77(f86(f28(a84,f3(a84)),f112(x17612,x17611,x17613)))
% 7.14/7.08 [1770]P78(x17703,x17701,x17702)+E(f86(f86(f23(a84),f86(f86(f24(a84),x17701),f113(x17702,x17701,x17703))),f112(x17702,x17701,x17703)),x17702)+P77(f86(f29(a84,x17701),f111(x17702,x17701,x17703)))+~P77(f86(x17703,f3(a84)))
% 7.14/7.08 [1771]P78(x17713,x17711,x17712)+E(f86(f86(f23(a84),f86(f86(f24(a84),x17711),f117(x17712,x17711,x17713))),f111(x17712,x17711,x17713)),x17712)+P77(f86(f28(a84,f3(a84)),f112(x17712,x17711,x17713)))+~P77(f86(x17713,f3(a84)))
% 7.14/7.08 [1789]P78(x17893,x17891,x17892)+E(x17891,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x17891),f113(x17892,x17891,x17893))),f112(x17892,x17891,x17893)),x17892)+~P77(f86(x17893,f117(x17892,x17891,x17893)))
% 7.14/7.08 [1790]P78(x17903,x17901,x17902)+E(x17901,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x17901),f117(x17902,x17901,x17903))),f111(x17902,x17901,x17903)),x17902)+~P77(f86(x17903,f113(x17902,x17901,x17903)))
% 7.14/7.08 [1792]P78(x17923,x17921,x17922)+E(f86(f86(f23(a84),f86(f86(f24(a84),x17921),f113(x17922,x17921,x17923))),f112(x17922,x17921,x17923)),x17922)+~P77(f86(x17923,f117(x17922,x17921,x17923)))+~P77(f86(x17923,f3(a84)))
% 7.14/7.08 [1793]P78(x17933,x17931,x17932)+E(f86(f86(f23(a84),f86(f86(f24(a84),x17931),f117(x17932,x17931,x17933))),f111(x17932,x17931,x17933)),x17932)+~P77(f86(x17933,f113(x17932,x17931,x17933)))+~P77(f86(x17933,f3(a84)))
% 7.14/7.08 [1813]P78(x18133,x18131,x18132)+E(x18131,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x18131),f113(x18132,x18131,x18133))),f112(x18132,x18131,x18133)),x18132)+P77(f86(f28(a84,f111(x18132,x18131,x18133)),f3(a84)))
% 7.14/7.08 [1831]P78(x18313,x18311,x18312)+E(f86(f86(f23(a84),f86(f86(f24(a84),x18311),f113(x18312,x18311,x18313))),f112(x18312,x18311,x18313)),x18312)+~P77(f86(x18313,f3(a84)))+P77(f86(f28(a84,f111(x18312,x18311,x18313)),f3(a84)))
% 7.14/7.08 [1837]~P77(f86(f28(a83,x18373),x18371))+P77(f86(f28(a83,x18371),x18372))+~P77(f86(f28(a83,x18373),x18372))+~P77(f86(f28(a83,f22(a83,x18371,x18373)),f22(a83,x18372,x18373)))
% 7.14/7.08 [1838]~P77(f86(f28(a83,x18383),x18381))+P77(f86(f29(a83,x18381),x18382))+~P77(f86(f28(a83,x18383),x18382))+~P77(f86(f29(a83,f22(a83,x18381,x18383)),f22(a83,x18382,x18383)))
% 7.14/7.08 [1858]P78(x18583,x18581,x18582)+E(x18581,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x18581),f117(x18582,x18581,x18583))),f111(x18582,x18581,x18583)),x18582)+E(f86(f86(f23(a84),f86(f86(f24(a84),x18581),f113(x18582,x18581,x18583))),f112(x18582,x18581,x18583)),x18582)
% 7.14/7.08 [1863]P78(x18633,x18631,x18632)+E(f86(f86(f23(a84),f86(f86(f24(a84),x18631),f117(x18632,x18631,x18633))),f111(x18632,x18631,x18633)),x18632)+E(f86(f86(f23(a84),f86(f86(f24(a84),x18631),f113(x18632,x18631,x18633))),f112(x18632,x18631,x18633)),x18632)+~P77(f86(x18633,f3(a84)))
% 7.14/7.08 [1907]~P56(x19071)+~E(x19073,f3(x19071))+~E(x19072,f3(x19071))+P77(f86(f28(x19071,f86(f86(f23(x19071),f86(f86(f24(x19071),x19072),x19072)),f86(f86(f24(x19071),x19073),x19073))),f3(x19071)))
% 7.14/7.08 [889]~E(x8893,x8891)+~P53(x8892)+E(x8891,f3(x8892))+E(f86(f86(f37(x8892),x8893),x8891),f16(x8892))
% 7.14/7.08 [941]~P53(x9413)+E(x9411,x9412)+E(x9412,f3(x9413))+~E(f86(f86(f37(x9413),x9411),x9412),f16(x9413))
% 7.14/7.08 [943]~P62(x9432)+E(x9431,f3(x9432))+E(x9433,f3(x9432))+~E(f86(f86(f24(x9432),x9433),x9431),f3(x9432))
% 7.14/7.08 [944]~P65(x9442)+E(x9441,f3(x9442))+E(x9443,f3(x9442))+~E(f86(f86(f24(x9442),x9443),x9441),f3(x9442))
% 7.14/7.08 [1191]P78(x11911,x11912,x11913)+~P77(f86(x11911,f3(a84)))+P77(f86(f29(a84,x11912),f3(a84)))+P77(f86(f29(a84,f3(a84)),x11912))
% 7.14/7.08 [1349]P78(x13492,x13491,x13493)+E(x13491,f3(a84))+P77(f86(f29(a84,x13491),f111(x13493,x13491,x13492)))+P77(f86(f29(a84,f3(a84)),x13491))
% 7.14/7.08 [1383]P78(x13831,x13832,x13833)+P77(f86(f29(a84,x13832),f111(x13833,x13832,x13831)))+~P77(f86(x13831,f3(a84)))+P77(f86(f29(a84,f3(a84)),x13832))
% 7.14/7.08 [1421]P78(x14212,x14211,x14213)+E(x14211,f3(a84))+~P77(f86(x14212,f117(x14213,x14211,x14212)))+P77(f86(f29(a84,f3(a84)),x14211))
% 7.14/7.08 [1468]P78(x14681,x14682,x14683)+~P77(f86(x14681,f117(x14683,x14682,x14681)))+~P77(f86(x14681,f3(a84)))+P77(f86(f29(a84,f3(a84)),x14682))
% 7.14/7.08 [1507]P78(x15072,x15071,x15073)+E(x15071,f3(a84))+P77(f86(f29(a84,x15071),f3(a84)))+P77(f86(f29(a84,f112(x15073,x15071,x15072)),x15071))
% 7.14/7.08 [1521]P78(x15212,x15211,x15213)+E(x15211,f3(a84))+P77(f86(f28(a84,f111(x15213,x15211,x15212)),f3(a84)))+P77(f86(f29(a84,f3(a84)),x15211))
% 7.14/7.08 [1545]P78(x15451,x15452,x15453)+~P77(f86(x15451,f3(a84)))+P77(f86(f29(a84,x15452),f3(a84)))+P77(f86(f29(a84,f112(x15453,x15452,x15451)),x15452))
% 7.14/7.08 [1550]P78(x15501,x15502,x15503)+~P77(f86(x15501,f3(a84)))+P77(f86(f28(a84,f111(x15503,x15502,x15501)),f3(a84)))+P77(f86(f29(a84,f3(a84)),x15502))
% 7.14/7.08 [1618]~P66(x16181)+~P77(f86(f28(x16181,x16183),f3(x16181)))+P77(f86(f28(x16181,f86(f86(f24(x16181),x16182),x16183)),f3(x16181)))+~P77(f86(f28(x16181,f3(x16181)),x16182))
% 7.14/7.08 [1620]~P66(x16201)+~P77(f86(f28(x16201,x16202),f3(x16201)))+P77(f86(f28(x16201,f86(f86(f24(x16201),x16202),x16203)),f3(x16201)))+~P77(f86(f28(x16201,f3(x16201)),x16203))
% 7.14/7.08 [1621]~P56(x16211)+~P77(f86(f28(x16211,x16213),f3(x16211)))+P77(f86(f28(x16211,f86(f86(f24(x16211),x16212),x16213)),f3(x16211)))+~P77(f86(f28(x16211,f3(x16211)),x16212))
% 7.14/7.08 [1622]~P56(x16221)+~P77(f86(f28(x16221,x16222),f3(x16221)))+P77(f86(f28(x16221,f86(f86(f24(x16221),x16222),x16223)),f3(x16221)))+~P77(f86(f28(x16221,f3(x16221)),x16223))
% 7.14/7.08 [1624]~P64(x16241)+~P77(f86(f29(x16241,x16243),f3(x16241)))+P77(f86(f29(x16241,f86(f86(f24(x16241),x16242),x16243)),f3(x16241)))+~P77(f86(f29(x16241,f3(x16241)),x16242))
% 7.14/7.08 [1625]~P64(x16251)+~P77(f86(f29(x16251,x16252),f3(x16251)))+P77(f86(f29(x16251,f86(f86(f24(x16251),x16252),x16253)),f3(x16251)))+~P77(f86(f29(x16251,f3(x16251)),x16253))
% 7.14/7.08 [1636]P78(x16362,x16361,x16363)+E(x16361,f3(a84))+P77(f86(f29(a84,x16361),f111(x16363,x16361,x16362)))+P77(f86(f29(a84,f112(x16363,x16361,x16362)),x16361))
% 7.14/7.08 [1674]P78(x16741,x16742,x16743)+P77(f86(f29(a84,x16742),f111(x16743,x16742,x16741)))+~P77(f86(x16741,f3(a84)))+P77(f86(f29(a84,f112(x16743,x16742,x16741)),x16742))
% 7.14/7.08 [1675]P78(x16753,x16751,x16752)+E(x16751,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x16751),f117(x16752,x16751,x16753))),f111(x16752,x16751,x16753)),x16752)+P77(f86(f29(a84,f3(a84)),x16751))
% 7.14/7.08 [1688]P78(x16882,x16881,x16883)+E(x16881,f3(a84))+~P77(f86(x16882,f117(x16883,x16881,x16882)))+P77(f86(f29(a84,f112(x16883,x16881,x16882)),x16881))
% 7.14/7.08 [1698]P78(x16983,x16981,x16982)+E(f86(f86(f23(a84),f86(f86(f24(a84),x16981),f117(x16982,x16981,x16983))),f111(x16982,x16981,x16983)),x16982)+~P77(f86(x16983,f3(a84)))+P77(f86(f29(a84,f3(a84)),x16981))
% 7.14/7.08 [1721]P78(x17211,x17212,x17213)+~P77(f86(x17211,f117(x17213,x17212,x17211)))+~P77(f86(x17211,f3(a84)))+P77(f86(f29(a84,f112(x17213,x17212,x17211)),x17212))
% 7.14/7.08 [1722]~P56(x17221)+~P77(f86(f28(x17221,f86(f86(f24(x17221),x17223),x17222)),f3(x17221)))+P77(f86(f28(x17221,x17222),f3(x17221)))+P77(f86(f28(x17221,f3(x17221)),x17222))
% 7.14/7.08 [1723]~P56(x17231)+~P77(f86(f28(x17231,f86(f86(f24(x17231),x17232),x17233)),f3(x17231)))+P77(f86(f28(x17231,x17232),f3(x17231)))+P77(f86(f28(x17231,f3(x17231)),x17232))
% 7.14/7.08 [1739]~P56(x17391)+~P77(f86(f28(x17391,f86(f86(f24(x17391),x17392),x17393)),f3(x17391)))+P77(f86(f28(x17391,f3(x17391)),x17392))+P77(f86(f28(x17391,f3(x17391)),x17393))
% 7.14/7.08 [1752]P78(x17522,x17521,x17523)+E(x17521,f3(a84))+P77(f86(f28(a84,f111(x17523,x17521,x17522)),f3(a84)))+P77(f86(f29(a84,f112(x17523,x17521,x17522)),x17521))
% 7.14/7.08 [1754]~P77(f86(f28(a84,x17542),x17543))+P77(f86(f28(a84,f20(a84,x17541,x17542)),f20(a84,x17541,x17543)))+~P77(f86(f29(a84,x17541),f3(a84)))+~P77(f86(f29(a84,f3(a84)),x17542))
% 7.14/7.08 [1756]~P77(f86(f28(a84,x17563),x17562))+P77(f86(f28(a84,f20(a84,x17561,x17562)),f20(a84,x17561,x17563)))+~P77(f86(f28(a84,f3(a84)),x17561))+~P77(f86(f29(a84,f3(a84)),x17563))
% 7.14/7.08 [1762]P78(x17621,x17622,x17623)+~P77(f86(x17621,f3(a84)))+P77(f86(f28(a84,f111(x17623,x17622,x17621)),f3(a84)))+P77(f86(f29(a84,f112(x17623,x17622,x17621)),x17622))
% 7.14/7.08 [1812]P78(x18123,x18121,x18122)+E(x18121,f3(a84))+E(f86(f86(f23(a84),f86(f86(f24(a84),x18121),f117(x18122,x18121,x18123))),f111(x18122,x18121,x18123)),x18122)+P77(f86(f29(a84,f112(x18122,x18121,x18123)),x18121))
% 7.14/7.08 [1830]P78(x18303,x18301,x18302)+E(f86(f86(f23(a84),f86(f86(f24(a84),x18301),f117(x18302,x18301,x18303))),f111(x18302,x18301,x18303)),x18302)+~P77(f86(x18303,f3(a84)))+P77(f86(f29(a84,f112(x18302,x18301,x18303)),x18301))
% 7.14/7.08 [1862]~P7(x18621)+~P77(f86(f29(x18621,x18622),f16(x18621)))+P77(f86(f29(x18621,f86(f86(f31(x18621),x18622),f86(f86(f23(a83),x18623),f16(a83)))),f16(x18621)))+~P77(f86(f29(x18621,f3(x18621)),x18622))
% 7.14/7.08 [1917]P77(f86(f28(a84,x19171),f3(a84)))+~P77(f86(f29(a84,f86(f86(f23(a84),f86(f86(f24(a84),x19173),x19171)),x19172)),f3(a84)))+~P77(f86(f28(a84,f3(a84)),x19172))+~P77(f86(f29(a84,f3(a84)),x19173))
% 7.14/7.08 [1949]~P35(x19491)+~P3(x19491,x19493)+~P3(x19491,x19492)+P3(x19491,f9(a83,x19491,x19491,f7(x19491,f121(x19491,x19491),a83,f23(x19491),x19492),x19493))
% 7.14/7.08 [1950]~P41(x19501)+~P3(x19501,x19503)+~P3(x19501,x19502)+P3(x19501,f9(a83,x19501,x19501,f7(x19501,f121(x19501,x19501),a83,f24(x19501),x19502),x19503))
% 7.14/7.08 [1282]~P56(x12821)+~E(x12823,f3(x12821))+~E(x12822,f3(x12821))+E(f86(f86(f23(x12821),f86(f86(f24(x12821),x12822),x12822)),f86(f86(f24(x12821),x12823),x12823)),f3(x12821))
% 7.14/7.08 [1449]~P70(x14491)+~P77(f86(f28(x14491,x14492),f3(x14491)))+~P77(f86(f28(x14491,x14493),f3(x14491)))+E(f86(f86(f24(x14491),f19(x14491,x14492)),f19(x14491,x14493)),f19(x14491,f86(f86(f24(x14491),x14492),x14493)))
% 7.14/7.08 [1453]~E(f86(f86(f23(a84),x14532),f86(f86(f24(a84),x14533),x14531)),x14533)+~P77(f86(f29(a84,x14532),x14533))+~P77(f86(f29(a84,f3(a84)),x14533))+P77(f86(f28(a84,f16(a84)),x14531))
% 7.14/7.08 [1454]~P70(x14541)+~P77(f86(f28(x14541,x14542),f3(x14541)))+E(f86(f86(f24(x14541),f19(x14541,x14542)),f19(x14541,x14543)),f19(x14541,f86(f86(f24(x14541),x14542),x14543)))+~P77(f86(f28(x14541,f3(x14541)),x14543))
% 7.14/7.08 [1455]~P70(x14551)+~P77(f86(f28(x14551,x14553),f3(x14551)))+E(f86(f86(f24(x14551),f19(x14551,x14552)),f19(x14551,x14553)),f19(x14551,f86(f86(f24(x14551),x14552),x14553)))+~P77(f86(f28(x14551,f3(x14551)),x14552))
% 7.14/7.08 [1459]~E(f86(f86(f23(a84),x14592),f86(f86(f24(a84),x14593),x14591)),x14593)+P77(f86(f28(a84,x14591),f16(a84)))+~P77(f86(f28(a84,f3(a84)),x14592))+~P77(f86(f29(a84,f3(a84)),x14593))
% 7.14/7.08 [1469]~P70(x14691)+E(f86(f86(f24(x14691),f19(x14691,x14692)),f19(x14691,x14693)),f19(x14691,f86(f86(f24(x14691),x14692),x14693)))+~P77(f86(f28(x14691,f3(x14691)),x14692))+~P77(f86(f28(x14691,f3(x14691)),x14693))
% 7.14/7.08 [1484]~P67(x14841)+~P77(f86(f28(x14841,x14843),f3(x14841)))+~P77(f86(f28(x14841,x14842),f3(x14841)))+P77(f86(f28(x14841,f3(x14841)),f86(f86(f24(x14841),x14842),x14843)))
% 7.14/7.08 [1485]~P56(x14851)+~P77(f86(f28(x14851,x14853),f3(x14851)))+~P77(f86(f28(x14851,x14852),f3(x14851)))+P77(f86(f28(x14851,f3(x14851)),f86(f86(f24(x14851),x14852),x14853)))
% 7.14/7.08 [1486]~P56(x14861)+~P77(f86(f29(x14861,x14863),f3(x14861)))+~P77(f86(f29(x14861,x14862),f3(x14861)))+P77(f86(f29(x14861,f3(x14861)),f86(f86(f24(x14861),x14862),x14863)))
% 7.14/7.08 [1501]~P7(x15011)+~P77(f86(f29(a83,f3(a83)),x15013))+~P77(f86(f29(x15011,f16(x15011)),x15012))+P77(f86(f29(x15011,f16(x15011)),f86(f86(f31(x15011),x15012),x15013)))
% 7.14/7.08 [1512]~P66(x15121)+~P77(f86(f28(x15121,f3(x15121)),x15123))+~P77(f86(f28(x15121,f3(x15121)),x15122))+P77(f86(f28(x15121,f3(x15121)),f86(f86(f24(x15121),x15122),x15123)))
% 7.14/7.08 [1513]~P67(x15131)+~P77(f86(f28(x15131,f3(x15131)),x15133))+~P77(f86(f28(x15131,f3(x15131)),x15132))+P77(f86(f28(x15131,f3(x15131)),f86(f86(f24(x15131),x15132),x15133)))
% 7.14/7.08 [1514]~P56(x15141)+~P77(f86(f28(x15141,f3(x15141)),x15143))+~P77(f86(f28(x15141,f3(x15141)),x15142))+P77(f86(f28(x15141,f3(x15141)),f86(f86(f24(x15141),x15142),x15143)))
% 7.14/7.08 [1517]~P8(x15171)+~P77(f86(f29(x15171,f3(x15171)),x15173))+~P77(f86(f29(x15171,f3(x15171)),x15172))+P77(f86(f29(x15171,f3(x15171)),f86(f86(f23(x15171),x15172),x15173)))
% 7.14/7.08 [1518]~P64(x15181)+~P77(f86(f29(x15181,f3(x15181)),x15183))+~P77(f86(f29(x15181,f3(x15181)),x15182))+P77(f86(f29(x15181,f3(x15181)),f86(f86(f24(x15181),x15182),x15183)))
% 7.14/7.08 [1519]~P7(x15191)+~P77(f86(f29(x15191,f16(x15191)),x15193))+~P77(f86(f29(x15191,f16(x15191)),x15192))+P77(f86(f29(x15191,f16(x15191)),f86(f86(f24(x15191),x15192),x15193)))
% 7.14/7.08 [1539]~P56(x15391)+P77(f86(f28(x15391,x15392),f3(x15391)))+P77(f86(f28(x15391,f3(x15391)),x15393))+~P77(f86(f28(x15391,f3(x15391)),f86(f86(f24(x15391),x15393),x15392)))
% 7.14/7.08 [1540]~P56(x15401)+P77(f86(f28(x15401,x15402),f3(x15401)))+P77(f86(f28(x15401,f3(x15401)),x15403))+~P77(f86(f28(x15401,f3(x15401)),f86(f86(f24(x15401),x15402),x15403)))
% 7.14/7.08 [1541]~P56(x15411)+P77(f86(f28(x15411,x15412),f3(x15411)))+P77(f86(f28(x15411,f3(x15411)),x15412))+~P77(f86(f28(x15411,f3(x15411)),f86(f86(f24(x15411),x15413),x15412)))
% 7.14/7.08 [1542]~P56(x15421)+P77(f86(f28(x15421,x15422),f3(x15421)))+P77(f86(f28(x15421,f3(x15421)),x15422))+~P77(f86(f28(x15421,f3(x15421)),f86(f86(f24(x15421),x15422),x15423)))
% 7.14/7.08 [1589]~P64(x15891)+P77(f86(f29(x15891,f3(x15891)),x15892))+~P77(f86(f29(x15891,f3(x15891)),x15893))+~P77(f86(f29(x15891,f3(x15891)),f86(f86(f24(x15891),x15893),x15892)))
% 7.14/7.08 [1590]~P64(x15901)+P77(f86(f29(x15901,f3(x15901)),x15902))+~P77(f86(f29(x15901,f3(x15901)),x15903))+~P77(f86(f29(x15901,f3(x15901)),f86(f86(f24(x15901),x15902),x15903)))
% 7.14/7.08 [1869]~P7(x18691)+~P77(f86(f29(x18691,x18692),f16(x18691)))+~P77(f86(f29(x18691,f3(x18691)),x18692))+P77(f86(f29(x18691,f86(f86(f24(x18691),x18692),f86(f86(f31(x18691),x18692),x18693))),f86(f86(f31(x18691),x18692),x18693)))
% 7.14/7.08 [1859]~P7(x18591)+~P77(f86(f28(x18591,x18592),f16(x18591)))+~P77(f86(f28(x18591,f3(x18591)),x18592))+P77(f86(f28(x18591,f86(f86(f31(x18591),x18592),f86(f86(f23(a83),x18593),f16(a83)))),x18592))
% 7.14/7.08 [1874]E(x18741,f20(a83,x18742,x18743))+~P77(f86(f29(a83,f3(a83)),x18743))+~P77(f86(f29(a83,x18742),f86(f86(f24(a83),x18743),f86(f86(f23(a83),x18741),f16(a83)))))+~P77(f86(f28(a83,f86(f86(f24(a83),x18743),x18741)),x18742))
% 7.14/7.08 [1901]~P56(x19012)+~E(x19011,f3(x19012))+~E(x19013,f3(x19012))+~P77(f86(f29(x19012,f3(x19012)),f86(f86(f23(x19012),f86(f86(f24(x19012),x19013),x19013)),f86(f86(f24(x19012),x19011),x19011))))
% 7.14/7.08 [1919]~P35(x19191)+P4(x19191,x19192)+~P77(f86(f29(a82,f3(a82)),x19193))+~P77(f86(f28(a82,f36(x19191,f86(x19192,f61(x19192,x19191,x19193)))),x19193))
% 7.14/7.08 [1920]~P35(x19201)+P4(x19201,x19202)+~P77(f86(f29(a82,f3(a82)),x19203))+~P77(f86(f28(a82,f36(x19201,f86(x19202,f64(x19202,x19203,x19201)))),x19203))
% 7.14/7.08 [1877]~P77(f86(f29(a84,x18772),x18773))+~P77(f86(f29(a84,f3(a84)),x18773))+P77(f86(f28(a84,f3(a84)),x18771))+~P77(f86(f28(a84,f3(a84)),f86(f86(f23(a84),f86(f86(f24(a84),x18773),x18771)),x18772)))
% 7.14/7.08 [1248]~P40(x12481)+~P77(f86(f28(x12481,x12484),x12483))+P77(f86(f28(x12481,x12482),x12483))+~P77(f86(f28(x12481,x12482),x12484))
% 7.14/7.08 [1249]~P37(x12491)+~P77(f86(f28(x12491,x12492),x12494))+P77(f86(f28(x12491,x12492),x12493))+~P77(f86(f28(x12491,x12494),x12493))
% 7.14/7.08 [1250]~P40(x12501)+~P77(f86(f29(x12501,x12504),x12503))+P77(f86(f29(x12501,x12502),x12503))+~P77(f86(f28(x12501,x12502),x12504))
% 7.14/7.08 [1251]~P40(x12511)+~P77(f86(f29(x12511,x12512),x12514))+P77(f86(f29(x12511,x12512),x12513))+~P77(f86(f28(x12511,x12514),x12513))
% 7.14/7.08 [1252]~P40(x12521)+~P77(f86(f29(x12521,x12524),x12523))+P77(f86(f29(x12521,x12522),x12523))+~P77(f86(f29(x12521,x12522),x12524))
% 7.14/7.08 [1253]~P37(x12531)+~P77(f86(f29(x12531,x12532),x12534))+P77(f86(f29(x12531,x12532),x12533))+~P77(f86(f28(x12531,x12534),x12533))
% 7.14/7.08 [1254]~P37(x12541)+~P77(f86(f29(x12541,x12544),x12543))+P77(f86(f29(x12541,x12542),x12543))+~P77(f86(f28(x12541,x12542),x12544))
% 7.14/7.08 [1255]~P37(x12551)+~P77(f86(f29(x12551,x12552),x12554))+P77(f86(f29(x12551,x12552),x12553))+~P77(f86(f29(x12551,x12554),x12553))
% 7.14/7.08 [1283]~P40(x12831)+~P5(x12831,x12832)+P77(f86(f28(x12831,f86(x12832,x12833)),f86(x12832,x12834)))+~P77(f86(f28(a83,x12834),x12833))
% 7.14/7.08 [1284]~P40(x12841)+~P6(x12841,x12842)+P77(f86(f28(x12841,f86(x12842,x12843)),f86(x12842,x12844)))+~P77(f86(f28(a83,x12843),x12844))
% 7.14/7.08 [1888]~P77(f86(f29(a82,x18884),x18882))+P77(f86(f28(a82,x18881),x18882))+~P77(f86(f29(a82,x18883),x18884))+~P77(f86(f29(a82,f19(a82,f22(a82,x18884,x18881))),f107(x18882,x18884,x18883)))
% 7.14/7.08 [1889]~P77(f86(f29(a82,x18891),x18893))+P77(f86(f28(a82,x18891),x18892))+~P77(f86(f29(a82,x18893),x18894))+~P77(f86(f29(a82,f19(a82,f22(a82,x18893,x18892))),f107(x18894,x18893,x18891)))
% 7.14/7.08 [991]~P53(x9912)+E(x9911,f3(x9912))+~E(f86(f86(f37(x9912),x9913),x9911),x9914)+E(x9913,f86(f86(f24(x9912),x9914),x9911))
% 7.14/7.08 [993]~P53(x9932)+E(x9931,f3(x9932))+~E(f86(f86(f24(x9932),x9933),x9931),x9934)+E(x9933,f86(f86(f37(x9932),x9934),x9931))
% 7.14/7.08 [994]~P53(x9942)+E(x9941,f3(x9942))+~E(x9943,f86(f86(f37(x9942),x9944),x9941))+E(f86(f86(f24(x9942),x9943),x9941),x9944)
% 7.14/7.08 [996]~P53(x9962)+E(x9961,f3(x9962))+~E(x9963,f86(f86(f24(x9962),x9964),x9961))+E(f86(f86(f37(x9962),x9963),x9961),x9964)
% 7.14/7.08 [1244]~P7(x12443)+E(x12441,x12442)+~E(f86(f86(f31(x12443),x12444),x12441),f86(f86(f31(x12443),x12444),x12442))+~P77(f86(f29(x12443,f16(x12443)),x12444))
% 7.14/7.08 [1529]~P38(x15292)+P77(f86(f29(f121(x15291,x15292),x15294),x15293))+~P77(f86(f28(f121(x15291,x15292),x15294),x15293))+P77(f86(f28(f121(x15291,x15292),x15293),x15294))
% 7.14/7.08 [1647]~P35(x16472)+E(x16471,f3(x16472))+~P77(f86(f28(a82,x16473),f3(a82)))+~P77(f86(f28(a82,f36(x16472,x16471)),f86(f86(f24(a82),x16473),f36(x16472,x16474))))
% 7.14/7.08 [1470]~P8(x14701)+~P77(f86(f28(x14701,x14702),x14703))+~P77(f86(f28(x14701,f3(x14701)),x14704))+P77(f86(f28(x14701,x14702),f86(f86(f23(x14701),x14703),x14704)))
% 7.14/7.08 [1471]~P8(x14711)+~P77(f86(f28(x14711,x14712),x14714))+~P77(f86(f28(x14711,f3(x14711)),x14713))+P77(f86(f28(x14711,x14712),f86(f86(f23(x14711),x14713),x14714)))
% 7.14/7.08 [1472]~P7(x14721)+~P77(f86(f29(x14721,x14722),x14724))+~P77(f86(f29(x14721,f3(x14721)),x14723))+P77(f86(f29(x14721,x14722),f86(f86(f23(x14721),x14723),x14724)))
% 7.14/7.08 [1473]~P8(x14731)+~P77(f86(f28(x14731,x14732),x14734))+~P77(f86(f29(x14731,f3(x14731)),x14733))+P77(f86(f29(x14731,x14732),f86(f86(f23(x14731),x14733),x14734)))
% 7.14/7.08 [1474]~P8(x14741)+~P77(f86(f29(x14741,x14742),x14744))+~P77(f86(f28(x14741,f3(x14741)),x14743))+P77(f86(f29(x14741,x14742),f86(f86(f23(x14741),x14743),x14744)))
% 7.14/7.08 [1508]~P15(x15082)+E(x15081,f3(x15082))+E(f86(f86(f37(x15082),f86(f86(f31(x15082),x15081),x15083)),f86(f86(f31(x15082),x15081),x15084)),f86(f86(f31(x15082),x15081),f22(a83,x15083,x15084)))+~P77(f86(f28(a83,x15084),x15083))
% 7.14/7.08 [1701]~P67(x17011)+~P77(f86(f28(x17011,x17014),x17013))+~P77(f86(f28(x17011,x17012),f3(x17011)))+P77(f86(f28(x17011,f86(f86(f24(x17011),x17012),x17013)),f86(f86(f24(x17011),x17012),x17014)))
% 7.14/7.08 [1702]~P56(x17021)+~P77(f86(f28(x17021,x17024),x17023))+~P77(f86(f29(x17021,x17022),f3(x17021)))+P77(f86(f28(x17021,f86(f86(f24(x17021),x17022),x17023)),f86(f86(f24(x17021),x17022),x17024)))
% 7.14/7.08 [1703]~P67(x17031)+~P77(f86(f28(x17031,x17034),x17032))+~P77(f86(f28(x17031,x17033),f3(x17031)))+P77(f86(f28(x17031,f86(f86(f24(x17031),x17032),x17033)),f86(f86(f24(x17031),x17034),x17033)))
% 7.14/7.08 [1707]~P56(x17071)+~P77(f86(f29(x17071,x17074),x17072))+~P77(f86(f29(x17071,x17073),f3(x17071)))+P77(f86(f29(x17071,f86(f86(f24(x17071),x17072),x17073)),f86(f86(f24(x17071),x17074),x17073)))
% 7.14/7.08 [1708]~P56(x17081)+~P77(f86(f29(x17081,x17084),x17083))+~P77(f86(f29(x17081,x17082),f3(x17081)))+P77(f86(f29(x17081,f86(f86(f24(x17081),x17082),x17083)),f86(f86(f24(x17081),x17082),x17084)))
% 7.14/7.08 [1713]~P7(x17131)+~P77(f86(f28(a83,x17133),x17134))+~P77(f86(f29(x17131,f16(x17131)),x17132))+P77(f86(f28(x17131,f86(f86(f31(x17131),x17132),x17133)),f86(f86(f31(x17131),x17132),x17134)))
% 7.14/7.08 [1714]~P7(x17141)+~P77(f86(f28(a83,x17143),x17144))+~P77(f86(f28(x17141,f16(x17141)),x17142))+P77(f86(f28(x17141,f86(f86(f31(x17141),x17142),x17143)),f86(f86(f31(x17141),x17142),x17144)))
% 7.14/7.08 [1716]~P7(x17161)+~P77(f86(f29(a83,x17163),x17164))+~P77(f86(f29(x17161,f16(x17161)),x17162))+P77(f86(f29(x17161,f86(f86(f31(x17161),x17162),x17163)),f86(f86(f31(x17161),x17162),x17164)))
% 7.14/7.08 [1724]~P69(x17241)+~P77(f86(f28(x17241,x17243),x17244))+~P77(f86(f28(x17241,f3(x17241)),x17242))+P77(f86(f28(x17241,f86(f86(f24(x17241),x17242),x17243)),f86(f86(f24(x17241),x17242),x17244)))
% 7.14/7.08 [1725]~P68(x17251)+~P77(f86(f28(x17251,x17253),x17254))+~P77(f86(f28(x17251,f3(x17251)),x17252))+P77(f86(f28(x17251,f86(f86(f24(x17251),x17252),x17253)),f86(f86(f24(x17251),x17252),x17254)))
% 7.14/7.08 [1726]~P56(x17261)+~P77(f86(f28(x17261,x17263),x17264))+~P77(f86(f29(x17261,f3(x17261)),x17262))+P77(f86(f28(x17261,f86(f86(f24(x17261),x17262),x17263)),f86(f86(f24(x17261),x17262),x17264)))
% 7.14/7.08 [1727]~P69(x17271)+~P77(f86(f28(x17271,x17272),x17274))+~P77(f86(f28(x17271,f3(x17271)),x17273))+P77(f86(f28(x17271,f86(f86(f24(x17271),x17272),x17273)),f86(f86(f24(x17271),x17274),x17273)))
% 7.14/7.08 [1728]~P7(x17281)+~P77(f86(f28(x17281,x17282),x17284))+~P77(f86(f28(x17281,f3(x17281)),x17282))+P77(f86(f28(x17281,f86(f86(f31(x17281),x17282),x17283)),f86(f86(f31(x17281),x17284),x17283)))
% 7.14/7.08 [1730]~P52(x17301)+~P77(f86(f29(x17301,x17303),x17304))+~P77(f86(f29(x17301,f3(x17301)),x17302))+P77(f86(f29(x17301,f86(f86(f24(x17301),x17302),x17303)),f86(f86(f24(x17301),x17302),x17304)))
% 7.14/7.08 [1731]~P64(x17311)+~P77(f86(f29(x17311,x17313),x17314))+~P77(f86(f29(x17311,f3(x17311)),x17312))+P77(f86(f29(x17311,f86(f86(f24(x17311),x17312),x17313)),f86(f86(f24(x17311),x17312),x17314)))
% 7.14/7.08 [1732]~P56(x17321)+~P77(f86(f29(x17321,x17322),x17324))+~P77(f86(f29(x17321,f3(x17321)),x17323))+P77(f86(f29(x17321,f86(f86(f24(x17321),x17322),x17323)),f86(f86(f24(x17321),x17324),x17323)))
% 7.14/7.08 [1733]~P64(x17331)+~P77(f86(f29(x17331,x17332),x17334))+~P77(f86(f29(x17331,f3(x17331)),x17333))+P77(f86(f29(x17331,f86(f86(f24(x17331),x17332),x17333)),f86(f86(f24(x17331),x17334),x17333)))
% 7.14/7.08 [1734]~P56(x17341)+~P77(f86(f29(x17341,x17343),x17344))+~P77(f86(f29(x17341,f3(x17341)),x17342))+P77(f86(f29(x17341,f86(f86(f24(x17341),x17342),x17343)),f86(f86(f24(x17341),x17342),x17344)))
% 7.14/7.08 [1796]~P56(x17961)+P77(f86(f29(x17961,x17963),x17962))+P77(f86(f29(x17961,x17962),x17963))+~P77(f86(f29(x17961,f86(f86(f24(x17961),x17964),x17962)),f86(f86(f24(x17961),x17964),x17963)))
% 7.14/7.08 [1797]~P56(x17971)+P77(f86(f29(x17971,x17973),x17972))+P77(f86(f29(x17971,x17972),x17973))+~P77(f86(f29(x17971,f86(f86(f24(x17971),x17972),x17974)),f86(f86(f24(x17971),x17973),x17974)))
% 7.14/7.08 [1798]~P56(x17981)+P77(f86(f29(x17981,x17982),x17983))+P77(f86(f29(x17981,x17984),f3(x17981)))+~P77(f86(f29(x17981,f86(f86(f24(x17981),x17982),x17984)),f86(f86(f24(x17981),x17983),x17984)))
% 7.14/7.08 [1799]~P56(x17991)+P77(f86(f29(x17991,x17992),x17993))+P77(f86(f29(x17991,x17994),f3(x17991)))+~P77(f86(f29(x17991,f86(f86(f24(x17991),x17994),x17992)),f86(f86(f24(x17991),x17994),x17993)))
% 7.14/7.08 [1802]~P56(x18021)+P77(f86(f29(x18021,x18022),x18023))+P77(f86(f29(x18021,f3(x18021)),x18024))+~P77(f86(f29(x18021,f86(f86(f24(x18021),x18024),x18023)),f86(f86(f24(x18021),x18024),x18022)))
% 7.14/7.08 [1803]~P56(x18031)+P77(f86(f29(x18031,x18032),x18033))+P77(f86(f29(x18031,f3(x18031)),x18034))+~P77(f86(f29(x18031,f86(f86(f24(x18031),x18033),x18034)),f86(f86(f24(x18031),x18032),x18034)))
% 7.14/7.08 [1810]~P56(x18101)+P77(f86(f29(x18101,x18102),f3(x18101)))+P77(f86(f29(x18101,f3(x18101)),x18102))+~P77(f86(f29(x18101,f86(f86(f24(x18101),x18103),x18102)),f86(f86(f24(x18101),x18104),x18102)))
% 7.14/7.08 [1811]~P56(x18111)+P77(f86(f29(x18111,x18112),f3(x18111)))+P77(f86(f29(x18111,f3(x18111)),x18112))+~P77(f86(f29(x18111,f86(f86(f24(x18111),x18112),x18113)),f86(f86(f24(x18111),x18112),x18114)))
% 7.14/7.08 [1814]~P56(x18141)+P77(f86(f28(x18141,x18142),x18143))+~P77(f86(f29(x18141,x18144),f3(x18141)))+~P77(f86(f28(x18141,f86(f86(f24(x18141),x18144),x18143)),f86(f86(f24(x18141),x18144),x18142)))
% 7.14/7.08 [1815]~P56(x18151)+P77(f86(f29(x18151,x18152),x18153))+~P77(f86(f29(x18151,x18154),f3(x18151)))+~P77(f86(f29(x18151,f86(f86(f24(x18151),x18154),x18153)),f86(f86(f24(x18151),x18154),x18152)))
% 7.14/7.08 [1817]~P7(x18173)+P77(f86(f28(a83,x18171),x18172))+~P77(f86(f29(x18173,f16(x18173)),x18174))+~P77(f86(f28(x18173,f86(f86(f31(x18173),x18174),x18171)),f86(f86(f31(x18173),x18174),x18172)))
% 7.14/7.08 [1819]~P7(x18193)+P77(f86(f29(a83,x18191),x18192))+~P77(f86(f29(x18193,f16(x18193)),x18194))+~P77(f86(f29(x18193,f86(f86(f31(x18193),x18194),x18191)),f86(f86(f31(x18193),x18194),x18192)))
% 7.14/7.08 [1820]~P56(x18201)+P77(f86(f28(x18201,x18202),x18203))+~P77(f86(f29(x18201,f3(x18201)),x18204))+~P77(f86(f28(x18201,f86(f86(f24(x18201),x18204),x18202)),f86(f86(f24(x18201),x18204),x18203)))
% 7.14/7.08 [1821]~P64(x18211)+P77(f86(f28(x18211,x18212),x18213))+~P77(f86(f29(x18211,f3(x18211)),x18214))+~P77(f86(f28(x18211,f86(f86(f24(x18211),x18214),x18212)),f86(f86(f24(x18211),x18214),x18213)))
% 7.14/7.08 [1822]~P64(x18221)+P77(f86(f28(x18221,x18222),x18223))+~P77(f86(f29(x18221,f3(x18221)),x18224))+~P77(f86(f28(x18221,f86(f86(f24(x18221),x18222),x18224)),f86(f86(f24(x18221),x18223),x18224)))
% 7.14/7.08 [1823]~P56(x18231)+P77(f86(f29(x18231,x18232),x18233))+~P77(f86(f29(x18231,f3(x18231)),x18234))+~P77(f86(f29(x18231,f86(f86(f24(x18231),x18234),x18232)),f86(f86(f24(x18231),x18234),x18233)))
% 7.14/7.08 [1824]~P64(x18241)+P77(f86(f29(x18241,x18242),x18243))+~P77(f86(f28(x18241,f3(x18241)),x18244))+~P77(f86(f29(x18241,f86(f86(f24(x18241),x18244),x18242)),f86(f86(f24(x18241),x18244),x18243)))
% 7.14/7.08 [1825]~P60(x18251)+P77(f86(f29(x18251,x18252),x18253))+~P77(f86(f28(x18251,f3(x18251)),x18254))+~P77(f86(f29(x18251,f86(f86(f24(x18251),x18254),x18252)),f86(f86(f24(x18251),x18254),x18253)))
% 7.14/7.08 [1826]~P7(x18261)+P77(f86(f29(x18261,x18262),x18263))+~P77(f86(f28(x18261,f3(x18261)),x18263))+~P77(f86(f29(x18261,f86(f86(f31(x18261),x18262),x18264)),f86(f86(f31(x18261),x18263),x18264)))
% 7.14/7.08 [1827]~P64(x18271)+P77(f86(f29(x18271,x18272),x18273))+~P77(f86(f28(x18271,f3(x18271)),x18274))+~P77(f86(f29(x18271,f86(f86(f24(x18271),x18272),x18274)),f86(f86(f24(x18271),x18273),x18274)))
% 7.14/7.08 [1828]~P60(x18281)+P77(f86(f29(x18281,x18282),x18283))+~P77(f86(f28(x18281,f3(x18281)),x18284))+~P77(f86(f29(x18281,f86(f86(f24(x18281),x18282),x18284)),f86(f86(f24(x18281),x18283),x18284)))
% 7.14/7.08 [1864]~P40(x18641)+~P2(x18641,x18642)+P77(f86(f28(x18641,f86(x18642,f86(f86(f23(a83),x18644),f16(a83)))),f86(x18642,x18644)))+P77(f86(f28(x18641,f86(x18642,x18643)),f86(x18642,f86(f86(f23(a83),x18643),f16(a83)))))
% 7.14/7.08 [1896]~P34(x18961)+~P77(f86(f29(x18961,f22(x18961,x18963,x18964)),x18962))+~P77(f86(f29(x18961,x18962),f86(f86(f23(x18961),x18963),x18964)))+P77(f86(f29(x18961,f19(x18961,f22(x18961,x18962,x18963))),x18964))
% 7.14/7.08 [1911]~P7(x19111)+P77(f86(f28(x19111,x19112),x19113))+~P77(f86(f28(x19111,f3(x19111)),x19113))+~P77(f86(f28(x19111,f86(f86(f31(x19111),x19112),f86(f86(f23(a83),x19114),f16(a83)))),f86(f86(f31(x19111),x19113),f86(f86(f23(a83),x19114),f16(a83)))))
% 7.14/7.08 [1884]~P77(f86(x18841,x18844))+P77(f86(x18841,f20(a83,x18842,x18843)))+~P77(f86(f29(a83,x18842),f86(f86(f24(a83),x18843),f86(f86(f23(a83),x18844),f16(a83)))))+~P77(f86(f28(a83,f86(f86(f24(a83),x18843),x18844)),x18842))
% 7.14/7.08 [1938]~P35(x19381)+~P77(f86(f29(a82,f3(a82)),x19384))+P77(f86(f28(a82,f36(x19381,f86(x19382,x19383))),f35(a83,f86(f86(f23(a83),f70(x19382,x19381)),f16(a83)))))+~P77(f86(f28(a82,f36(x19381,f86(x19382,f71(x19382,x19381,x19384)))),x19384))
% 7.14/7.08 [1939]~P35(x19391)+~P77(f86(f29(a82,f3(a82)),x19394))+P77(f86(f29(a82,f36(x19391,f86(x19392,x19393))),f35(a83,f86(f86(f23(a83),f75(x19392,x19391)),f16(a83)))))+~P77(f86(f28(a82,f36(x19391,f86(x19392,f76(x19392,x19391,x19394)))),x19394))
% 7.14/7.08 [1058]~P13(x10585)+E(x10581,x10582)+~E(x10583,x10584)+~E(f22(x10585,x10583,x10584),f22(x10585,x10581,x10582))
% 7.14/7.08 [1296]~P28(x12961)+~E(f22(x12961,x12964,x12965),f22(x12961,x12962,x12963))+~P77(f86(f28(x12961,x12964),x12965))+P77(f86(f28(x12961,x12962),x12963))
% 7.14/7.08 [1298]~P28(x12981)+~E(f22(x12981,x12984,x12985),f22(x12981,x12982,x12983))+~P77(f86(f29(x12981,x12984),x12985))+P77(f86(f29(x12981,x12982),x12983))
% 7.14/7.08 [1694]~P30(x16941)+~P77(f86(f28(x16941,x16943),x16945))+~P77(f86(f28(x16941,x16942),x16944))+P77(f86(f28(x16941,f86(f86(f23(x16941),x16942),x16943)),f86(f86(f23(x16941),x16944),x16945)))
% 7.14/7.08 [1695]~P31(x16951)+~P77(f86(f28(x16951,x16953),x16955))+~P77(f86(f29(x16951,x16952),x16954))+P77(f86(f29(x16951,f86(f86(f23(x16951),x16952),x16953)),f86(f86(f23(x16951),x16954),x16955)))
% 7.14/7.08 [1696]~P31(x16961)+~P77(f86(f28(x16961,x16962),x16964))+~P77(f86(f29(x16961,x16963),x16965))+P77(f86(f29(x16961,f86(f86(f23(x16961),x16962),x16963)),f86(f86(f23(x16961),x16964),x16965)))
% 7.14/7.08 [1697]~P31(x16971)+~P77(f86(f29(x16971,x16973),x16975))+~P77(f86(f29(x16971,x16972),x16974))+P77(f86(f29(x16971,f86(f86(f23(x16971),x16972),x16973)),f86(f86(f23(x16971),x16974),x16975)))
% 7.14/7.08 [1767]~P76(x17675)+E(x17671,x17672)+E(x17673,x17674)+~E(f86(f86(f23(x17675),f86(f86(f24(x17675),x17673),x17671)),f86(f86(f24(x17675),x17674),x17672)),f86(f86(f23(x17675),f86(f86(f24(x17675),x17673),x17672)),f86(f86(f24(x17675),x17674),x17671)))
% 7.14/7.08 [1867]~P35(x18671)+~P77(f86(f29(a82,f36(x18671,x18673)),x18675))+~P77(f86(f29(a82,f36(x18671,x18672)),x18674))+P77(f86(f29(a82,f36(x18671,f86(f86(f23(x18671),x18672),x18673))),f86(f86(f23(a82),x18674),x18675)))
% 7.14/7.08 [1868]~P41(x18681)+~P77(f86(f29(a82,f36(x18681,x18683)),x18685))+~P77(f86(f29(a82,f36(x18681,x18682)),x18684))+P77(f86(f29(a82,f36(x18681,f86(f86(f24(x18681),x18682),x18683))),f86(f86(f24(a82),x18684),x18685)))
% 7.14/7.08 [1878]~P34(x18781)+~P77(f86(f29(x18781,f19(x18781,x18782)),x18784))+~P77(f86(f29(x18781,f19(x18781,x18783)),x18785))+P77(f86(f29(x18781,f86(f86(f24(x18781),f19(x18781,x18782)),f19(x18781,x18783))),f86(f86(f24(x18781),x18784),x18785)))
% 7.14/7.08 [1923]~E(f36(a85,x19231),f16(a82))+P77(f86(f29(a82,f36(a85,f86(f86(f23(a85),x19231),f16(a85)))),f16(a82)))+P77(f86(f29(a82,f36(a85,f22(a85,x19231,f16(a85)))),f16(a82)))+P77(f86(f29(a82,f36(a85,f86(f86(f23(a85),x19231),a17))),f16(a82)))+P77(f86(f29(a82,f36(a85,f22(a85,x19231,a17))),f16(a82)))
% 7.14/7.08 [1347]~P8(x13472)+E(x13471,f3(x13472))+~E(f86(f86(f23(x13472),x13473),x13471),f3(x13472))+~P77(f86(f28(x13472,f3(x13472)),x13473))+~P77(f86(f28(x13472,f3(x13472)),x13471))
% 7.14/7.08 [1348]~P8(x13482)+E(x13481,f3(x13482))+~E(f86(f86(f23(x13482),x13481),x13483),f3(x13482))+~P77(f86(f28(x13482,f3(x13482)),x13483))+~P77(f86(f28(x13482,f3(x13482)),x13481))
% 7.14/7.08 [1396]E(x13961,f95(x13962,x13963))+~E(f86(f86(f31(a82),x13961),x13963),x13962)+~P77(f86(f29(a82,f3(a82)),x13962))+~P77(f86(f29(a82,f3(a82)),x13961))+~P77(f86(f29(a83,f3(a83)),x13963))
% 7.14/7.08 [1709]~P34(x17091)+~P77(f86(f28(x17091,x17092),f16(x17091)))+~P77(f86(f28(x17091,f3(x17091)),x17092))+~P77(f86(f28(x17091,f3(x17091)),x17093))+P77(f86(f28(x17091,f86(f86(f24(x17091),x17092),x17093)),x17093))
% 7.14/7.08 [1710]~P34(x17101)+~P77(f86(f28(x17101,x17103),f16(x17101)))+~P77(f86(f28(x17101,f3(x17101)),x17103))+~P77(f86(f28(x17101,f3(x17101)),x17102))+P77(f86(f28(x17101,f86(f86(f24(x17101),x17102),x17103)),x17102))
% 7.14/7.08 [1609]~P7(x16093)+E(x16091,x16092)+~E(f86(f86(f31(x16093),x16091),f86(f86(f23(a83),x16094),f16(a83))),f86(f86(f31(x16093),x16092),f86(f86(f23(a83),x16094),f16(a83))))+~P77(f86(f28(x16093,f3(x16093)),x16092))+~P77(f86(f28(x16093,f3(x16093)),x16091))
% 7.14/7.08 [1763]~P7(x17631)+~P77(f86(f28(x17631,x17632),f16(x17631)))+~P77(f86(f28(a83,x17634),x17633))+~P77(f86(f28(x17631,f3(x17631)),x17632))+P77(f86(f28(x17631,f86(f86(f31(x17631),x17632),x17633)),f86(f86(f31(x17631),x17632),x17634)))
% 7.14/7.08 [1764]~P7(x17641)+~P77(f86(f29(x17641,x17642),f16(x17641)))+~P77(f86(f29(a83,x17644),x17643))+~P77(f86(f29(x17641,f3(x17641)),x17642))+P77(f86(f29(x17641,f86(f86(f31(x17641),x17642),x17643)),f86(f86(f31(x17641),x17642),x17644)))
% 7.14/7.08 [1765]~P7(x17651)+~P77(f86(f29(x17651,x17652),x17654))+~P77(f86(f28(x17651,f3(x17651)),x17652))+~P77(f86(f29(a83,f3(a83)),x17653))+P77(f86(f29(x17651,f86(f86(f31(x17651),x17652),x17653)),f86(f86(f31(x17651),x17654),x17653)))
% 7.14/7.08 [1840]~P17(x18401)+~P77(f86(f28(x18401,x18403),x18404))+~P77(f86(f28(x18401,x18402),f3(x18401)))+~P77(f86(f29(x18401,f3(x18401)),f86(f86(f24(x18401),x18403),x18404)))+P77(f86(f28(x18401,f86(f86(f37(x18401),x18402),x18403)),f86(f86(f37(x18401),x18402),x18404)))
% 7.14/7.08 [1842]~P18(x18421)+~P77(f86(f28(x18421,x18424),x18423))+~P77(f86(f28(x18421,f3(x18421)),x18422))+~P77(f86(f29(x18421,f3(x18421)),f86(f86(f24(x18421),x18423),x18424)))+P77(f86(f28(x18421,f86(f86(f37(x18421),x18422),x18423)),f86(f86(f37(x18421),x18422),x18424)))
% 7.14/7.08 [1885]~P35(x18854)+~P38(x18851)+P77(f86(f28(x18851,x18852),f108(x18853,x18852,x18851,x18854)))+~P77(f86(f28(x18851,x18852),x18855))+P77(f86(f29(a82,f36(x18854,f86(x18853,x18855))),f86(f86(f23(a82),f16(a82)),f36(x18854,f86(x18853,x18852)))))
% 7.14/7.08 [1973]~P35(x19731)+~P38(x19735)+~P77(f86(f28(x19735,x19734),x19733))+~P77(f86(f29(a82,f36(x19731,f22(x19731,f86(x19732,x19734),f86(x19732,f108(x19732,x19734,x19735,x19731))))),f16(a82)))+P77(f86(f29(a82,f36(x19731,f86(x19732,x19733))),f86(f86(f23(a82),f16(a82)),f36(x19731,f86(x19732,x19734)))))
% 7.14/7.08 [1666]E(x16661,f3(a83))+P77(f86(x16662,x16663))+~P77(f86(x16662,f20(a83,x16664,x16661)))+~P77(f86(f29(a83,x16665),x16661))+~E(x16664,f86(f86(f23(a83),f86(f86(f24(a83),x16661),x16663)),x16665))
% 7.14/7.08 [1940]~P77(f86(f29(a84,x19403),x19405))+P77(f86(f28(a84,x19401),x19402))+~P77(f86(f29(a84,x19403),x19404))+~P77(f86(f28(a84,x19404),f3(a84)))+~P77(f86(f28(a84,f86(f86(f23(a84),f86(f86(f24(a84),x19403),x19402)),x19405)),f86(f86(f23(a84),f86(f86(f24(a84),x19403),x19401)),x19404)))
% 7.14/7.08 [1941]P77(f86(f28(a84,x19411),x19412))+~P77(f86(f29(a84,x19413),x19414))+~P77(f86(f29(a84,x19415),x19414))+~P77(f86(f28(a84,f3(a84)),x19415))+~P77(f86(f28(a84,f86(f86(f23(a84),f86(f86(f24(a84),x19414),x19411)),x19415)),f86(f86(f23(a84),f86(f86(f24(a84),x19414),x19412)),x19413)))
% 7.14/7.08 [1393]~P76(x13934)+E(x13931,x13932)+~E(x13935,x13936)+E(x13933,f3(x13934))+~E(f86(f86(f23(x13934),x13935),f86(f86(f24(x13934),x13933),x13931)),f86(f86(f23(x13934),x13936),f86(f86(f24(x13934),x13933),x13932)))
% 7.14/7.08 [952]~P58(x9522)+~P62(x9522)+~P63(x9522)+~P43(x9522)+E(x9521,f3(x9522))+~E(f86(f86(f31(x9522),x9521),x9523),f3(x9522))
% 7.14/7.08 [960]~P58(x9602)+~P62(x9602)+~P63(x9602)+~P43(x9602)+~E(x9601,f3(a83))+~E(f86(f86(f31(x9602),x9603),x9601),f3(x9602))
% 7.14/7.08 [1323]~P8(x13231)+~E(x13233,f3(x13231))+~E(x13232,f3(x13231))+E(f86(f86(f23(x13231),x13232),x13233),f3(x13231))+~P77(f86(f28(x13231,f3(x13231)),x13233))+~P77(f86(f28(x13231,f3(x13231)),x13232))
% 7.14/7.08 [1509]~P7(x15093)+E(x15091,x15092)+~E(f86(f86(f31(x15093),x15091),x15094),f86(f86(f31(x15093),x15092),x15094))+~P77(f86(f28(x15093,f3(x15093)),x15092))+~P77(f86(f28(x15093,f3(x15093)),x15091))+~P77(f86(f29(a83,f3(a83)),x15094))
% 7.14/7.08 [1574]E(f20(a84,x15742,x15741),x15743)+E(x15741,f3(a84))+~P77(f86(f29(a84,x15741),x15744))+~P77(f86(f28(a84,x15744),f3(a84)))+~E(x15742,f86(f86(f23(a84),f86(f86(f24(a84),x15741),x15743)),x15744))+P77(f86(f29(a84,f3(a84)),x15741))
% 7.14/7.08 [1610]E(f20(a84,x16102,x16101),x16103)+E(x16101,f3(a84))+~P77(f86(f29(a84,x16104),x16101))+~E(x16102,f86(f86(f23(a84),f86(f86(f24(a84),x16101),x16103)),x16104))+~P77(f86(f28(a84,f3(a84)),x16104))+~P77(f86(f29(a84,f3(a84)),x16101))
% 7.14/7.08 [1804]~P69(x18041)+~P77(f86(f28(x18041,x18043),x18045))+~P77(f86(f28(x18041,x18042),x18044))+~P77(f86(f28(x18041,f3(x18041)),x18043))+~P77(f86(f28(x18041,f3(x18041)),x18044))+P77(f86(f28(x18041,f86(f86(f24(x18041),x18042),x18043)),f86(f86(f24(x18041),x18044),x18045)))
% 7.14/7.08 [1805]~P69(x18051)+~P77(f86(f28(x18051,x18053),x18055))+~P77(f86(f28(x18051,x18052),x18054))+~P77(f86(f28(x18051,f3(x18051)),x18053))+~P77(f86(f28(x18051,f3(x18051)),x18052))+P77(f86(f28(x18051,f86(f86(f24(x18051),x18052),x18053)),f86(f86(f24(x18051),x18054),x18055)))
% 7.14/7.08 [1806]~P64(x18061)+~P77(f86(f28(x18061,x18063),x18065))+~P77(f86(f29(x18061,x18062),x18064))+~P77(f86(f28(x18061,f3(x18061)),x18062))+~P77(f86(f29(x18061,f3(x18061)),x18063))+P77(f86(f29(x18061,f86(f86(f24(x18061),x18062),x18063)),f86(f86(f24(x18061),x18064),x18065)))
% 7.14/7.08 [1807]~P64(x18071)+~P77(f86(f28(x18071,x18072),x18074))+~P77(f86(f29(x18071,x18073),x18075))+~P77(f86(f28(x18071,f3(x18071)),x18073))+~P77(f86(f29(x18071,f3(x18071)),x18072))+P77(f86(f29(x18071,f86(f86(f24(x18071),x18072),x18073)),f86(f86(f24(x18071),x18074),x18075)))
% 7.14/7.08 [1808]~P64(x18081)+~P77(f86(f29(x18081,x18083),x18085))+~P77(f86(f29(x18081,x18082),x18084))+~P77(f86(f28(x18081,f3(x18081)),x18083))+~P77(f86(f28(x18081,f3(x18081)),x18082))+P77(f86(f29(x18081,f86(f86(f24(x18081),x18082),x18083)),f86(f86(f24(x18081),x18084),x18085)))
% 7.14/7.08 [1809]~P64(x18091)+~P77(f86(f29(x18091,x18093),x18095))+~P77(f86(f29(x18091,x18092),x18094))+~P77(f86(f28(x18091,f3(x18091)),x18093))+~P77(f86(f29(x18091,f3(x18091)),x18094))+P77(f86(f29(x18091,f86(f86(f24(x18091),x18092),x18093)),f86(f86(f24(x18091),x18094),x18095)))
% 7.14/7.08 [1637]~P78(x16371,x16374,x16373)+P77(f86(x16371,x16372))+~P77(f86(f29(a84,x16374),x16375))+~P77(f86(f29(a84,x16374),f3(a84)))+~P77(f86(f28(a84,x16375),f3(a84)))+~E(x16373,f86(f86(f23(a84),f86(f86(f24(a84),x16374),x16372)),x16375))
% 7.14/7.08 [1648]~P78(x16481,x16484,x16483)+P77(f86(x16481,x16482))+~P77(f86(f29(a84,x16485),x16484))+~E(x16483,f86(f86(f23(a84),f86(f86(f24(a84),x16484),x16482)),x16485))+~P77(f86(f28(a84,f3(a84)),x16485))+~P77(f86(f29(a84,f3(a84)),x16484))
% 7.14/7.08 [1572]~P40(x15721)+~P2(x15721,x15722)+P77(f86(f28(x15721,f86(x15722,x15723)),f86(x15722,x15724)))+P77(f86(f28(x15721,f86(x15722,x15725)),f86(x15722,x15726)))+~P77(f86(f28(a83,x15724),x15723))+~P77(f86(f28(a83,x15725),x15726))
% 7.14/7.08 [931]~P58(x9312)+~P62(x9312)+~P63(x9312)+~P43(x9312)+~E(x9313,f3(x9312))+E(x9311,f3(a83))+E(f86(f86(f31(x9312),x9313),x9311),f3(x9312))
% 7.14/7.08 [1680]E(f20(a84,x16802,x16801),x16803)+E(x16801,f3(a84))+~P77(f86(f29(a84,x16804),x16801))+~P77(f86(f29(a84,x16801),x16804))+~P77(f86(f28(a84,x16804),f3(a84)))+~E(x16802,f86(f86(f23(a84),f86(f86(f24(a84),x16801),x16803)),x16804))+~P77(f86(f28(a84,f3(a84)),x16804))
% 7.14/7.08 [1929]~P77(f86(f28(a84,x19295),x19293))+~P77(f86(f29(a84,x19294),x19293))+P77(f86(f28(a84,x19291),x19292))+~P77(f86(f29(a84,f86(f86(f23(a84),f86(f86(f24(a84),x19295),x19291)),x19296)),f3(a84)))+~E(f86(f86(f23(a84),f86(f86(f24(a84),x19293),x19292)),x19294),f86(f86(f23(a84),f86(f86(f24(a84),x19295),x19291)),x19296))+~P77(f86(f28(a84,f3(a84)),x19296))+~P77(f86(f29(a84,f3(a84)),x19295))
% 7.14/7.08 [1906]~P77(f86(f28(a84,x19065),x19063))+~P77(f86(f29(a84,x19066),x19065))+P77(f86(f28(a84,x19061),x19062))+~E(f86(f86(f23(a84),f86(f86(f24(a84),x19063),x19061)),x19064),f86(f86(f23(a84),f86(f86(f24(a84),x19065),x19062)),x19066))+~P77(f86(f28(a84,f3(a84)),x19064))+~P77(f86(f29(a84,f3(a84)),x19065))+~P77(f86(f28(a84,f3(a84)),f86(f86(f23(a84),f86(f86(f24(a84),x19065),x19062)),x19066)))
% 7.14/7.08 [1921]~P61(x19211)+~E(f86(f86(f23(x19211),x19212),x19214),f16(x19211))+~P77(f86(f28(x19211,x19215),x19216))+~P77(f86(f28(x19211,x19213),x19216))+~P77(f86(f28(x19211,f3(x19211)),x19214))+~P77(f86(f28(x19211,f3(x19211)),x19212))+P77(f86(f28(x19211,f86(f86(f23(x19211),f86(f86(f24(x19211),x19212),x19213)),f86(f86(f24(x19211),x19214),x19215))),x19216))
% 7.14/7.08 [1922]~P59(x19221)+~E(f86(f86(f23(x19221),x19222),x19224),f16(x19221))+~P77(f86(f29(x19221,x19225),x19226))+~P77(f86(f29(x19221,x19223),x19226))+~P77(f86(f28(x19221,f3(x19221)),x19224))+~P77(f86(f28(x19221,f3(x19221)),x19222))+P77(f86(f29(x19221,f86(f86(f23(x19221),f86(f86(f24(x19221),x19222),x19223)),f86(f86(f24(x19221),x19224),x19225))),x19226))
% 7.14/7.08 %EqnAxiom
% 7.14/7.08 [1]E(x11,x11)
% 7.14/7.08 [2]E(x22,x21)+~E(x21,x22)
% 7.14/7.08 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 7.14/7.08 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 7.14/7.08 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 7.14/7.08 [6]~E(x61,x62)+E(f16(x61),f16(x62))
% 7.14/7.08 [7]~E(x71,x72)+E(f86(x71,x73),f86(x72,x73))
% 7.14/7.08 [8]~E(x81,x82)+E(f86(x83,x81),f86(x83,x82))
% 7.14/7.08 [9]~E(x91,x92)+E(f26(x91),f26(x92))
% 7.14/7.08 [10]~E(x101,x102)+E(f29(x101,x103),f29(x102,x103))
% 7.14/7.08 [11]~E(x111,x112)+E(f29(x113,x111),f29(x113,x112))
% 7.14/7.08 [12]~E(x121,x122)+E(f23(x121),f23(x122))
% 7.14/7.08 [13]~E(x131,x132)+E(f37(x131),f37(x132))
% 7.14/7.08 [14]~E(x141,x142)+E(f24(x141),f24(x142))
% 7.14/7.08 [15]~E(x151,x152)+E(f31(x151),f31(x152))
% 7.14/7.08 [16]~E(x161,x162)+E(f33(x161),f33(x162))
% 7.14/7.08 [17]~E(x171,x172)+E(f34(x171),f34(x172))
% 7.14/7.08 [18]~E(x181,x182)+E(f28(x181,x183),f28(x182,x183))
% 7.14/7.08 [19]~E(x191,x192)+E(f28(x193,x191),f28(x193,x192))
% 7.14/7.08 [20]~E(x201,x202)+E(f74(x201,x203,x204),f74(x202,x203,x204))
% 7.14/7.08 [21]~E(x211,x212)+E(f74(x213,x211,x214),f74(x213,x212,x214))
% 7.14/7.08 [22]~E(x221,x222)+E(f74(x223,x224,x221),f74(x223,x224,x222))
% 7.14/7.08 [23]~E(x231,x232)+E(f35(x231,x233),f35(x232,x233))
% 7.14/7.08 [24]~E(x241,x242)+E(f35(x243,x241),f35(x243,x242))
% 7.14/7.08 [25]~E(x251,x252)+E(f30(x251,x253),f30(x252,x253))
% 7.14/7.08 [26]~E(x261,x262)+E(f30(x263,x261),f30(x263,x262))
% 7.14/7.08 [27]~E(x271,x272)+E(f121(x271,x273),f121(x272,x273))
% 7.14/7.08 [28]~E(x281,x282)+E(f121(x283,x281),f121(x283,x282))
% 7.14/7.08 [29]~E(x291,x292)+E(f22(x291,x293,x294),f22(x292,x293,x294))
% 7.14/7.08 [30]~E(x301,x302)+E(f22(x303,x301,x304),f22(x303,x302,x304))
% 7.14/7.08 [31]~E(x311,x312)+E(f22(x313,x314,x311),f22(x313,x314,x312))
% 7.14/7.08 [32]~E(x321,x322)+E(f107(x321,x323,x324),f107(x322,x323,x324))
% 7.14/7.08 [33]~E(x331,x332)+E(f107(x333,x331,x334),f107(x333,x332,x334))
% 7.14/7.08 [34]~E(x341,x342)+E(f107(x343,x344,x341),f107(x343,x344,x342))
% 7.14/7.08 [35]~E(x351,x352)+E(f20(x351,x353,x354),f20(x352,x353,x354))
% 7.14/7.08 [36]~E(x361,x362)+E(f20(x363,x361,x364),f20(x363,x362,x364))
% 7.14/7.08 [37]~E(x371,x372)+E(f20(x373,x374,x371),f20(x373,x374,x372))
% 7.14/7.08 [38]~E(x381,x382)+E(f67(x381,x383,x384,x385),f67(x382,x383,x384,x385))
% 7.14/7.08 [39]~E(x391,x392)+E(f67(x393,x391,x394,x395),f67(x393,x392,x394,x395))
% 7.14/7.08 [40]~E(x401,x402)+E(f67(x403,x404,x401,x405),f67(x403,x404,x402,x405))
% 7.14/7.08 [41]~E(x411,x412)+E(f67(x413,x414,x415,x411),f67(x413,x414,x415,x412))
% 7.14/7.08 [42]~E(x421,x422)+E(f8(x421,x423,x424,x425,x426),f8(x422,x423,x424,x425,x426))
% 7.14/7.08 [43]~E(x431,x432)+E(f8(x433,x431,x434,x435,x436),f8(x433,x432,x434,x435,x436))
% 7.14/7.08 [44]~E(x441,x442)+E(f8(x443,x444,x441,x445,x446),f8(x443,x444,x442,x445,x446))
% 7.14/7.08 [45]~E(x451,x452)+E(f8(x453,x454,x455,x451,x456),f8(x453,x454,x455,x452,x456))
% 7.14/7.08 [46]~E(x461,x462)+E(f8(x463,x464,x465,x466,x461),f8(x463,x464,x465,x466,x462))
% 7.14/7.08 [47]~E(x471,x472)+E(f53(x471,x473),f53(x472,x473))
% 7.14/7.08 [48]~E(x481,x482)+E(f53(x483,x481),f53(x483,x482))
% 7.14/7.08 [49]~E(x491,x492)+E(f36(x491,x493),f36(x492,x493))
% 7.14/7.08 [50]~E(x501,x502)+E(f36(x503,x501),f36(x503,x502))
% 7.14/7.08 [51]~E(x511,x512)+E(f19(x511,x513),f19(x512,x513))
% 7.14/7.08 [52]~E(x521,x522)+E(f19(x523,x521),f19(x523,x522))
% 7.14/7.08 [53]~E(x531,x532)+E(f32(x531,x533,x534),f32(x532,x533,x534))
% 7.14/7.08 [54]~E(x541,x542)+E(f32(x543,x541,x544),f32(x543,x542,x544))
% 7.14/7.08 [55]~E(x551,x552)+E(f32(x553,x554,x551),f32(x553,x554,x552))
% 7.14/7.08 [56]~E(x561,x562)+E(f18(x561,x563),f18(x562,x563))
% 7.14/7.08 [57]~E(x571,x572)+E(f18(x573,x571),f18(x573,x572))
% 7.14/7.08 [58]~E(x581,x582)+E(f109(x581,x583,x584),f109(x582,x583,x584))
% 7.14/7.08 [59]~E(x591,x592)+E(f109(x593,x591,x594),f109(x593,x592,x594))
% 7.14/7.08 [60]~E(x601,x602)+E(f109(x603,x604,x601),f109(x603,x604,x602))
% 7.14/7.08 [61]~E(x611,x612)+E(f11(x611,x613),f11(x612,x613))
% 7.14/7.08 [62]~E(x621,x622)+E(f11(x623,x621),f11(x623,x622))
% 7.21/7.08 [63]~E(x631,x632)+E(f100(x631,x633),f100(x632,x633))
% 7.21/7.08 [64]~E(x641,x642)+E(f100(x643,x641),f100(x643,x642))
% 7.21/7.08 [65]~E(x651,x652)+E(f68(x651,x653),f68(x652,x653))
% 7.21/7.08 [66]~E(x661,x662)+E(f68(x663,x661),f68(x663,x662))
% 7.21/7.08 [67]~E(x671,x672)+E(f102(x671,x673,x674),f102(x672,x673,x674))
% 7.21/7.08 [68]~E(x681,x682)+E(f102(x683,x681,x684),f102(x683,x682,x684))
% 7.21/7.08 [69]~E(x691,x692)+E(f102(x693,x694,x691),f102(x693,x694,x692))
% 7.21/7.08 [70]~E(x701,x702)+E(f41(x701),f41(x702))
% 7.21/7.08 [71]~E(x711,x712)+E(f95(x711,x713),f95(x712,x713))
% 7.21/7.08 [72]~E(x721,x722)+E(f95(x723,x721),f95(x723,x722))
% 7.21/7.08 [73]~E(x731,x732)+E(f79(x731),f79(x732))
% 7.21/7.08 [74]~E(x741,x742)+E(f113(x741,x743,x744),f113(x742,x743,x744))
% 7.21/7.08 [75]~E(x751,x752)+E(f113(x753,x751,x754),f113(x753,x752,x754))
% 7.21/7.08 [76]~E(x761,x762)+E(f113(x763,x764,x761),f113(x763,x764,x762))
% 7.21/7.08 [77]~E(x771,x772)+E(f120(x771),f120(x772))
% 7.21/7.08 [78]~E(x781,x782)+E(f25(x781,x783),f25(x782,x783))
% 7.21/7.08 [79]~E(x791,x792)+E(f25(x793,x791),f25(x793,x792))
% 7.21/7.08 [80]~E(x801,x802)+E(f106(x801,x803,x804),f106(x802,x803,x804))
% 7.21/7.08 [81]~E(x811,x812)+E(f106(x813,x811,x814),f106(x813,x812,x814))
% 7.21/7.08 [82]~E(x821,x822)+E(f106(x823,x824,x821),f106(x823,x824,x822))
% 7.21/7.08 [83]~E(x831,x832)+E(f54(x831,x833),f54(x832,x833))
% 7.21/7.08 [84]~E(x841,x842)+E(f54(x843,x841),f54(x843,x842))
% 7.21/7.08 [85]~E(x851,x852)+E(f111(x851,x853,x854),f111(x852,x853,x854))
% 7.21/7.08 [86]~E(x861,x862)+E(f111(x863,x861,x864),f111(x863,x862,x864))
% 7.21/7.08 [87]~E(x871,x872)+E(f111(x873,x874,x871),f111(x873,x874,x872))
% 7.21/7.08 [88]~E(x881,x882)+E(f112(x881,x883,x884),f112(x882,x883,x884))
% 7.21/7.08 [89]~E(x891,x892)+E(f112(x893,x891,x894),f112(x893,x892,x894))
% 7.21/7.08 [90]~E(x901,x902)+E(f112(x903,x904,x901),f112(x903,x904,x902))
% 7.21/7.08 [91]~E(x911,x912)+E(f47(x911,x913),f47(x912,x913))
% 7.21/7.08 [92]~E(x921,x922)+E(f47(x923,x921),f47(x923,x922))
% 7.21/7.08 [93]~E(x931,x932)+E(f51(x931),f51(x932))
% 7.21/7.08 [94]~E(x941,x942)+E(f117(x941,x943,x944),f117(x942,x943,x944))
% 7.21/7.08 [95]~E(x951,x952)+E(f117(x953,x951,x954),f117(x953,x952,x954))
% 7.21/7.08 [96]~E(x961,x962)+E(f117(x963,x964,x961),f117(x963,x964,x962))
% 7.21/7.08 [97]~E(x971,x972)+E(f71(x971,x973,x974),f71(x972,x973,x974))
% 7.21/7.08 [98]~E(x981,x982)+E(f71(x983,x981,x984),f71(x983,x982,x984))
% 7.21/7.08 [99]~E(x991,x992)+E(f71(x993,x994,x991),f71(x993,x994,x992))
% 7.21/7.08 [100]~E(x1001,x1002)+E(f42(x1001),f42(x1002))
% 7.21/7.08 [101]~E(x1011,x1012)+E(f7(x1011,x1013,x1014,x1015,x1016),f7(x1012,x1013,x1014,x1015,x1016))
% 7.21/7.08 [102]~E(x1021,x1022)+E(f7(x1023,x1021,x1024,x1025,x1026),f7(x1023,x1022,x1024,x1025,x1026))
% 7.21/7.08 [103]~E(x1031,x1032)+E(f7(x1033,x1034,x1031,x1035,x1036),f7(x1033,x1034,x1032,x1035,x1036))
% 7.21/7.08 [104]~E(x1041,x1042)+E(f7(x1043,x1044,x1045,x1041,x1046),f7(x1043,x1044,x1045,x1042,x1046))
% 7.21/7.08 [105]~E(x1051,x1052)+E(f7(x1053,x1054,x1055,x1056,x1051),f7(x1053,x1054,x1055,x1056,x1052))
% 7.21/7.08 [106]~E(x1061,x1062)+E(f66(x1061,x1063),f66(x1062,x1063))
% 7.21/7.08 [107]~E(x1071,x1072)+E(f66(x1073,x1071),f66(x1073,x1072))
% 7.21/7.08 [108]~E(x1081,x1082)+E(f114(x1081,x1083,x1084),f114(x1082,x1083,x1084))
% 7.21/7.08 [109]~E(x1091,x1092)+E(f114(x1093,x1091,x1094),f114(x1093,x1092,x1094))
% 7.21/7.08 [110]~E(x1101,x1102)+E(f114(x1103,x1104,x1101),f114(x1103,x1104,x1102))
% 7.21/7.08 [111]~E(x1111,x1112)+E(f81(x1111,x1113),f81(x1112,x1113))
% 7.21/7.08 [112]~E(x1121,x1122)+E(f81(x1123,x1121),f81(x1123,x1122))
% 7.21/7.08 [113]~E(x1131,x1132)+E(f52(x1131,x1133),f52(x1132,x1133))
% 7.21/7.08 [114]~E(x1141,x1142)+E(f52(x1143,x1141),f52(x1143,x1142))
% 7.21/7.08 [115]~E(x1151,x1152)+E(f63(x1151,x1153,x1154,x1155),f63(x1152,x1153,x1154,x1155))
% 7.21/7.08 [116]~E(x1161,x1162)+E(f63(x1163,x1161,x1164,x1165),f63(x1163,x1162,x1164,x1165))
% 7.21/7.08 [117]~E(x1171,x1172)+E(f63(x1173,x1174,x1171,x1175),f63(x1173,x1174,x1172,x1175))
% 7.21/7.08 [118]~E(x1181,x1182)+E(f63(x1183,x1184,x1185,x1181),f63(x1183,x1184,x1185,x1182))
% 7.21/7.08 [119]~E(x1191,x1192)+E(f57(x1191,x1193),f57(x1192,x1193))
% 7.21/7.08 [120]~E(x1201,x1202)+E(f57(x1203,x1201),f57(x1203,x1202))
% 7.21/7.08 [121]~E(x1211,x1212)+E(f62(x1211,x1213),f62(x1212,x1213))
% 7.21/7.08 [122]~E(x1221,x1222)+E(f62(x1223,x1221),f62(x1223,x1222))
% 7.21/7.08 [123]~E(x1231,x1232)+E(f108(x1231,x1233,x1234,x1235),f108(x1232,x1233,x1234,x1235))
% 7.21/7.08 [124]~E(x1241,x1242)+E(f108(x1243,x1241,x1244,x1245),f108(x1243,x1242,x1244,x1245))
% 7.21/7.08 [125]~E(x1251,x1252)+E(f108(x1253,x1254,x1251,x1255),f108(x1253,x1254,x1252,x1255))
% 7.21/7.08 [126]~E(x1261,x1262)+E(f108(x1263,x1264,x1265,x1261),f108(x1263,x1264,x1265,x1262))
% 7.21/7.08 [127]~E(x1271,x1272)+E(f69(x1271,x1273,x1274),f69(x1272,x1273,x1274))
% 7.21/7.08 [128]~E(x1281,x1282)+E(f69(x1283,x1281,x1284),f69(x1283,x1282,x1284))
% 7.21/7.08 [129]~E(x1291,x1292)+E(f69(x1293,x1294,x1291),f69(x1293,x1294,x1292))
% 7.21/7.08 [130]~E(x1301,x1302)+E(f96(x1301,x1303),f96(x1302,x1303))
% 7.21/7.08 [131]~E(x1311,x1312)+E(f96(x1313,x1311),f96(x1313,x1312))
% 7.21/7.08 [132]~E(x1321,x1322)+E(f103(x1321,x1323),f103(x1322,x1323))
% 7.21/7.08 [133]~E(x1331,x1332)+E(f103(x1333,x1331),f103(x1333,x1332))
% 7.21/7.08 [134]~E(x1341,x1342)+E(f48(x1341,x1343),f48(x1342,x1343))
% 7.21/7.08 [135]~E(x1351,x1352)+E(f48(x1353,x1351),f48(x1353,x1352))
% 7.21/7.08 [136]~E(x1361,x1362)+E(f78(x1361,x1363),f78(x1362,x1363))
% 7.21/7.08 [137]~E(x1371,x1372)+E(f78(x1373,x1371),f78(x1373,x1372))
% 7.21/7.08 [138]~E(x1381,x1382)+E(f70(x1381,x1383),f70(x1382,x1383))
% 7.21/7.08 [139]~E(x1391,x1392)+E(f70(x1393,x1391),f70(x1393,x1392))
% 7.21/7.08 [140]~E(x1401,x1402)+E(f101(x1401),f101(x1402))
% 7.21/7.08 [141]~E(x1411,x1412)+E(f94(x1411,x1413),f94(x1412,x1413))
% 7.21/7.08 [142]~E(x1421,x1422)+E(f94(x1423,x1421),f94(x1423,x1422))
% 7.21/7.08 [143]~E(x1431,x1432)+E(f59(x1431,x1433),f59(x1432,x1433))
% 7.21/7.08 [144]~E(x1441,x1442)+E(f59(x1443,x1441),f59(x1443,x1442))
% 7.21/7.08 [145]~E(x1451,x1452)+E(f13(x1451),f13(x1452))
% 7.21/7.08 [146]~E(x1461,x1462)+E(f115(x1461,x1463,x1464),f115(x1462,x1463,x1464))
% 7.21/7.08 [147]~E(x1471,x1472)+E(f115(x1473,x1471,x1474),f115(x1473,x1472,x1474))
% 7.21/7.08 [148]~E(x1481,x1482)+E(f115(x1483,x1484,x1481),f115(x1483,x1484,x1482))
% 7.21/7.08 [149]~E(x1491,x1492)+E(f12(x1491),f12(x1492))
% 7.21/7.08 [150]~E(x1501,x1502)+E(f64(x1501,x1503,x1504),f64(x1502,x1503,x1504))
% 7.21/7.08 [151]~E(x1511,x1512)+E(f64(x1513,x1511,x1514),f64(x1513,x1512,x1514))
% 7.21/7.08 [152]~E(x1521,x1522)+E(f64(x1523,x1524,x1521),f64(x1523,x1524,x1522))
% 7.21/7.08 [153]~E(x1531,x1532)+E(f88(x1531,x1533),f88(x1532,x1533))
% 7.21/7.08 [154]~E(x1541,x1542)+E(f88(x1543,x1541),f88(x1543,x1542))
% 7.21/7.08 [155]~E(x1551,x1552)+E(f46(x1551),f46(x1552))
% 7.21/7.08 [156]~E(x1561,x1562)+E(f98(x1561,x1563),f98(x1562,x1563))
% 7.21/7.08 [157]~E(x1571,x1572)+E(f98(x1573,x1571),f98(x1573,x1572))
% 7.21/7.08 [158]~E(x1581,x1582)+E(f27(x1581,x1583),f27(x1582,x1583))
% 7.21/7.08 [159]~E(x1591,x1592)+E(f27(x1593,x1591),f27(x1593,x1592))
% 7.21/7.08 [160]~E(x1601,x1602)+E(f65(x1601),f65(x1602))
% 7.21/7.08 [161]~E(x1611,x1612)+E(f99(x1611,x1613),f99(x1612,x1613))
% 7.21/7.08 [162]~E(x1621,x1622)+E(f99(x1623,x1621),f99(x1623,x1622))
% 7.21/7.08 [163]~E(x1631,x1632)+E(f72(x1631),f72(x1632))
% 7.21/7.08 [164]~E(x1641,x1642)+E(f110(x1641,x1643),f110(x1642,x1643))
% 7.21/7.08 [165]~E(x1651,x1652)+E(f110(x1653,x1651),f110(x1653,x1652))
% 7.21/7.08 [166]~E(x1661,x1662)+E(f118(x1661,x1663),f118(x1662,x1663))
% 7.21/7.08 [167]~E(x1671,x1672)+E(f118(x1673,x1671),f118(x1673,x1672))
% 7.21/7.08 [168]~E(x1681,x1682)+E(f105(x1681),f105(x1682))
% 7.21/7.08 [169]~E(x1691,x1692)+E(f80(x1691,x1693),f80(x1692,x1693))
% 7.21/7.08 [170]~E(x1701,x1702)+E(f80(x1703,x1701),f80(x1703,x1702))
% 7.21/7.08 [171]~E(x1711,x1712)+E(f89(x1711),f89(x1712))
% 7.21/7.08 [172]~E(x1721,x1722)+E(f73(x1721,x1723),f73(x1722,x1723))
% 7.21/7.08 [173]~E(x1731,x1732)+E(f73(x1733,x1731),f73(x1733,x1732))
% 7.21/7.08 [174]~E(x1741,x1742)+E(f6(x1741,x1743,x1744),f6(x1742,x1743,x1744))
% 7.21/7.08 [175]~E(x1751,x1752)+E(f6(x1753,x1751,x1754),f6(x1753,x1752,x1754))
% 7.21/7.08 [176]~E(x1761,x1762)+E(f6(x1763,x1764,x1761),f6(x1763,x1764,x1762))
% 7.21/7.08 [177]~E(x1771,x1772)+E(f38(x1771),f38(x1772))
% 7.21/7.08 [178]~E(x1781,x1782)+E(f60(x1781,x1783),f60(x1782,x1783))
% 7.21/7.08 [179]~E(x1791,x1792)+E(f60(x1793,x1791),f60(x1793,x1792))
% 7.21/7.08 [180]~E(x1801,x1802)+E(f87(x1801,x1803),f87(x1802,x1803))
% 7.21/7.08 [181]~E(x1811,x1812)+E(f87(x1813,x1811),f87(x1813,x1812))
% 7.21/7.08 [182]~E(x1821,x1822)+E(f61(x1821,x1823,x1824),f61(x1822,x1823,x1824))
% 7.21/7.08 [183]~E(x1831,x1832)+E(f61(x1833,x1831,x1834),f61(x1833,x1832,x1834))
% 7.21/7.08 [184]~E(x1841,x1842)+E(f61(x1843,x1844,x1841),f61(x1843,x1844,x1842))
% 7.21/7.08 [185]~E(x1851,x1852)+E(f21(x1851,x1853),f21(x1852,x1853))
% 7.21/7.08 [186]~E(x1861,x1862)+E(f21(x1863,x1861),f21(x1863,x1862))
% 7.21/7.08 [187]~E(x1871,x1872)+E(f50(x1871,x1873),f50(x1872,x1873))
% 7.21/7.08 [188]~E(x1881,x1882)+E(f50(x1883,x1881),f50(x1883,x1882))
% 7.21/7.08 [189]~E(x1891,x1892)+E(f76(x1891,x1893,x1894),f76(x1892,x1893,x1894))
% 7.21/7.08 [190]~E(x1901,x1902)+E(f76(x1903,x1901,x1904),f76(x1903,x1902,x1904))
% 7.21/7.08 [191]~E(x1911,x1912)+E(f76(x1913,x1914,x1911),f76(x1913,x1914,x1912))
% 7.21/7.08 [192]~E(x1921,x1922)+E(f55(x1921),f55(x1922))
% 7.21/7.08 [193]~E(x1931,x1932)+E(f97(x1931,x1933),f97(x1932,x1933))
% 7.21/7.08 [194]~E(x1941,x1942)+E(f97(x1943,x1941),f97(x1943,x1942))
% 7.21/7.08 [195]~E(x1951,x1952)+E(f90(x1951,x1953),f90(x1952,x1953))
% 7.21/7.08 [196]~E(x1961,x1962)+E(f90(x1963,x1961),f90(x1963,x1962))
% 7.21/7.08 [197]~E(x1971,x1972)+E(f77(x1971,x1973),f77(x1972,x1973))
% 7.21/7.08 [198]~E(x1981,x1982)+E(f77(x1983,x1981),f77(x1983,x1982))
% 7.21/7.08 [199]~E(x1991,x1992)+E(f58(x1991,x1993),f58(x1992,x1993))
% 7.21/7.08 [200]~E(x2001,x2002)+E(f58(x2003,x2001),f58(x2003,x2002))
% 7.21/7.08 [201]~E(x2011,x2012)+E(f56(x2011,x2013),f56(x2012,x2013))
% 7.21/7.08 [202]~E(x2021,x2022)+E(f56(x2023,x2021),f56(x2023,x2022))
% 7.21/7.08 [203]~E(x2031,x2032)+E(f91(x2031,x2033),f91(x2032,x2033))
% 7.21/7.08 [204]~E(x2041,x2042)+E(f91(x2043,x2041),f91(x2043,x2042))
% 7.21/7.08 [205]~E(x2051,x2052)+E(f92(x2051,x2053,x2054),f92(x2052,x2053,x2054))
% 7.21/7.08 [206]~E(x2061,x2062)+E(f92(x2063,x2061,x2064),f92(x2063,x2062,x2064))
% 7.21/7.08 [207]~E(x2071,x2072)+E(f92(x2073,x2074,x2071),f92(x2073,x2074,x2072))
% 7.21/7.08 [208]~E(x2081,x2082)+E(f9(x2081,x2083,x2084,x2085,x2086),f9(x2082,x2083,x2084,x2085,x2086))
% 7.21/7.08 [209]~E(x2091,x2092)+E(f9(x2093,x2091,x2094,x2095,x2096),f9(x2093,x2092,x2094,x2095,x2096))
% 7.21/7.08 [210]~E(x2101,x2102)+E(f9(x2103,x2104,x2101,x2105,x2106),f9(x2103,x2104,x2102,x2105,x2106))
% 7.21/7.08 [211]~E(x2111,x2112)+E(f9(x2113,x2114,x2115,x2111,x2116),f9(x2113,x2114,x2115,x2112,x2116))
% 7.21/7.08 [212]~E(x2121,x2122)+E(f9(x2123,x2124,x2125,x2126,x2121),f9(x2123,x2124,x2125,x2126,x2122))
% 7.21/7.08 [213]~E(x2131,x2132)+E(f14(x2131,x2133,x2134),f14(x2132,x2133,x2134))
% 7.21/7.08 [214]~E(x2141,x2142)+E(f14(x2143,x2141,x2144),f14(x2143,x2142,x2144))
% 7.21/7.08 [215]~E(x2151,x2152)+E(f14(x2153,x2154,x2151),f14(x2153,x2154,x2152))
% 7.21/7.08 [216]~E(x2161,x2162)+E(f75(x2161,x2163),f75(x2162,x2163))
% 7.21/7.08 [217]~E(x2171,x2172)+E(f75(x2173,x2171),f75(x2173,x2172))
% 7.21/7.08 [218]~E(x2181,x2182)+E(f104(x2181,x2183),f104(x2182,x2183))
% 7.21/7.08 [219]~E(x2191,x2192)+E(f104(x2193,x2191),f104(x2193,x2192))
% 7.21/7.08 [220]~E(x2201,x2202)+E(f93(x2201,x2203,x2204),f93(x2202,x2203,x2204))
% 7.21/7.08 [221]~E(x2211,x2212)+E(f93(x2213,x2211,x2214),f93(x2213,x2212,x2214))
% 7.21/7.08 [222]~E(x2221,x2222)+E(f93(x2223,x2224,x2221),f93(x2223,x2224,x2222))
% 7.21/7.08 [223]~E(x2231,x2232)+E(f15(x2231,x2233,x2234),f15(x2232,x2233,x2234))
% 7.21/7.08 [224]~E(x2241,x2242)+E(f15(x2243,x2241,x2244),f15(x2243,x2242,x2244))
% 7.21/7.08 [225]~E(x2251,x2252)+E(f15(x2253,x2254,x2251),f15(x2253,x2254,x2252))
% 7.21/7.08 [226]~P1(x2261)+P1(x2262)+~E(x2261,x2262)
% 7.21/7.08 [227]~P77(x2271)+P77(x2272)+~E(x2271,x2272)
% 7.21/7.08 [228]~P67(x2281)+P67(x2282)+~E(x2281,x2282)
% 7.21/7.08 [229]~P7(x2291)+P7(x2292)+~E(x2291,x2292)
% 7.21/7.08 [230]P5(x2302,x2303)+~E(x2301,x2302)+~P5(x2301,x2303)
% 7.21/7.08 [231]P5(x2313,x2312)+~E(x2311,x2312)+~P5(x2313,x2311)
% 7.21/7.08 [232]~P40(x2321)+P40(x2322)+~E(x2321,x2322)
% 7.21/7.08 [233]~P8(x2331)+P8(x2332)+~E(x2331,x2332)
% 7.21/7.08 [234]~P14(x2341)+P14(x2342)+~E(x2341,x2342)
% 7.21/7.08 [235]~P38(x2351)+P38(x2352)+~E(x2351,x2352)
% 7.21/7.08 [236]~P9(x2361)+P9(x2362)+~E(x2361,x2362)
% 7.21/7.08 [237]~P13(x2371)+P13(x2372)+~E(x2371,x2372)
% 7.21/7.08 [238]~P32(x2381)+P32(x2382)+~E(x2381,x2382)
% 7.21/7.08 [239]P6(x2392,x2393)+~E(x2391,x2392)+~P6(x2391,x2393)
% 7.21/7.08 [240]P6(x2403,x2402)+~E(x2401,x2402)+~P6(x2403,x2401)
% 7.21/7.08 [241]~P35(x2411)+P35(x2412)+~E(x2411,x2412)
% 7.21/7.08 [242]~P56(x2421)+P56(x2422)+~E(x2421,x2422)
% 7.21/7.08 [243]~P34(x2431)+P34(x2432)+~E(x2431,x2432)
% 7.21/7.08 [244]P78(x2442,x2443,x2444)+~E(x2441,x2442)+~P78(x2441,x2443,x2444)
% 7.21/7.08 [245]P78(x2453,x2452,x2454)+~E(x2451,x2452)+~P78(x2453,x2451,x2454)
% 7.21/7.08 [246]P78(x2463,x2464,x2462)+~E(x2461,x2462)+~P78(x2463,x2464,x2461)
% 7.21/7.08 [247]~P10(x2471)+P10(x2472)+~E(x2471,x2472)
% 7.21/7.08 [248]~P64(x2481)+P64(x2482)+~E(x2481,x2482)
% 7.21/7.08 [249]~P76(x2491)+P76(x2492)+~E(x2491,x2492)
% 7.21/7.08 [250]~P39(x2501)+P39(x2502)+~E(x2501,x2502)
% 7.21/7.08 [251]~P11(x2511)+P11(x2512)+~E(x2511,x2512)
% 7.21/7.08 [252]~P41(x2521)+P41(x2522)+~E(x2521,x2522)
% 7.21/7.08 [253]~P43(x2531)+P43(x2532)+~E(x2531,x2532)
% 7.21/7.08 [254]~P47(x2541)+P47(x2542)+~E(x2541,x2542)
% 7.21/7.08 [255]~P12(x2551)+P12(x2552)+~E(x2551,x2552)
% 7.21/7.08 [256]~P54(x2561)+P54(x2562)+~E(x2561,x2562)
% 7.21/7.08 [257]~P65(x2571)+P65(x2572)+~E(x2571,x2572)
% 7.21/7.08 [258]~P63(x2581)+P63(x2582)+~E(x2581,x2582)
% 7.21/7.08 [259]~P21(x2591)+P21(x2592)+~E(x2591,x2592)
% 7.21/7.08 [260]~P27(x2601)+P27(x2602)+~E(x2601,x2602)
% 7.21/7.08 [261]~P25(x2611)+P25(x2612)+~E(x2611,x2612)
% 7.21/7.08 [262]~P23(x2621)+P23(x2622)+~E(x2621,x2622)
% 7.21/7.08 [263]~P22(x2631)+P22(x2632)+~E(x2631,x2632)
% 7.21/7.08 [264]~P24(x2641)+P24(x2642)+~E(x2641,x2642)
% 7.21/7.08 [265]~P53(x2651)+P53(x2652)+~E(x2651,x2652)
% 7.21/7.08 [266]~P37(x2661)+P37(x2662)+~E(x2661,x2662)
% 7.21/7.08 [267]~P70(x2671)+P70(x2672)+~E(x2671,x2672)
% 7.21/7.08 [268]~P29(x2681)+P29(x2682)+~E(x2681,x2682)
% 7.21/7.08 [269]~P72(x2691)+P72(x2692)+~E(x2691,x2692)
% 7.21/7.08 [270]P4(x2702,x2703)+~E(x2701,x2702)+~P4(x2701,x2703)
% 7.21/7.08 [271]P4(x2713,x2712)+~E(x2711,x2712)+~P4(x2713,x2711)
% 7.21/7.08 [272]~P33(x2721)+P33(x2722)+~E(x2721,x2722)
% 7.21/7.08 [273]P2(x2732,x2733)+~E(x2731,x2732)+~P2(x2731,x2733)
% 7.21/7.08 [274]P2(x2743,x2742)+~E(x2741,x2742)+~P2(x2743,x2741)
% 7.21/7.08 [275]P3(x2752,x2753)+~E(x2751,x2752)+~P3(x2751,x2753)
% 7.21/7.08 [276]P3(x2763,x2762)+~E(x2761,x2762)+~P3(x2763,x2761)
% 7.21/7.08 [277]~P66(x2771)+P66(x2772)+~E(x2771,x2772)
% 7.21/7.08 [278]~P28(x2781)+P28(x2782)+~E(x2781,x2782)
% 7.21/7.08 [279]~P30(x2791)+P30(x2792)+~E(x2791,x2792)
% 7.21/7.08 [280]~P45(x2801)+P45(x2802)+~E(x2801,x2802)
% 7.21/7.08 [281]~P50(x2811)+P50(x2812)+~E(x2811,x2812)
% 7.21/7.08 [282]~P31(x2821)+P31(x2822)+~E(x2821,x2822)
% 7.21/7.08 [283]~P69(x2831)+P69(x2832)+~E(x2831,x2832)
% 7.21/7.08 [284]~P48(x2841)+P48(x2842)+~E(x2841,x2842)
% 7.21/7.08 [285]~P58(x2851)+P58(x2852)+~E(x2851,x2852)
% 7.21/7.08 [286]~P46(x2861)+P46(x2862)+~E(x2861,x2862)
% 7.21/7.08 [287]~P51(x2871)+P51(x2872)+~E(x2871,x2872)
% 7.21/7.08 [288]~P20(x2881)+P20(x2882)+~E(x2881,x2882)
% 7.21/7.08 [289]~P75(x2891)+P75(x2892)+~E(x2891,x2892)
% 7.21/7.08 [290]~P44(x2901)+P44(x2902)+~E(x2901,x2902)
% 7.21/7.08 [291]~P36(x2911)+P36(x2912)+~E(x2911,x2912)
% 7.21/7.08 [292]~P62(x2921)+P62(x2922)+~E(x2921,x2922)
% 7.21/7.08 [293]~P49(x2931)+P49(x2932)+~E(x2931,x2932)
% 7.21/7.08 [294]~P17(x2941)+P17(x2942)+~E(x2941,x2942)
% 7.21/7.08 [295]~P26(x2951)+P26(x2952)+~E(x2951,x2952)
% 7.21/7.08 [296]~P61(x2961)+P61(x2962)+~E(x2961,x2962)
% 7.21/7.08 [297]~P42(x2971)+P42(x2972)+~E(x2971,x2972)
% 7.21/7.08 [298]~P15(x2981)+P15(x2982)+~E(x2981,x2982)
% 7.21/7.08 [299]~P16(x2991)+P16(x2992)+~E(x2991,x2992)
% 7.21/7.08 [300]~P73(x3001)+P73(x3002)+~E(x3001,x3002)
% 7.21/7.08 [301]~P55(x3011)+P55(x3012)+~E(x3011,x3012)
% 7.21/7.08 [302]~P52(x3021)+P52(x3022)+~E(x3021,x3022)
% 7.21/7.08 [303]~P57(x3031)+P57(x3032)+~E(x3031,x3032)
% 7.21/7.08 [304]~P60(x3041)+P60(x3042)+~E(x3041,x3042)
% 7.21/7.08 [305]~P74(x3051)+P74(x3052)+~E(x3051,x3052)
% 7.21/7.08 [306]~P68(x3061)+P68(x3062)+~E(x3061,x3062)
% 7.21/7.08 [307]~P59(x3071)+P59(x3072)+~E(x3071,x3072)
% 7.21/7.08 [308]~P71(x3081)+P71(x3082)+~E(x3081,x3082)
% 7.21/7.08 [309]~P19(x3091)+P19(x3092)+~E(x3091,x3092)
% 7.21/7.08 [310]~P18(x3101)+P18(x3102)+~E(x3101,x3102)
% 7.21/7.08
% 7.21/7.08 %-------------------------------------------
% 7.21/7.09 cnf(1989,plain,
% 7.21/7.09 (E(f20(a84,x19891,f3(a84)),f3(a84))),
% 7.21/7.09 inference(equality_inference,[],[855])).
% 7.21/7.09 cnf(2003,plain,
% 7.21/7.09 (~P62(x20031)+~P63(x20031)+~P43(x20031)+~P58(x20031)+E(x20032,f3(a83))+E(f86(f86(f31(x20031),f3(x20031)),x20032),f3(x20031))),
% 7.21/7.09 inference(equality_inference,[],[931])).
% 7.21/7.09 cnf(2004,plain,
% 7.21/7.09 (E(f86(f86(f24(a83),x20041),f3(a83)),f86(f86(f24(a83),x20042),f3(a83)))),
% 7.21/7.09 inference(equality_inference,[],[932])).
% 7.21/7.09 cnf(2005,plain,
% 7.21/7.09 (E(f86(f86(f24(a83),f3(a83)),x20051),f86(f86(f24(a83),f3(a83)),x20052))),
% 7.21/7.09 inference(equality_inference,[],[934])).
% 7.21/7.09 cnf(2006,plain,
% 7.21/7.09 (E(f86(f86(f31(a83),x20061),f3(a83)),f86(f86(f23(a83),f3(a83)),f16(a83)))),
% 7.21/7.09 inference(equality_inference,[],[945])).
% 7.21/7.09 cnf(2007,plain,
% 7.21/7.09 (~P77(f86(f29(a82,x20071),x20071))),
% 7.21/7.09 inference(equality_inference,[],[953])).
% 7.21/7.09 cnf(2009,plain,
% 7.21/7.09 (~P77(f86(f29(a84,x20091),x20091))),
% 7.21/7.09 inference(equality_inference,[],[959])).
% 7.21/7.09 cnf(2012,plain,
% 7.21/7.09 (~P78(x20121,f3(a84),x20122)+P77(f86(x20121,f3(a84)))),
% 7.21/7.09 inference(equality_inference,[],[966])).
% 7.21/7.09 cnf(2034,plain,
% 7.21/7.09 (P77(f86(f28(a82,f35(a83,f3(a83))),f3(a82)))),
% 7.21/7.09 inference(equality_inference,[],[1053])).
% 7.21/7.09 cnf(2035,plain,
% 7.21/7.09 (P77(f86(f29(a84,f19(a84,f3(a84))),f16(a84)))),
% 7.21/7.09 inference(equality_inference,[],[1054])).
% 7.21/7.09 cnf(2044,plain,
% 7.21/7.09 (E(f20(a83,f86(f86(f24(a83),f3(a83)),x20441),f86(f86(f24(a83),f3(a83)),x20442)),f3(a83))),
% 7.21/7.09 inference(equality_inference,[],[1131])).
% 7.21/7.09 cnf(2046,plain,
% 7.21/7.09 (E(x20461,f86(f86(f23(a83),f22(a83,x20461,x20462)),x20462))+~P77(f86(f28(a83,x20462),x20461))),
% 7.21/7.09 inference(equality_inference,[],[1143])).
% 7.21/7.09 cnf(2049,plain,
% 7.21/7.09 (P77(f86(f29(a84,x20491),f86(f86(f23(a84),x20491),f16(a84))))),
% 7.21/7.09 inference(equality_inference,[],[1174])).
% 7.21/7.09 cnf(2053,plain,
% 7.21/7.09 (P77(f86(f29(a83,f3(a83)),f86(f86(f31(a83),x20531),f3(a83))))),
% 7.21/7.09 inference(equality_inference,[],[1182])).
% 7.21/7.09 cnf(2057,plain,
% 7.21/7.09 (P77(f86(x20571,f20(a83,x20572,f3(a83))))+~P77(f86(x20571,f3(a83)))),
% 7.21/7.09 inference(equality_inference,[],[1204])).
% 7.21/7.09 cnf(2063,plain,
% 7.21/7.09 (~P77(f86(x20631,f20(a83,x20632,f3(a83))))+P77(f86(x20631,f3(a83)))),
% 7.21/7.09 inference(equality_inference,[],[1324])).
% 7.21/7.09 cnf(2064,plain,
% 7.21/7.09 (~P77(f86(f29(a82,f3(a82)),f86(f86(f24(a82),f3(a82)),f3(a82))))),
% 7.21/7.09 inference(equality_inference,[],[1341])).
% 7.21/7.09 cnf(2066,plain,
% 7.21/7.09 (P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x20661)),f3(a83))))),
% 7.21/7.09 inference(equality_inference,[],[1363])).
% 7.21/7.09 cnf(2068,plain,
% 7.21/7.09 (P77(f86(x20681,x20682))+~P77(f86(x20681,f22(a83,f86(f86(f23(a83),x20683),x20682),x20683)))),
% 7.21/7.09 inference(equality_inference,[],[1374])).
% 7.21/7.09 cnf(2072,plain,
% 7.21/7.09 (E(x20721,f3(a83))+~P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,f3(a84))),x20721)))),
% 7.21/7.09 inference(equality_inference,[],[1551])).
% 7.21/7.09 cnf(2084,plain,
% 7.21/7.09 (~P77(f86(f28(a83,x20841),x20841))+E(x20842,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x20841,x20841)),x20843)),x20842))),
% 7.21/7.09 inference(equality_inference,[],[1875])).
% 7.21/7.09 cnf(2085,plain,
% 7.21/7.09 (~P77(f86(f28(a83,x20851),x20851))+E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x20851,x20851)),x20852)),x20853),x20853)),
% 7.21/7.09 inference(equality_inference,[],[1876])).
% 7.21/7.09 cnf(2094,plain,
% 7.21/7.09 (~P77(f86(f29(a82,f3(a82)),f86(f86(f23(a82),a123),f16(a82))))),
% 7.21/7.09 inference(scs_inference,[],[694,1942])).
% 7.21/7.09 cnf(2095,plain,
% 7.21/7.09 (P77(f86(f28(a82,f19(a82,f86(a5,f86(a124,x20951)))),f86(f86(f23(a82),a123),f16(a82))))),
% 7.21/7.09 inference(rename_variables,[],[694])).
% 7.21/7.09 cnf(2096,plain,
% 7.21/7.09 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x20961),x20962),x20961)),x20962))),
% 7.21/7.09 inference(scs_inference,[],[694,568,1942,2068])).
% 7.21/7.09 cnf(2097,plain,
% 7.21/7.09 (P77(f86(f28(a82,x20971),x20971))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2106,plain,
% 7.21/7.09 (~E(f86(f86(f23(a83),x21061),f16(a83)),x21061)),
% 7.21/7.09 inference(rename_variables,[],[727])).
% 7.21/7.09 cnf(2108,plain,
% 7.21/7.09 (~E(f16(a83),f3(a83))),
% 7.21/7.09 inference(scs_inference,[],[694,724,727,2106,568,1942,2068,813,814,815,816,840])).
% 7.21/7.09 cnf(2109,plain,
% 7.21/7.09 (~E(f86(f86(f23(a83),x21091),f16(a83)),x21091)),
% 7.21/7.09 inference(rename_variables,[],[727])).
% 7.21/7.09 cnf(2119,plain,
% 7.21/7.09 (~E(x21191,f86(f86(f23(a83),f86(f86(f23(a83),x21191),f16(a83))),x21192))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,724,727,2106,568,655,743,1942,2068,813,814,815,816,840,953,958,959,962,998])).
% 7.21/7.09 cnf(2124,plain,
% 7.21/7.09 (~P77(f86(f29(a83,x21241),x21241))),
% 7.21/7.09 inference(rename_variables,[],[735])).
% 7.21/7.09 cnf(2126,plain,
% 7.21/7.09 (E(f16(a83),f86(f86(f23(a83),f3(a83)),f16(a83)))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,724,727,2106,550,568,735,655,743,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094])).
% 7.21/7.09 cnf(2129,plain,
% 7.21/7.09 (~E(f86(f86(f23(a83),x21291),f86(f86(f23(a83),x21292),f16(a83))),x21292)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,724,727,2106,550,568,735,655,743,741,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173])).
% 7.21/7.09 cnf(2130,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x21301),x21302)),x21302))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2132,plain,
% 7.21/7.09 (~E(f86(f86(f23(a84),x21321),f16(a84)),x21321)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2009,724,727,2106,550,568,735,655,743,741,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174])).
% 7.21/7.09 cnf(2133,plain,
% 7.21/7.09 (~P77(f86(f29(a84,x21331),x21331))),
% 7.21/7.09 inference(rename_variables,[],[2009])).
% 7.21/7.09 cnf(2136,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x21361),x21362)),x21362))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2143,plain,
% 7.21/7.09 (P77(f86(f28(a82,x21431),x21431))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2146,plain,
% 7.21/7.09 (~P77(f86(f29(a82,x21461),x21461))),
% 7.21/7.09 inference(rename_variables,[],[2007])).
% 7.21/7.09 cnf(2148,plain,
% 7.21/7.09 (~P77(f86(f29(a84,f3(a84)),f86(f86(f31(a84),f19(a84,f3(a84))),f86(f86(f23(a83),f3(a83)),f16(a83)))))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,724,727,2106,2109,550,568,2097,569,735,2124,655,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072])).
% 7.21/7.09 cnf(2149,plain,
% 7.21/7.09 (~E(f86(f86(f23(a83),x21491),f16(a83)),x21491)),
% 7.21/7.09 inference(rename_variables,[],[727])).
% 7.21/7.09 cnf(2151,plain,
% 7.21/7.09 (E(x21511,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x21512,x21512)),x21513)),x21511))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,724,727,2106,2109,550,568,2097,569,735,2124,655,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084])).
% 7.21/7.09 cnf(2153,plain,
% 7.21/7.09 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x21531,x21531)),x21532)),x21533),x21533)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,724,727,2106,2109,550,568,2097,569,735,2124,655,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085])).
% 7.21/7.09 cnf(2157,plain,
% 7.21/7.09 (~E(f86(f86(f23(a83),x21571),f16(a83)),x21571)),
% 7.21/7.09 inference(rename_variables,[],[727])).
% 7.21/7.09 cnf(2160,plain,
% 7.21/7.09 (P77(f86(f28(a83,f20(a83,x21601,x21602)),x21601))),
% 7.21/7.09 inference(rename_variables,[],[670])).
% 7.21/7.09 cnf(2174,plain,
% 7.21/7.09 (E(f86(f86(f23(a83),x21741),f66(x21741,x21741)),x21741)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,2006,724,727,2106,2109,2149,550,568,2097,569,570,735,2124,655,669,670,624,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066])).
% 7.21/7.09 cnf(2176,plain,
% 7.21/7.09 (E(f86(f86(f23(a83),x21761),f87(x21761,x21761)),x21761)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,2006,724,727,2106,2109,2149,550,568,2097,569,570,735,2124,655,669,670,624,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067])).
% 7.21/7.09 cnf(2182,plain,
% 7.21/7.09 (P77(f86(f28(a82,f3(a82)),f34(f16(a82))))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2009,2006,724,727,2106,2109,2149,550,568,2097,2143,569,570,735,2124,655,669,670,624,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128])).
% 7.21/7.09 cnf(2183,plain,
% 7.21/7.09 (P77(f86(f28(a82,x21831),x21831))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2186,plain,
% 7.21/7.09 (P77(f86(f28(a82,x21861),x21861))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2204,plain,
% 7.21/7.09 (~P77(f86(f29(a83,x22041),x22041))),
% 7.21/7.09 inference(rename_variables,[],[735])).
% 7.21/7.09 cnf(2207,plain,
% 7.21/7.09 (P77(f86(f28(a82,x22071),x22071))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2210,plain,
% 7.21/7.09 (P77(f86(f28(a82,x22101),x22101))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2212,plain,
% 7.21/7.09 (~P78(f29(a82,f20(a84,x22121,x22122)),x22122,x22121)),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,569,570,735,2124,655,669,670,624,743,741,2130,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227])).
% 7.21/7.09 cnf(2213,plain,
% 7.21/7.09 (~P77(f86(f29(a82,x22131),x22131))),
% 7.21/7.09 inference(rename_variables,[],[2007])).
% 7.21/7.09 cnf(2226,plain,
% 7.21/7.09 (P77(f86(f28(a82,x22261),x22261))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2229,plain,
% 7.21/7.09 (P77(f86(f28(a82,x22291),x22291))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2232,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x22321),x22322)),x22322))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2234,plain,
% 7.21/7.09 (P77(f86(f28(a83,x22341),f33(f35(a83,x22341))))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,576,743,741,2130,2136,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256])).
% 7.21/7.09 cnf(2235,plain,
% 7.21/7.09 (P77(f86(f28(a82,x22351),x22351))),
% 7.21/7.09 inference(rename_variables,[],[568])).
% 7.21/7.09 cnf(2240,plain,
% 7.21/7.09 (~P77(f86(f28(a83,f86(f86(f23(a83),x22401),f16(a83))),x22401))),
% 7.21/7.09 inference(rename_variables,[],[743])).
% 7.21/7.09 cnf(2243,plain,
% 7.21/7.09 (~P77(f86(f28(a83,f86(f86(f23(a83),x22431),f16(a83))),x22431))),
% 7.21/7.09 inference(rename_variables,[],[743])).
% 7.21/7.09 cnf(2245,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x22451),f86(f86(f23(a83),x22452),x22453))),x22453))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,576,743,2240,741,2130,2136,2232,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270])).
% 7.21/7.09 cnf(2246,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x22461),x22462)),x22462))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2249,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x22491),x22492)),x22492))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2251,plain,
% 7.21/7.09 (~P77(f86(f28(a83,f86(f86(f23(a83),x22511),f86(f86(f23(a83),x22512),f16(a83)))),x22512))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288])).
% 7.21/7.09 cnf(2252,plain,
% 7.21/7.09 (~P77(f86(f29(a83,f86(f86(f23(a83),x22521),x22522)),x22522))),
% 7.21/7.09 inference(rename_variables,[],[741])).
% 7.21/7.09 cnf(2254,plain,
% 7.21/7.09 (~P77(f86(f28(a84,f86(f86(f23(a84),x22541),f16(a84))),x22541))),
% 7.21/7.09 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291])).
% 7.21/7.10 cnf(2255,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x22551),x22551))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2257,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),x22571),f16(a84))),x22571))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292])).
% 7.21/7.10 cnf(2258,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x22581),x22581))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2263,plain,
% 7.21/7.10 (P77(f86(f28(a82,x22631),f35(a83,f26(x22631))))),
% 7.21/7.10 inference(rename_variables,[],[599])).
% 7.21/7.10 cnf(2267,plain,
% 7.21/7.10 (P77(f86(f29(a83,f3(a83)),f22(a83,f86(f86(f31(a83),x22671),f3(a83)),f3(a83))))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,569,570,735,2124,691,655,669,670,624,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322])).
% 7.21/7.10 cnf(2271,plain,
% 7.21/7.10 (P78(f28(a82,f20(a84,x22711,x22712)),x22712,x22711)),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,691,655,669,670,624,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342])).
% 7.21/7.10 cnf(2272,plain,
% 7.21/7.10 (P77(f86(f28(a82,x22721),x22721))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2280,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x22801,f16(a84))),x22801))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,691,655,669,670,624,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436])).
% 7.21/7.10 cnf(2281,plain,
% 7.21/7.10 (P77(f86(f28(a84,x22811),x22811))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2285,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x22851),f22(a83,x22851,x22852)))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,2204,691,655,669,670,624,683,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439])).
% 7.21/7.10 cnf(2291,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f23(a83),x22911),x22912)),x22913)),x22912))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,2204,691,655,669,670,624,683,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566])).
% 7.21/7.10 cnf(2293,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f22(a84,f86(f86(f23(a84),x22931),f16(a84)),f16(a84))),x22931))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,2204,691,655,669,670,624,683,599,576,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568])).
% 7.21/7.10 cnf(2296,plain,
% 7.21/7.10 (P77(f86(f28(a83,x22961),f86(f86(f24(a83),x22961),x22961)))),
% 7.21/7.10 inference(rename_variables,[],[621])).
% 7.21/7.10 cnf(2299,plain,
% 7.21/7.10 (P77(f86(f28(a83,x22991),f86(f86(f24(a83),x22991),x22991)))),
% 7.21/7.10 inference(rename_variables,[],[621])).
% 7.21/7.10 cnf(2302,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23021),f86(f86(f24(a83),x23021),x23021)))),
% 7.21/7.10 inference(rename_variables,[],[621])).
% 7.21/7.10 cnf(2306,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f24(a83),f86(f86(f23(a83),x23061),f16(a83))),f86(f86(f23(a83),x23061),f16(a83)))),x23061))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,2204,691,655,669,670,624,683,599,576,621,2296,2299,2302,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635])).
% 7.21/7.10 cnf(2310,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x23101),x23101))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2312,plain,
% 7.21/7.10 (P77(f86(f28(a83,f22(a83,f86(f86(f23(a83),x23121),x23122),x23122)),x23121))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,570,735,2124,2204,691,655,669,670,624,683,599,576,621,2296,2299,2302,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670])).
% 7.21/7.10 cnf(2313,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23131),x23131))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2318,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23181),x23181))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2320,plain,
% 7.21/7.10 (P77(f86(f29(a83,x23201),f86(f86(f23(a83),f86(f86(f23(a83),x23201),f16(a83))),x23202)))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,570,735,2124,2204,691,655,669,670,624,696,683,599,576,621,2296,2299,2302,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759])).
% 7.21/7.10 cnf(2324,plain,
% 7.21/7.10 (P77(f86(f28(a82,x23241),f35(a83,f26(x23241))))),
% 7.21/7.10 inference(rename_variables,[],[599])).
% 7.21/7.10 cnf(2326,plain,
% 7.21/7.10 (P77(f86(f28(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f31(a83),f86(f86(f23(a83),f3(a83)),f16(a83))),x23261)))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843])).
% 7.21/7.10 cnf(2327,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23271),x23271))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2330,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x23301),f16(a83))),x23301))),
% 7.21/7.10 inference(rename_variables,[],[743])).
% 7.21/7.10 cnf(2332,plain,
% 7.21/7.10 (E(f3(a83),f20(a83,x23321,f3(a83)))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085])).
% 7.21/7.10 cnf(2334,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x23341),f16(a83))),x23342),x23341)),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,372,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927])).
% 7.21/7.10 cnf(2340,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23401),f86(f86(f23(a83),f86(f86(f23(a83),x23402),x23401)),f16(a83))))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,326,372,380,383,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028])).
% 7.21/7.10 cnf(2342,plain,
% 7.21/7.10 (P77(f86(f29(a83,f86(f86(f24(a83),x23421),f3(a83))),f86(f86(f23(a83),f3(a83)),f16(a83))))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,326,372,380,383,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033])).
% 7.21/7.10 cnf(2344,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f23(a83),x23441),f16(a83))),x23442)),x23441))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,326,372,380,383,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097])).
% 7.21/7.10 cnf(2348,plain,
% 7.21/7.10 (P77(f86(f28(a82,f35(a83,f3(a83))),f35(a83,x23481)))),
% 7.21/7.10 inference(scs_inference,[],[694,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,326,372,380,383,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,595,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217])).
% 7.21/7.10 cnf(2352,plain,
% 7.21/7.10 (P77(f86(f28(a82,f86(a5,f86(a124,x23521))),f86(f86(f23(a82),a123),f16(a82))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,320,326,372,380,383,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,569,2313,2318,570,735,2124,2204,595,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277])).
% 7.21/7.10 cnf(2355,plain,
% 7.21/7.10 (P77(f86(f28(a82,x23551),x23551))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2359,plain,
% 7.21/7.10 (P77(f86(f28(a83,x23591),f86(f86(f23(a83),x23592),f86(f86(f23(a83),x23591),f16(a83)))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,320,326,355,372,380,383,474,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,569,2313,2318,570,735,2124,2204,595,691,655,669,670,624,696,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775])).
% 7.21/7.10 cnf(2361,plain,
% 7.21/7.10 (P77(f86(f29(a82,x23611),f35(a83,f33(f86(f86(f23(a82),x23611),f16(a82))))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2009,2133,2255,2006,2034,724,727,2106,2109,2149,733,320,326,354,355,372,380,383,474,550,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,569,2313,2318,570,735,2124,2204,595,691,655,669,670,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779])).
% 7.21/7.10 cnf(2362,plain,
% 7.21/7.10 (P77(f86(f29(a82,x23621),f86(f86(f23(a82),f35(a83,f33(x23621))),f16(a82))))),
% 7.21/7.10 inference(rename_variables,[],[676])).
% 7.21/7.10 cnf(2365,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x23651),x23651))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2374,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x23741),f16(a83)),x23741)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2377,plain,
% 7.21/7.10 (E(f86(f6(x23771,x23772,x23773),x23774),x23773)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2380,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x23801),f16(a83)),x23801)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2385,plain,
% 7.21/7.10 (E(f22(a83,f3(a83),x23851),f3(a83))),
% 7.21/7.10 inference(rename_variables,[],[565])).
% 7.21/7.10 cnf(2388,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x23881),x23881))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2390,plain,
% 7.21/7.10 (~E(x23901,f86(f86(f23(a84),x23901),f16(a84)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2213,2365,2009,2133,2255,2006,2049,2034,1989,724,727,2106,2109,2149,2157,2374,733,320,322,326,354,355,367,372,380,381,383,392,474,711,593,550,565,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,569,2313,2318,570,735,2124,2204,595,691,655,669,670,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978])).
% 7.21/7.10 cnf(2398,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x23981),f16(a83)),x23981)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2405,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x24051),f16(a83)),x24051)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2407,plain,
% 7.21/7.10 (~E(x24071,f86(f86(f23(a83),f86(f86(f23(a84),f22(a83,x24071,f22(a83,x24071,x24072))),f16(a84))),f22(a83,x24071,x24072)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2213,2365,2009,2133,2255,2006,2049,2034,2035,1989,724,727,2106,2109,2149,2157,2374,2380,2398,733,320,322,326,354,355,367,372,380,381,383,384,392,474,711,593,550,565,2385,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,569,2313,2318,570,735,2124,2204,595,596,691,655,669,670,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138])).
% 7.21/7.10 cnf(2409,plain,
% 7.21/7.10 (~E(f22(a83,f86(f86(f23(a83),f86(f86(f23(a83),x24091),f3(a83))),f16(a83)),f3(a83)),x24091)),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2213,2365,2009,2133,2255,2006,2049,2034,2035,1989,724,727,2106,2109,2149,2157,2374,2380,2398,2405,733,320,322,326,354,355,367,372,380,381,383,384,392,474,711,593,550,565,2385,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,569,2313,2318,570,735,2124,2204,595,596,691,655,669,670,578,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143])).
% 7.21/7.10 cnf(2410,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x24101))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2411,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x24111),f16(a83)),x24111)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2414,plain,
% 7.21/7.10 (P77(f86(f28(a82,x24141),x24141))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2419,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x24191),x24191))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2422,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x24221),x24221))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2425,plain,
% 7.21/7.10 (P77(f86(f29(a83,x24251),f86(f86(f23(a83),x24251),f16(a83))))),
% 7.21/7.10 inference(rename_variables,[],[624])).
% 7.21/7.10 cnf(2428,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x24281),x24281))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2430,plain,
% 7.21/7.10 (~E(f86(f86(f23(a84),f86(f86(f24(a84),x24301),x24302)),f16(a84)),f86(f86(f23(a84),f86(f86(f24(a84),x24303),x24302)),f86(f86(f24(a84),f22(a84,x24301,x24303)),x24302)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,727,2106,2109,2149,2157,2374,2380,2398,2405,733,320,322,326,354,355,367,372,380,381,383,384,392,474,481,711,593,550,565,2385,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,569,2313,2318,570,735,2124,2204,2310,2422,595,596,691,655,669,670,578,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881])).
% 7.21/7.10 cnf(2433,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x24331),f16(a83)),x24331)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2435,plain,
% 7.21/7.10 (E(f86(f6(x24351,x24352,x24353),x24354),x24353)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2437,plain,
% 7.21/7.10 (P78(f28(a82,f20(a84,x24371,f86(f86(f24(a83),f3(a83)),x24372))),f86(f86(f24(a83),f3(a83)),x24373),x24371)),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,322,326,354,355,367,372,380,381,383,384,392,474,481,711,593,2377,550,565,2385,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,569,2313,2318,570,735,2124,2204,2310,2422,595,596,691,655,669,670,578,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245])).
% 7.21/7.10 cnf(2439,plain,
% 7.21/7.10 (P2(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),f3(a83)),f16(a83)))),x24391)),a82),f7(a85,a82,a83,a10,f7(a83,a85,a83,a124,a1)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,322,326,354,355,367,372,380,381,383,384,392,474,481,711,593,2377,550,565,2385,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,569,2313,2318,570,735,2124,2204,2310,2422,595,596,691,655,669,670,578,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273])).
% 7.21/7.10 cnf(2440,plain,
% 7.21/7.10 (P3(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),f3(a83)),f16(a83)))),x24401)),a82),f7(a85,a82,a83,a10,f7(a83,a85,a83,a124,a1)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,322,326,354,355,367,372,380,381,383,384,392,474,481,711,593,2377,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,569,2313,2318,570,735,2124,2204,2310,2422,595,596,691,655,669,670,578,624,696,676,683,599,2263,576,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275])).
% 7.21/7.10 cnf(2442,plain,
% 7.21/7.10 (E(f86(f6(x24421,x24422,x24423),x24424),x24423)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2446,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x24461),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(2449,plain,
% 7.21/7.10 (P77(f86(f28(a82,x24491),x24491))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2456,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x24561))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2459,plain,
% 7.21/7.10 (P77(f86(f28(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x24591)),x24592)))),
% 7.21/7.10 inference(rename_variables,[],[662])).
% 7.21/7.10 cnf(2462,plain,
% 7.21/7.10 (P77(f86(f28(a82,f3(a82)),f35(a83,x24621)))),
% 7.21/7.10 inference(rename_variables,[],[595])).
% 7.21/7.10 cnf(2465,plain,
% 7.21/7.10 (P77(f86(f28(a83,f22(a83,x24651,x24652)),x24651))),
% 7.21/7.10 inference(rename_variables,[],[669])).
% 7.21/7.10 cnf(2466,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x24661))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2472,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f31(a84),f19(a84,x24721)),f3(a83))),f3(a84)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,321,322,326,327,354,355,367,371,372,373,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,569,2313,2318,570,735,2124,2204,2310,2422,595,596,738,691,585,655,669,670,578,2410,2456,624,696,676,683,599,2263,576,662,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161])).
% 7.21/7.10 cnf(2478,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f16(a84)),f3(a84)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,569,2313,2318,570,735,2124,2204,2310,2422,595,596,611,738,691,585,586,655,669,670,578,2410,2456,624,696,676,683,599,2263,576,662,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166])).
% 7.21/7.10 cnf(2481,plain,
% 7.21/7.10 (P77(f86(f28(a82,f3(a82)),f22(a82,f86(f86(f37(a82),f35(a83,x24811)),f35(a83,x24812)),f35(a83,f20(a83,x24811,x24812)))))),
% 7.21/7.10 inference(rename_variables,[],[707])).
% 7.21/7.10 cnf(2484,plain,
% 7.21/7.10 (P77(f86(f28(a82,f3(a82)),f22(a82,f86(f86(f37(a82),f35(a83,x24841)),f35(a83,x24842)),f35(a83,f20(a83,x24841,x24842)))))),
% 7.21/7.10 inference(rename_variables,[],[707])).
% 7.21/7.10 cnf(2496,plain,
% 7.21/7.10 (P77(f86(f28(a82,x24961),x24961))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2499,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x24991),x24991))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2502,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25021),x25021))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2509,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x25091),x25091))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2510,plain,
% 7.21/7.10 (P77(f86(f28(a82,x25101),x25101))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2517,plain,
% 7.21/7.10 (P77(f86(f28(a82,x25171),x25171))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2519,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),x25191),f102(x25191,x25191,f29(a82,f22(a83,x25191,x25191)))),x25191)),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,569,2313,2318,570,2281,735,2124,2204,2310,2422,2428,2509,595,596,611,738,715,691,585,586,655,669,670,578,2410,2456,624,696,676,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366])).
% 7.21/7.10 cnf(2520,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25201),x25201))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2523,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25231),x25231))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2526,plain,
% 7.21/7.10 (P77(f86(f28(a82,x25261),x25261))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2533,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25331),x25331))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2536,plain,
% 7.21/7.10 (P77(f86(f29(a82,x25361),f86(f86(f23(a82),f35(a83,f33(x25361))),f16(a82))))),
% 7.21/7.10 inference(rename_variables,[],[676])).
% 7.21/7.10 cnf(2541,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25411),x25411))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2544,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25441),x25441))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2546,plain,
% 7.21/7.10 (P77(f86(f28(a84,f3(a84)),f20(a84,f3(a84),f86(f86(f31(a84),f19(a84,x25461)),f3(a83)))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,316,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,569,2313,2318,2327,570,2281,2502,2541,2544,735,2124,2204,2310,2422,2428,2509,595,596,611,738,715,691,585,586,655,669,670,578,2410,2456,624,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458])).
% 7.21/7.10 cnf(2547,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25471),x25471))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2549,plain,
% 7.21/7.10 (P77(f86(f29(a83,f3(a83)),f16(a83)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2009,2133,2255,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,733,316,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,569,2313,2318,2327,570,2281,2502,2541,2544,735,2124,2204,2310,2422,2428,2509,595,596,611,738,715,691,585,586,655,669,670,578,2410,2456,624,2425,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478])).
% 7.21/7.10 cnf(2550,plain,
% 7.21/7.10 (P77(f86(f29(a83,x25501),f86(f86(f23(a83),x25501),f16(a83))))),
% 7.21/7.10 inference(rename_variables,[],[624])).
% 7.21/7.10 cnf(2551,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x25511),x25511))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2555,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x25551),f16(a83)),x25551)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2558,plain,
% 7.21/7.10 (P77(f86(f28(a82,x25581),x25581))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2559,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x25591),f16(a83)),x25591)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2562,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25621),x25621))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2563,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x25631),f16(a83)),x25631)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2566,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x25661),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(2571,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x25711),x25711))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2572,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25721),x25721))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2575,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25751),x25751))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2578,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25781),x25781))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2580,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f31(a83),x25801),f3(a83))),f86(f86(f23(a83),f3(a83)),f16(a83))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2009,2133,2255,2258,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,570,2281,2502,2541,2544,2547,735,2124,2204,2310,2422,2428,2509,2551,595,596,611,738,2446,715,691,585,586,655,669,670,578,2410,2456,624,2425,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546])).
% 7.21/7.10 cnf(2581,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x25811),x25811))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2583,plain,
% 7.21/7.10 (P77(f86(f28(a84,f20(a84,f3(a84),f86(f86(f31(a84),f19(a84,x25831)),f3(a83)))),f3(a84)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2009,2133,2255,2258,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,354,355,367,371,372,373,379,380,381,383,384,392,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,595,596,611,738,2446,715,691,585,586,655,669,670,578,2410,2456,624,2425,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581])).
% 7.21/7.10 cnf(2584,plain,
% 7.21/7.10 (P77(f86(f28(a84,x25841),x25841))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2589,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f19(a82,x25891)),f16(a82))),x25891))),
% 7.21/7.10 inference(rename_variables,[],[744])).
% 7.21/7.10 cnf(2594,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x25941),x25941))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2597,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x25971),x25971))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2601,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26011),f86(f86(f23(a83),f22(a83,x26011,x26011)),x26011)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,371,372,373,379,380,381,383,384,392,427,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,595,596,611,738,2446,715,691,585,586,655,669,670,578,2410,2456,624,2425,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,744,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685])).
% 7.21/7.10 cnf(2604,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26041),x26041))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2607,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x26071),f16(a83))),x26071))),
% 7.21/7.10 inference(rename_variables,[],[743])).
% 7.21/7.10 cnf(2608,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x26081))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2611,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x26111),x26111))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2613,plain,
% 7.21/7.10 (P77(f86(f28(a83,x26131),f22(a83,f86(f86(f23(a83),x26131),f3(a83)),f3(a83))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,371,372,373,379,380,381,383,384,392,427,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,715,691,585,586,655,669,670,578,2410,2456,2466,2608,624,2425,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,744,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755])).
% 7.21/7.10 cnf(2614,plain,
% 7.21/7.10 (P77(f86(f28(a83,x26141),x26141))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2615,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x26151))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2620,plain,
% 7.21/7.10 (P77(f86(f29(a83,x26201),f86(f86(f23(a83),x26201),f16(a83))))),
% 7.21/7.10 inference(rename_variables,[],[624])).
% 7.21/7.10 cnf(2621,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26211),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(2623,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x26231),x26232)),f16(a83))),f86(f86(f23(a83),f86(f86(f24(a83),x26231),x26232)),f86(f86(f24(a83),f22(a83,x26231,x26231)),x26232))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,371,372,373,379,380,381,383,384,392,427,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,715,691,585,586,655,669,670,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,744,672,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963])).
% 7.21/7.10 cnf(2624,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x26241),f16(a83))),x26241))),
% 7.21/7.10 inference(rename_variables,[],[743])).
% 7.21/7.10 cnf(2627,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26271),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(2632,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),f86(f86(f24(a84),x26321),x26322)),f16(a84))),f86(f86(f23(a84),f86(f86(f24(a84),x26323),x26322)),f86(f86(f24(a84),f22(a84,x26321,x26323)),x26322))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,715,691,585,586,655,669,670,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967])).
% 7.21/7.10 cnf(2638,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26381),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(2640,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x26401),f16(a84)),f16(a84))),x26401))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,2627,715,739,691,585,586,655,669,670,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049])).
% 7.21/7.10 cnf(2648,plain,
% 7.21/7.10 (E(f3(a84),f20(a84,f3(a84),f3(a84)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,576,662,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115])).
% 7.21/7.10 cnf(2651,plain,
% 7.21/7.10 (P77(f86(f28(a84,f3(a84)),f86(f86(f31(a84),f19(a84,x26511)),x26512)))),
% 7.21/7.10 inference(rename_variables,[],[662])).
% 7.21/7.10 cnf(2653,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x26531),f16(a83))),f22(a83,x26531,x26532)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248])).
% 7.21/7.10 cnf(2656,plain,
% 7.21/7.10 (P77(f86(f28(a82,f19(a82,f86(a5,f86(a124,x26561)))),f35(a83,f26(f86(f86(f23(a82),a123),f16(a82))))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249])).
% 7.21/7.10 cnf(2659,plain,
% 7.21/7.10 (P77(f86(f29(a82,f35(a83,f3(a83))),f86(f86(f23(a82),f16(a82)),f19(a82,x26591))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250])).
% 7.21/7.10 cnf(2662,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26621),x26621))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2664,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f16(a82)),f19(a82,x26641))),f3(a82)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,596,611,710,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252])).
% 7.21/7.10 cnf(2665,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26651),x26651))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2668,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26681),x26681))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2670,plain,
% 7.21/7.10 (P77(f86(f29(a82,f3(a82)),f86(f86(f23(a82),f35(a83,f33(f35(a83,x26701)))),f16(a82))))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254])).
% 7.21/7.10 cnf(2671,plain,
% 7.21/7.10 (P77(f86(f29(a82,x26711),f86(f86(f23(a82),f35(a83,f33(x26711))),f16(a82))))),
% 7.21/7.10 inference(rename_variables,[],[676])).
% 7.21/7.10 cnf(2673,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),f22(a83,f3(a83),x26731)),f16(a83))),f22(a83,f22(a83,f3(a83),x26731),x26732)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2009,2133,2255,2258,2571,2597,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255])).
% 7.21/7.10 cnf(2675,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x26751),x26751))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(2677,plain,
% 7.21/7.10 (~E(f22(a84,f3(a84),f86(f86(f31(a84),f19(a84,x26771)),f3(a83))),f22(a84,x26772,x26772))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2009,2133,2255,2258,2571,2597,2611,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298])).
% 7.21/7.10 cnf(2679,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f24(a83),x26791),x26792)),f16(a83))),f86(f86(f24(a83),f22(a83,x26791,x26791)),x26792)))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2009,2133,2255,2258,2571,2597,2611,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,316,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471])).
% 7.21/7.10 cnf(2680,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x26801))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2683,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26831),x26831))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2685,plain,
% 7.21/7.10 (~P77(f86(f28(a82,f86(f86(f23(a82),f86(f86(f23(a82),f16(a82)),f19(a82,x26851))),x26852)),x26852))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2009,2133,2255,2258,2571,2597,2611,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,316,317,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473])).
% 7.21/7.10 cnf(2686,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26861),x26861))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2688,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x26881)),x26881))),
% 7.21/7.10 inference(scs_inference,[],[694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,316,317,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,492,711,593,2377,2435,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474])).
% 7.21/7.10 cnf(2689,plain,
% 7.21/7.10 (~P77(f86(f29(a82,x26891),x26891))),
% 7.21/7.10 inference(rename_variables,[],[2007])).
% 7.21/7.10 cnf(2690,plain,
% 7.21/7.10 (P77(f86(f28(a82,x26901),x26901))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2695,plain,
% 7.21/7.10 (E(f86(f6(x26951,x26952,x26953),x26954),x26953)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2697,plain,
% 7.21/7.10 (~E(f20(a84,f16(a84),f16(a84)),f3(a84))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,316,317,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,484,492,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,569,2313,2318,2327,2614,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,624,2425,2550,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141])).
% 7.21/7.10 cnf(2698,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x26981),x26981))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(2704,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27041),x27041))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2711,plain,
% 7.21/7.10 (P77(f86(f28(a82,x27111),x27111))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2713,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f3(a83)),f54(f86(f86(f31(a83),x27131),f3(a83)),f29(a83,f3(a83)))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,437,474,475,481,484,492,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,569,2313,2318,2327,2614,2704,570,2281,2502,2541,2544,2547,2572,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,624,2425,2550,2620,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238])).
% 7.21/7.10 cnf(2715,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27151),x27151))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2718,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x27181))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2721,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x27211))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2724,plain,
% 7.21/7.10 (P77(f86(f28(a82,x27241),x27241))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2727,plain,
% 7.21/7.10 (P77(f86(f28(a84,x27271),x27271))),
% 7.21/7.10 inference(rename_variables,[],[570])).
% 7.21/7.10 cnf(2734,plain,
% 7.21/7.10 (P77(f86(f28(a82,x27341),x27341))),
% 7.21/7.10 inference(rename_variables,[],[568])).
% 7.21/7.10 cnf(2736,plain,
% 7.21/7.10 (P77(f86(f28(a82,f86(f86(f24(a82),f3(a82)),f3(a82))),f3(a82)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,367,368,371,372,373,379,380,381,382,383,384,392,427,433,437,457,458,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,570,2281,2502,2541,2544,2547,2572,2584,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,624,2425,2550,2620,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618])).
% 7.21/7.10 cnf(2740,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27401),x27401))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2747,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f16(a83)),f86(f86(f24(a83),f22(a83,f3(a83),f3(a83))),x27471)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,358,367,368,371,372,373,379,380,381,382,383,384,392,427,433,434,437,444,445,457,458,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,624,2425,2550,2620,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694])).
% 7.21/7.10 cnf(2748,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27481),x27481))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2750,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f31(a83),x27501),f3(a83))),x27502)),x27502))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,358,361,367,368,371,372,373,379,380,381,382,383,384,392,427,433,434,437,444,445,457,458,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,624,2425,2550,2620,695,696,676,2362,2536,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695])).
% 7.21/7.10 cnf(2753,plain,
% 7.21/7.10 (~P77(f86(f28(a82,f19(a82,f86(f86(f23(a82),x27531),f86(f86(f23(a82),f35(a83,f33(f16(a82)))),f16(a82))))),x27531))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,358,360,361,367,368,371,372,373,379,380,381,382,383,384,392,427,433,434,437,444,445,457,458,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,624,2425,2550,2620,695,696,676,2362,2536,2671,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696])).
% 7.21/7.10 cnf(2755,plain,
% 7.21/7.10 (P77(f86(f29(a82,x27551),f86(f86(f23(a82),f35(a83,f33(x27551))),f16(a82))))),
% 7.21/7.10 inference(rename_variables,[],[676])).
% 7.21/7.10 cnf(2762,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f22(a82,f16(a82),f19(a82,f22(a82,f3(a82),f16(a82))))),f3(a82)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,733,314,315,316,317,318,320,321,322,326,327,353,354,355,358,360,361,367,368,371,372,373,379,380,381,382,383,384,392,427,433,434,437,444,445,457,458,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896])).
% 7.21/7.10 cnf(2763,plain,
% 7.21/7.10 (P77(f86(f29(a82,f3(a82)),f86(f86(f23(a82),f16(a82)),f19(a82,x27631))))),
% 7.21/7.10 inference(rename_variables,[],[655])).
% 7.21/7.10 cnf(2770,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),x27701),f16(a83)),x27701)),
% 7.21/7.10 inference(rename_variables,[],[727])).
% 7.21/7.10 cnf(2773,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x27731))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(2774,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27741),x27741))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2783,plain,
% 7.21/7.10 (P77(f86(f28(a83,x27831),x27831))),
% 7.21/7.10 inference(rename_variables,[],[569])).
% 7.21/7.10 cnf(2788,plain,
% 7.21/7.10 (~E(f86(f86(f23(a82),f16(a82)),f19(a82,f22(a82,f3(a82),f16(a82)))),f3(a82))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905])).
% 7.21/7.10 cnf(2790,plain,
% 7.21/7.10 (P77(f86(f28(a82,f3(a82)),f86(f86(f23(a82),f16(a82)),f19(a82,f22(a82,f3(a82),f16(a82))))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005])).
% 7.21/7.10 cnf(2798,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),f22(a83,x27981,f3(a83))),f3(a83))),f16(a83)),x27981)),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30])).
% 7.21/7.10 cnf(2807,plain,
% 7.21/7.10 (P77(f86(f28(a84,f3(a84)),f86(f86(f23(a84),f16(a84)),f16(a84))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007])).
% 7.21/7.10 cnf(2809,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),f3(a83)),f16(a83))),f86(f86(f24(a83),x28091),f3(a83))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078])).
% 7.21/7.10 cnf(2813,plain,
% 7.21/7.10 (P77(f86(f29(a83,x28131),f86(f86(f23(a83),f33(f35(a83,x28131))),f16(a83))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315])).
% 7.21/7.10 cnf(2819,plain,
% 7.21/7.10 (P77(f86(f28(a83,f86(f86(f24(a83),f22(a83,f3(a83),f3(a83))),f16(a83))),f86(f86(f24(a83),f3(a83)),f16(a83))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430])).
% 7.21/7.10 cnf(2821,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f3(a83)),f86(f86(f24(a83),x28211),f3(a83))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463])).
% 7.21/7.10 cnf(2823,plain,
% 7.21/7.10 (~P77(f86(f28(a84,f22(a84,f16(a84),f3(a84))),f3(a84)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676])).
% 7.21/7.10 cnf(2831,plain,
% 7.21/7.10 (~E(f86(f86(f23(a84),f86(f86(f24(a84),x28311),x28312)),f86(f86(f23(a84),f86(f86(f24(a84),x28313),x28312)),f16(a84))),f86(f86(f23(a84),f86(f86(f24(a84),x28314),x28312)),f86(f86(f24(a84),f22(a84,x28313,f22(a84,x28314,x28311))),x28312)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,2763,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676,1009,1081,1093,1880])).
% 7.21/7.10 cnf(2836,plain,
% 7.21/7.10 (E(f86(f6(x28361,x28362,x28363),x28364),x28363)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2838,plain,
% 7.21/7.10 (E(f86(f6(x28381,x28382,x28383),x28384),x28383)),
% 7.21/7.10 inference(rename_variables,[],[593])).
% 7.21/7.10 cnf(2839,plain,
% 7.21/7.10 (P4(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,f86(f86(f23(a83),f3(a83)),f16(a83)),f86(f86(f23(a83),f3(a83)),f16(a83)))),x28391)),a82),f86(f31(a82),f22(a82,f86(f86(f37(a82),f35(a83,x28392)),f35(a83,x28393)),f35(a83,f20(a83,x28392,x28393)))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,2695,2836,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,2763,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676,1009,1081,1093,1880,1893,226,243,270])).
% 7.21/7.10 cnf(2842,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f16(a84)),f86(f86(f24(a84),f22(a84,x28421,x28421)),x28422)))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,356,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,2695,2836,2838,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,2763,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676,1009,1081,1093,1880,1893,226,243,270,278,1631])).
% 7.21/7.10 cnf(2846,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f31(a83),x28461),f3(a83))),f86(f86(f23(a83),x28462),f3(a83)))),x28462))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,356,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,2695,2836,2838,550,565,2385,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,2783,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,2763,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676,1009,1081,1093,1880,1893,226,243,270,278,1631,1672,1470])).
% 7.21/7.10 cnf(2849,plain,
% 7.21/7.10 (P77(f86(f29(a84,f3(a84)),f86(f86(f23(a84),f16(a84)),f16(a84))))),
% 7.21/7.10 inference(scs_inference,[],[722,694,2095,2005,2053,2066,2064,2007,2146,2213,2365,2388,2419,2499,2520,2523,2533,2562,2575,2578,2594,2662,2665,2668,2683,2686,2689,2009,2133,2255,2258,2571,2597,2611,2698,2006,2049,2034,2035,2044,1989,724,725,727,2106,2109,2149,2157,2374,2380,2398,2405,2411,2433,2555,2559,2563,2770,733,533,314,315,316,317,318,319,320,321,322,326,327,353,354,355,356,358,360,361,363,366,367,368,371,372,373,379,380,381,382,383,384,392,404,407,411,414,427,433,434,437,444,445,457,458,466,469,474,475,481,484,492,499,711,593,2377,2435,2442,2695,2836,2838,550,565,2385,566,579,718,717,594,568,2097,2143,2183,2186,2207,2210,2226,2229,2235,2272,2355,2414,2449,2496,2510,2517,2526,2558,2690,2711,2724,2734,569,2313,2318,2327,2614,2704,2715,2740,2748,2774,2783,570,2281,2502,2541,2544,2547,2572,2584,2727,735,2124,2204,2310,2422,2428,2509,2551,2581,2604,2675,595,2462,596,611,710,657,738,2446,2566,2621,2627,2638,715,739,691,585,586,655,2763,669,2465,670,2160,578,2410,2456,2466,2608,2615,2680,2718,2721,2773,624,2425,2550,2620,695,696,676,2362,2536,2671,2755,683,599,2263,2324,576,662,2459,2651,707,2481,2484,621,2296,2299,2302,743,2240,2243,2330,2607,2624,744,2589,672,641,741,2130,2136,2232,2246,2249,2252,1942,2068,813,814,815,816,840,953,958,959,962,998,1016,1021,1094,1173,1174,1180,1352,2046,2057,2063,2072,2084,2085,2,7,8,967,969,970,1010,1047,1048,1060,1066,1067,1091,1117,1128,1129,1172,1178,1179,1185,1188,1189,1190,1198,1200,1201,1227,1231,1233,1234,1239,1240,1241,1242,1245,1256,1262,1266,1268,1270,1272,1288,1291,1292,1312,1314,1321,1322,1338,1342,1353,1370,1371,1436,1437,1439,1482,1560,1566,1568,1577,1578,1602,1626,1635,1661,1670,1678,1719,1759,1839,1843,1860,1085,927,929,981,1028,1033,1097,1099,1217,1261,1277,1374,1677,1775,1779,1882,227,830,831,832,834,837,930,940,966,978,979,1004,1019,1051,1100,1138,1143,1204,1243,1324,1365,1527,1644,1881,3,237,244,245,246,273,275,295,881,1012,1063,1064,1069,1088,1089,1132,1133,1134,1157,1161,1164,1165,1166,1211,1212,1213,1237,1273,1274,1301,1320,1333,1334,1335,1344,1346,1351,1359,1366,1367,1372,1382,1392,1420,1438,1450,1451,1457,1458,1478,1481,1489,1502,1523,1534,1537,1543,1544,1546,1581,1595,1633,1667,1668,1669,1671,1685,1687,1735,1736,1755,1768,1886,1963,1964,1965,1967,1039,1045,1049,1107,1109,1115,1202,1248,1249,1250,1251,1252,1253,1254,1255,1298,1471,1472,1473,1474,1058,1090,1141,1244,1310,1170,1191,1238,1283,1414,1454,1455,1469,1508,1605,1618,1620,1621,1622,1694,1695,1696,1697,1712,1896,1347,1393,1609,952,1323,1509,2003,905,1005,903,908,911,30,924,925,968,1006,1007,1078,1079,1315,1361,1386,1430,1463,1676,1009,1081,1093,1880,1893,226,243,270,278,1631,1672,1470,1135])).
% 7.21/7.10 cnf(2869,plain,
% 7.21/7.10 (~P77(f86(f28(a82,f19(a82,f86(f86(f23(a82),x28691),f86(f86(f23(a82),f35(a83,f33(f16(a82)))),f16(a82))))),x28691))),
% 7.21/7.10 inference(rename_variables,[],[2753])).
% 7.21/7.10 cnf(2874,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f22(a84,f86(f86(f23(a84),x28741),f16(a84)),f16(a84))),x28741))),
% 7.21/7.10 inference(rename_variables,[],[2293])).
% 7.21/7.10 cnf(2879,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x28791,x28791)),x28792)),x28793),x28793)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(2887,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),f86(f86(f23(a83),x28871),f16(a83))),x28872)),x28871))),
% 7.21/7.10 inference(rename_variables,[],[2344])).
% 7.21/7.10 cnf(2902,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),x29021),f16(a84))),x29021))),
% 7.21/7.10 inference(rename_variables,[],[2257])).
% 7.21/7.10 cnf(2907,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x29071),x29072),x29071)),x29072))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(2914,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),x29141),x29142)),x29141))),
% 7.21/7.10 inference(rename_variables,[],[742])).
% 7.21/7.10 cnf(2917,plain,
% 7.21/7.10 (P77(f86(f28(a82,x29171),f35(a83,f26(x29171))))),
% 7.21/7.10 inference(rename_variables,[],[599])).
% 7.21/7.10 cnf(2930,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x29301),f16(a83))),x29302),x29301)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(2933,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f31(a83),x29331),f3(a83))),x29332)),x29332))),
% 7.21/7.10 inference(rename_variables,[],[2750])).
% 7.21/7.10 cnf(2936,plain,
% 7.21/7.10 (P77(f86(f28(a83,x29361),f86(f86(f23(a83),x29361),x29362)))),
% 7.21/7.10 inference(rename_variables,[],[620])).
% 7.21/7.10 cnf(2945,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x29451),f16(a84)),f16(a84))),x29451))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(2948,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x29481),f16(a83))),x29482),x29481)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(2951,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),x29511),f16(a84))),x29511))),
% 7.21/7.10 inference(rename_variables,[],[2257])).
% 7.21/7.10 cnf(2954,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),x29541),x29542)),x29541))),
% 7.21/7.10 inference(rename_variables,[],[742])).
% 7.21/7.10 cnf(2957,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x29571),f86(f86(f23(a83),f22(a83,x29571,x29571)),x29571)))),
% 7.21/7.10 inference(rename_variables,[],[2601])).
% 7.21/7.10 cnf(2964,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x29641),f16(a83))),x29642),x29641)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(2971,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x29711)),x29711))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(2985,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),x29851),f87(x29851,x29851)),x29851)),
% 7.21/7.10 inference(rename_variables,[],[2176])).
% 7.21/7.10 cnf(2988,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x29881,f16(a84))),x29881))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(2995,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x29951),x29952),x29951)),x29952))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3004,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x30041),f16(a83))),f22(a83,x30041,x30042)))),
% 7.21/7.10 inference(rename_variables,[],[2653])).
% 7.21/7.10 cnf(3011,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x30111),f16(a83))),x30112),x30111)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3023,plain,
% 7.21/7.10 (P77(f86(f28(a82,x30231),f35(a83,f26(x30231))))),
% 7.21/7.10 inference(rename_variables,[],[599])).
% 7.21/7.10 cnf(3032,plain,
% 7.21/7.10 (P77(f86(f29(a84,x30321),f86(f86(f23(a84),x30321),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3035,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x30351)),x30351))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3038,plain,
% 7.21/7.10 (P77(f86(f29(a82,x30381),f35(a83,f33(f86(f86(f23(a82),x30381),f16(a82))))))),
% 7.21/7.10 inference(rename_variables,[],[2361])).
% 7.21/7.10 cnf(3045,plain,
% 7.21/7.10 (P77(f86(f28(a83,x30451),f86(f86(f23(a83),x30451),x30452)))),
% 7.21/7.10 inference(rename_variables,[],[620])).
% 7.21/7.10 cnf(3073,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),f86(f86(f31(a83),x30731),f3(a83))),x30732)),x30732))),
% 7.21/7.10 inference(rename_variables,[],[2750])).
% 7.21/7.10 cnf(3086,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),x30861),f16(a84))),x30861))),
% 7.21/7.10 inference(rename_variables,[],[2257])).
% 7.21/7.10 cnf(3113,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x31131),f16(a83))),x31132),x31131)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3116,plain,
% 7.21/7.10 (E(f22(a83,x31161,f86(f86(f23(a83),x31161),x31162)),f3(a83))),
% 7.21/7.10 inference(rename_variables,[],[598])).
% 7.21/7.10 cnf(3119,plain,
% 7.21/7.10 (E(x31191,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31192,x31192)),x31193)),x31191))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3121,plain,
% 7.21/7.10 (E(x31211,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31212,x31212)),x31213)),x31211))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3123,plain,
% 7.21/7.10 (E(x31231,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31232,x31232)),x31233)),x31231))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3125,plain,
% 7.21/7.10 (E(x31251,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31252,x31252)),x31253)),x31251))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3127,plain,
% 7.21/7.10 (E(x31271,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31272,x31272)),x31273)),x31271))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3129,plain,
% 7.21/7.10 (E(x31291,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31292,x31292)),x31293)),x31291))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3131,plain,
% 7.21/7.10 (E(x31311,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31312,x31312)),x31313)),x31311))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3133,plain,
% 7.21/7.10 (E(x31331,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31332,x31332)),x31333)),x31331))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3135,plain,
% 7.21/7.10 (E(x31351,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31352,x31352)),x31353)),x31351))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3137,plain,
% 7.21/7.10 (E(x31371,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31372,x31372)),x31373)),x31371))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3139,plain,
% 7.21/7.10 (E(x31391,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31392,x31392)),x31393)),x31391))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3141,plain,
% 7.21/7.10 (E(x31411,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31412,x31412)),x31413)),x31411))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3143,plain,
% 7.21/7.10 (E(x31431,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31432,x31432)),x31433)),x31431))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3145,plain,
% 7.21/7.10 (E(x31451,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31452,x31452)),x31453)),x31451))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3147,plain,
% 7.21/7.10 (E(x31471,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31472,x31472)),x31473)),x31471))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3149,plain,
% 7.21/7.10 (E(x31491,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31492,x31492)),x31493)),x31491))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3151,plain,
% 7.21/7.10 (E(x31511,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31512,x31512)),x31513)),x31511))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3153,plain,
% 7.21/7.10 (E(x31531,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31532,x31532)),x31533)),x31531))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3155,plain,
% 7.21/7.10 (E(x31551,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31552,x31552)),x31553)),x31551))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3157,plain,
% 7.21/7.10 (E(x31571,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31572,x31572)),x31573)),x31571))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3159,plain,
% 7.21/7.10 (E(x31591,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31592,x31592)),x31593)),x31591))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3161,plain,
% 7.21/7.10 (E(x31611,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31612,x31612)),x31613)),x31611))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3163,plain,
% 7.21/7.10 (E(x31631,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31632,x31632)),x31633)),x31631))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3165,plain,
% 7.21/7.10 (E(x31651,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31652,x31652)),x31653)),x31651))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3167,plain,
% 7.21/7.10 (E(x31671,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31672,x31672)),x31673)),x31671))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3169,plain,
% 7.21/7.10 (E(x31691,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31692,x31692)),x31693)),x31691))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3171,plain,
% 7.21/7.10 (E(x31711,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31712,x31712)),x31713)),x31711))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3173,plain,
% 7.21/7.10 (E(x31731,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31732,x31732)),x31733)),x31731))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3175,plain,
% 7.21/7.10 (E(x31751,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31752,x31752)),x31753)),x31751))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3177,plain,
% 7.21/7.10 (E(x31771,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31772,x31772)),x31773)),x31771))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3179,plain,
% 7.21/7.10 (E(x31791,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31792,x31792)),x31793)),x31791))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3181,plain,
% 7.21/7.10 (E(x31811,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31812,x31812)),x31813)),x31811))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3183,plain,
% 7.21/7.10 (E(x31831,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31832,x31832)),x31833)),x31831))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3185,plain,
% 7.21/7.10 (E(x31851,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31852,x31852)),x31853)),x31851))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3187,plain,
% 7.21/7.10 (E(x31871,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31872,x31872)),x31873)),x31871))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3189,plain,
% 7.21/7.10 (E(x31891,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31892,x31892)),x31893)),x31891))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3191,plain,
% 7.21/7.10 (E(x31911,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31912,x31912)),x31913)),x31911))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3193,plain,
% 7.21/7.10 (E(x31931,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31932,x31932)),x31933)),x31931))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3195,plain,
% 7.21/7.10 (E(x31951,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31952,x31952)),x31953)),x31951))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3197,plain,
% 7.21/7.10 (E(x31971,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31972,x31972)),x31973)),x31971))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3199,plain,
% 7.21/7.10 (E(x31991,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x31992,x31992)),x31993)),x31991))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3201,plain,
% 7.21/7.10 (E(x32011,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32012,x32012)),x32013)),x32011))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3203,plain,
% 7.21/7.10 (E(x32031,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32032,x32032)),x32033)),x32031))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3205,plain,
% 7.21/7.10 (E(x32051,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32052,x32052)),x32053)),x32051))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3207,plain,
% 7.21/7.10 (E(x32071,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32072,x32072)),x32073)),x32071))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3209,plain,
% 7.21/7.10 (E(x32091,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32092,x32092)),x32093)),x32091))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3211,plain,
% 7.21/7.10 (E(x32111,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32112,x32112)),x32113)),x32111))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3213,plain,
% 7.21/7.10 (E(x32131,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32132,x32132)),x32133)),x32131))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3215,plain,
% 7.21/7.10 (E(x32151,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32152,x32152)),x32153)),x32151))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3217,plain,
% 7.21/7.10 (E(x32171,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32172,x32172)),x32173)),x32171))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3219,plain,
% 7.21/7.10 (E(x32191,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32192,x32192)),x32193)),x32191))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3221,plain,
% 7.21/7.10 (E(x32211,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32212,x32212)),x32213)),x32211))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3223,plain,
% 7.21/7.10 (E(x32231,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32232,x32232)),x32233)),x32231))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3225,plain,
% 7.21/7.10 (E(x32251,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32252,x32252)),x32253)),x32251))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3227,plain,
% 7.21/7.10 (E(x32271,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32272,x32272)),x32273)),x32271))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3229,plain,
% 7.21/7.10 (E(x32291,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32292,x32292)),x32293)),x32291))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3231,plain,
% 7.21/7.10 (E(x32311,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32312,x32312)),x32313)),x32311))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3233,plain,
% 7.21/7.10 (E(x32331,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32332,x32332)),x32333)),x32331))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3235,plain,
% 7.21/7.10 (E(x32351,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32352,x32352)),x32353)),x32351))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3237,plain,
% 7.21/7.10 (E(x32371,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32372,x32372)),x32373)),x32371))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3239,plain,
% 7.21/7.10 (E(x32391,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32392,x32392)),x32393)),x32391))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3241,plain,
% 7.21/7.10 (E(x32411,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32412,x32412)),x32413)),x32411))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3243,plain,
% 7.21/7.10 (E(x32431,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32432,x32432)),x32433)),x32431))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3245,plain,
% 7.21/7.10 (E(x32451,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32452,x32452)),x32453)),x32451))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3247,plain,
% 7.21/7.10 (E(x32471,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x32472,x32472)),x32473)),x32471))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3249,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x32491),f16(a84)),f16(a84))),x32491))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3250,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32501,f16(a84))),x32501))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3253,plain,
% 7.21/7.10 (P77(f86(f28(a83,f22(a83,f86(f86(f23(a83),x32531),x32532),x32532)),x32531))),
% 7.21/7.10 inference(rename_variables,[],[2312])).
% 7.21/7.10 cnf(3256,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x32561),f16(a84)),f16(a84))),x32561))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3259,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x32591),x32592),x32591)),x32592))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3260,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x32601),f16(a83))),x32602),x32601)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3267,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x32671),f16(a84)),f16(a84))),x32671))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3268,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32681,f16(a84))),x32681))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3271,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32711,f16(a84))),x32711))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3274,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32741,f16(a84))),x32741))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3277,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32771,f16(a84))),x32771))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3280,plain,
% 7.21/7.10 (P77(f86(f29(a84,x32801),f86(f86(f23(a84),x32801),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3281,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32811,f16(a84))),x32811))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3284,plain,
% 7.21/7.10 (P77(f86(f29(a84,x32841),f86(f86(f23(a84),x32841),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3287,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32871,f16(a84))),x32871))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3290,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x32901,f16(a84))),x32901))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3293,plain,
% 7.21/7.10 (~P77(f86(f28(a84,f86(f86(f23(a84),x32931),f16(a84))),x32931))),
% 7.21/7.10 inference(rename_variables,[],[2254])).
% 7.21/7.10 cnf(3299,plain,
% 7.21/7.10 (P77(f86(f29(a84,x32991),f86(f86(f23(a84),x32991),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3312,plain,
% 7.21/7.10 (E(x33121,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x33122,x33122)),x33123)),x33121))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3313,plain,
% 7.21/7.10 (P77(f86(f28(a83,x33131),f86(f86(f23(a83),x33132),f86(f86(f23(a83),x33131),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3316,plain,
% 7.21/7.10 (~P77(f86(f28(a84,f86(f86(f23(a84),x33161),f16(a84))),x33161))),
% 7.21/7.10 inference(rename_variables,[],[2254])).
% 7.21/7.10 cnf(3321,plain,
% 7.21/7.10 (P77(f86(f29(a83,f3(a83)),f86(f86(f23(a83),x33211),f16(a83))))),
% 7.21/7.10 inference(rename_variables,[],[628])).
% 7.21/7.10 cnf(3324,plain,
% 7.21/7.10 (P77(f86(f29(a83,f3(a83)),f86(f86(f23(a83),x33241),f16(a83))))),
% 7.21/7.10 inference(rename_variables,[],[628])).
% 7.21/7.10 cnf(3325,plain,
% 7.21/7.10 (P77(f86(f28(a83,f22(a83,f86(f86(f23(a83),x33251),x33252),x33252)),x33251))),
% 7.21/7.10 inference(rename_variables,[],[2312])).
% 7.21/7.10 cnf(3332,plain,
% 7.21/7.10 (P77(f86(f28(a83,x33321),f86(f86(f23(a83),x33322),f86(f86(f23(a83),x33321),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3335,plain,
% 7.21/7.10 (P77(f86(f28(a83,x33351),f86(f86(f23(a83),x33352),f86(f86(f23(a83),x33351),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3344,plain,
% 7.21/7.10 (P77(f86(f28(a83,f22(a83,f86(f86(f23(a83),x33441),x33442),x33442)),x33441))),
% 7.21/7.10 inference(rename_variables,[],[2312])).
% 7.21/7.10 cnf(3347,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x33471)),x33471))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3352,plain,
% 7.21/7.10 (P77(f86(f29(a84,x33521),f86(f86(f23(a84),x33521),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3359,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x33591),f16(a83))),x33592),x33591)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3362,plain,
% 7.21/7.10 (~P77(f86(f29(a83,f86(f86(f23(a83),x33621),x33622)),x33621))),
% 7.21/7.10 inference(rename_variables,[],[742])).
% 7.21/7.10 cnf(3365,plain,
% 7.21/7.10 (P77(f86(f29(a84,x33651),f86(f86(f23(a84),x33651),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3366,plain,
% 7.21/7.10 (~P77(f86(f28(a84,f86(f86(f23(a84),x33661),f16(a84))),x33661))),
% 7.21/7.10 inference(rename_variables,[],[2254])).
% 7.21/7.10 cnf(3378,plain,
% 7.21/7.10 (P77(f86(f28(a83,x33781),f86(f86(f23(a83),x33782),f86(f86(f23(a83),x33781),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3379,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x33791,x33791)),x33792)),x33793),x33793)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(3384,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x33841),x33842),x33841)),x33842))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3390,plain,
% 7.21/7.10 (P77(f86(f29(a82,x33901),f35(a83,f33(f86(f86(f23(a82),x33901),f16(a82))))))),
% 7.21/7.10 inference(rename_variables,[],[2361])).
% 7.21/7.10 cnf(3397,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x33971),x33971))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(3409,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x34091)),x34091))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3410,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x34101,x34101)),x34102)),x34103),x34103)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(3420,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x34201),f16(a84)),f16(a84))),x34201))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3426,plain,
% 7.21/7.10 (~E(f86(f86(f23(a84),x34261),f16(a84)),x34261)),
% 7.21/7.10 inference(rename_variables,[],[2132])).
% 7.21/7.10 cnf(3437,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x34371),x34372),x34371)),x34372))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3440,plain,
% 7.21/7.10 (~P77(f86(f28(a83,f86(f86(f23(a83),x34401),f16(a83))),f22(a83,x34401,x34402)))),
% 7.21/7.10 inference(rename_variables,[],[2653])).
% 7.21/7.10 cnf(3441,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x34411))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(3449,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x34491),f16(a83))),x34492),x34491)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3452,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x34521),x34522),x34521)),x34522))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3453,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x34531,x34531)),x34532)),x34533),x34533)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(3456,plain,
% 7.21/7.10 (P77(f86(f29(a82,x34561),f35(a83,f33(f86(f86(f23(a82),x34561),f16(a82))))))),
% 7.21/7.10 inference(rename_variables,[],[2361])).
% 7.21/7.10 cnf(3464,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x34641,f16(a84))),x34641))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3465,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x34651),f16(a83))),x34652),x34651)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3472,plain,
% 7.21/7.10 (E(x34721,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x34722,x34722)),x34723)),x34721))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3474,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x34741),f16(a84)),f16(a84))),x34741))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3475,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x34751),f16(a83))),x34752),x34751)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3478,plain,
% 7.21/7.10 (P78(f28(a82,f20(a84,x34781,f86(f86(f24(a83),f3(a83)),x34782))),f86(f86(f24(a83),f3(a83)),x34783),x34781)),
% 7.21/7.10 inference(rename_variables,[],[2437])).
% 7.21/7.10 cnf(3483,plain,
% 7.21/7.10 (P77(f86(f29(a84,x34831),f86(f86(f23(a84),x34831),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3486,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x34861)),x34861))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3487,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x34871,x34871)),x34872)),x34873),x34873)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(3492,plain,
% 7.21/7.10 (P77(f86(f28(a83,x34921),f86(f86(f23(a83),x34922),x34921)))),
% 7.21/7.10 inference(rename_variables,[],[619])).
% 7.21/7.10 cnf(3493,plain,
% 7.21/7.10 (P77(f86(f28(a83,x34931),f86(f86(f23(a83),x34932),f86(f86(f23(a83),x34931),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3496,plain,
% 7.21/7.10 (E(f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x34961,x34961)),x34962)),x34963),x34963)),
% 7.21/7.10 inference(rename_variables,[],[2153])).
% 7.21/7.10 cnf(3499,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x34991),f3(a83)))),
% 7.21/7.10 inference(rename_variables,[],[738])).
% 7.21/7.10 cnf(3502,plain,
% 7.21/7.10 (P77(f86(f29(a84,x35021),f86(f86(f23(a84),x35021),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3508,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35081)),x35081))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3513,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35131)),x35131))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3516,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35161)),x35161))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3521,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x35211),f16(a83))),x35212),x35211)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3528,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35281)),x35281))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3535,plain,
% 7.21/7.10 (E(x35351,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x35352,x35352)),x35353)),x35351))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3537,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x35371))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(3540,plain,
% 7.21/7.10 (~P77(f86(f29(a83,x35401),x35401))),
% 7.21/7.10 inference(rename_variables,[],[735])).
% 7.21/7.10 cnf(3554,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x35541),f16(a83))),x35542),x35541)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3559,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35591)),x35591))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3568,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x35681),f16(a83))),x35682),x35681)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3575,plain,
% 7.21/7.10 (P77(f86(f29(a83,x35751),f86(f86(f23(a83),f86(f86(f23(a83),x35751),f16(a83))),x35752)))),
% 7.21/7.10 inference(rename_variables,[],[2320])).
% 7.21/7.10 cnf(3576,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x35761),f16(a83))),x35762),x35761)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3583,plain,
% 7.21/7.10 (E(x35831,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x35832,x35832)),x35833)),x35831))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3591,plain,
% 7.21/7.10 (P78(f28(a82,f20(a84,x35911,f86(f86(f24(a83),f3(a83)),x35912))),f86(f86(f24(a83),f3(a83)),x35913),x35911)),
% 7.21/7.10 inference(rename_variables,[],[2437])).
% 7.21/7.10 cnf(3593,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x35931)),x35931))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3601,plain,
% 7.21/7.10 (E(x36011,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36012,x36012)),x36013)),x36011))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3603,plain,
% 7.21/7.10 (E(x36031,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36032,x36032)),x36033)),x36031))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3606,plain,
% 7.21/7.10 (~P78(f29(a82,f20(a84,x36061,x36062)),x36062,x36061)),
% 7.21/7.10 inference(rename_variables,[],[2212])).
% 7.21/7.10 cnf(3608,plain,
% 7.21/7.10 (E(x36081,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36082,x36082)),x36083)),x36081))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3610,plain,
% 7.21/7.10 (E(x36101,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36102,x36102)),x36103)),x36101))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3612,plain,
% 7.21/7.10 (E(x36121,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36122,x36122)),x36123)),x36121))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3614,plain,
% 7.21/7.10 (E(x36141,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36142,x36142)),x36143)),x36141))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3616,plain,
% 7.21/7.10 (E(x36161,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36162,x36162)),x36163)),x36161))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3618,plain,
% 7.21/7.10 (E(x36181,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36182,x36182)),x36183)),x36181))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3620,plain,
% 7.21/7.10 (E(x36201,f86(f86(f23(a83),f86(f86(f24(a83),f22(a83,x36202,x36202)),x36203)),x36201))),
% 7.21/7.10 inference(rename_variables,[],[2151])).
% 7.21/7.10 cnf(3624,plain,
% 7.21/7.10 (~P77(f86(f28(a82,f86(f86(f23(a82),f86(f86(f23(a82),f16(a82)),f19(a82,x36241))),x36242)),x36242))),
% 7.21/7.10 inference(rename_variables,[],[2685])).
% 7.21/7.10 cnf(3627,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f86(f86(f23(a84),x36271),f16(a84))),x36271))),
% 7.21/7.10 inference(rename_variables,[],[2257])).
% 7.21/7.10 cnf(3628,plain,
% 7.21/7.10 (~E(f86(f86(f23(a84),x36281),f16(a84)),x36281)),
% 7.21/7.10 inference(rename_variables,[],[2132])).
% 7.21/7.10 cnf(3629,plain,
% 7.21/7.10 (~P78(f29(a82,f20(a84,x36291,x36292)),x36292,x36291)),
% 7.21/7.10 inference(rename_variables,[],[2212])).
% 7.21/7.10 cnf(3638,plain,
% 7.21/7.10 (P77(f86(f29(a84,f22(a84,x36381,f16(a84))),x36381))),
% 7.21/7.10 inference(rename_variables,[],[2280])).
% 7.21/7.10 cnf(3644,plain,
% 7.21/7.10 (P77(f86(f29(a84,x36441),f86(f86(f23(a84),x36441),f16(a84))))),
% 7.21/7.10 inference(rename_variables,[],[2049])).
% 7.21/7.10 cnf(3649,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x36491)),x36491))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3655,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x36551)),x36551))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3658,plain,
% 7.21/7.10 (~P77(f86(f29(a84,f16(a84)),f86(f86(f24(a84),f22(a84,x36581,x36581)),x36582)))),
% 7.21/7.10 inference(rename_variables,[],[2842])).
% 7.21/7.10 cnf(3661,plain,
% 7.21/7.10 (~P77(f86(f29(a84,x36611),x36611))),
% 7.21/7.10 inference(rename_variables,[],[2009])).
% 7.21/7.10 cnf(3662,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x36621),x36622),x36621)),x36622))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3665,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x36651),x36652),x36651)),x36652))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3668,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x36681),x36682),x36681)),x36682))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3671,plain,
% 7.21/7.10 (P77(f86(f28(a82,f22(a83,f86(f86(f23(a83),x36711),x36712),x36711)),x36712))),
% 7.21/7.10 inference(rename_variables,[],[2096])).
% 7.21/7.10 cnf(3674,plain,
% 7.21/7.10 (P77(f86(f28(a83,x36741),f86(f86(f23(a83),x36742),x36741)))),
% 7.21/7.10 inference(rename_variables,[],[619])).
% 7.21/7.10 cnf(3681,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x36811),f16(a84)),f16(a84))),x36811))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3684,plain,
% 7.21/7.10 (~P77(f86(f28(a82,f86(f86(f23(a82),f86(f86(f23(a82),f16(a82)),f19(a82,x36841))),x36842)),x36842))),
% 7.21/7.10 inference(rename_variables,[],[2685])).
% 7.21/7.10 cnf(3692,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x36921),f16(a84)),f16(a84))),x36921))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3695,plain,
% 7.21/7.10 (P77(f86(f29(a82,f35(a83,f3(a83))),f86(f86(f23(a82),f16(a82)),f19(a82,x36951))))),
% 7.21/7.10 inference(rename_variables,[],[2659])).
% 7.21/7.10 cnf(3702,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x37021),f16(a84)),f16(a84))),x37021))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3711,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x37111)),x37111))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3718,plain,
% 7.21/7.10 (P77(f86(f28(a83,x37181),f86(f86(f23(a83),x37182),f86(f86(f23(a83),x37181),f16(a83)))))),
% 7.21/7.10 inference(rename_variables,[],[2359])).
% 7.21/7.10 cnf(3719,plain,
% 7.21/7.10 (~E(f86(f86(f23(a83),f86(f86(f23(a83),x37191),f16(a83))),x37192),x37191)),
% 7.21/7.10 inference(rename_variables,[],[2334])).
% 7.21/7.10 cnf(3722,plain,
% 7.21/7.10 (~P77(f86(f29(a82,f86(f86(f23(a82),f3(a82)),x37221)),x37221))),
% 7.21/7.10 inference(rename_variables,[],[2688])).
% 7.21/7.10 cnf(3728,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x37281),f16(a84)),f16(a84))),x37281))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3735,plain,
% 7.21/7.10 (P77(f86(f28(a83,f3(a83)),x37351))),
% 7.21/7.10 inference(rename_variables,[],[578])).
% 7.21/7.10 cnf(3736,plain,
% 7.21/7.10 (~E(f86(f86(f23(a84),x37361),f16(a84)),x37361)),
% 7.21/7.10 inference(rename_variables,[],[2132])).
% 7.21/7.10 cnf(3739,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x37391),f16(a84)),f16(a84))),x37391))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3742,plain,
% 7.21/7.10 (P77(f86(f28(a84,f22(a84,f86(f86(f23(a84),x37421),f16(a84)),f16(a84))),x37421))),
% 7.21/7.10 inference(rename_variables,[],[2640])).
% 7.21/7.10 cnf(3776,plain,
% 7.21/7.10 ($false),
% 7.21/7.10 inference(scs_inference,[],[311,2332,2094,2790,2334,2930,2948,2964,3011,3113,3260,3359,3449,3465,3475,3521,3554,3568,3576,3719,2670,2688,2971,3035,3347,3409,3486,3508,3513,3516,3528,3559,3593,3649,3655,3711,3722,2685,3624,3684,2344,2887,2846,2342,2096,2907,2995,3259,3384,3437,3452,3662,3665,3668,3671,2640,2945,3249,3256,3267,3420,3474,3681,3692,3702,3728,3739,3742,2359,3313,3332,3335,3378,3493,3718,2659,3695,2679,2352,2348,2340,2653,3004,3440,2673,2361,3038,3390,3456,2656,2664,2823,2677,2648,2788,2053,2004,2066,2049,3032,3280,3284,3299,3352,3365,3483,3502,3644,2108,2126,2849,2148,2151,3119,3121,3123,3125,3127,3129,3131,3133,3135,3137,3139,3141,3143,3145,3147,3149,3151,3153,3155,3157,3159,3161,3163,3165,3167,3169,3171,3173,3175,3177,3179,3181,3183,3185,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205,3207,3209,3211,3213,3215,3217,3219,3221,3223,3225,3227,3229,3231,3233,3235,3237,3239,3241,3243,3245,3247,3312,3472,3535,3583,3601,3603,3608,3610,3612,3614,3616,3618,3620,2153,2879,3379,3410,3453,3487,3496,2119,2407,2129,2831,2132,3426,3628,3736,2390,2798,2437,3478,3591,2430,2409,2440,2439,2839,2697,2007,2009,3397,3661,727,725,742,2914,2954,3362,628,3321,3324,555,575,620,2936,3045,585,597,619,3492,3674,598,3116,2326,2807,2713,2842,3658,2747,2174,2176,2985,2519,2821,2809,2182,2291,2245,2750,2933,3073,2306,2251,2267,2546,2580,2254,3293,3316,3366,2257,2902,2951,3086,3627,2320,3575,2601,2957,2312,3253,3325,3344,2280,2988,3250,3268,3271,3274,3277,3281,3287,3290,3464,3638,2623,2753,2869,2293,2874,2632,2234,2212,3606,3629,2271,2819,2813,2285,2549,2613,2478,2736,2472,2583,2762,526,323,328,330,332,334,336,340,344,348,352,357,362,364,369,374,375,385,386,391,394,396,398,402,405,408,412,415,419,423,428,431,435,436,438,441,446,448,451,453,454,459,461,463,467,470,476,479,482,485,488,491,493,495,497,500,501,503,505,506,507,510,514,518,692,698,572,314,319,321,355,356,358,361,367,390,433,434,437,444,458,474,566,579,735,3540,738,3499,670,578,3441,3537,3735,599,2917,3023,316,327,353,360,373,379,392,445,475,570,595,683,315,318,372,380,381,382,481,317,320,371,384,383,326,31,1142,1195,1488,1073,912,2012,1559,1567,1091,1188,1322,1016,1231,1007,1174,1048,1342,1021,1635,1180,1128,1430,968,1626,962,1178,814,1268,1577,903,953,998,1436,813,1292,1272,1245,1270,925,815,1047,1602,1227,1234,1312,840,2072,1262,911,2068,1439,908,2057,1200,1678,1661,1860,1201,1352,816,1079,958,1239,1173,1129,8,1067,1242,1353,2063,1315,1066,1010,1578,1288,1060,1437,1078,1482,959,1233,1117,1463,1185,1006,1370,1266,1190,2,1670,1759,1172,1291,2046,1256,905,1005,1338,1241,1198,1189,969,970,1240,1371,7,1082,234,235,236,238,241,242,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,271,272,274,276,277,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,1207,1218,1219,1360,1418,1452,1530,1582,1583,1585,1588,1689,1720,1966,1875,1216,1536,1627,1035,1036,1038,1876,1535,1693,1391,1440,1505,1638,1692,930,1450,881,1133,1544,1028,1237,1165,1667,832,1365,1534,1051,1457,1963,1138,1458,1217,1372,1438,1301,978,1736,1134,1164,1335,1595,1324,1775,1085,1157,1581,1964,1101,1143,927,1537,1374,1735,1261,1880,830,1204,1069,1089,1273,1489,1334,1064,278,1359,245,1676,1886,966,1033,1755,834,1012,1451,872,1366,1768,1420,1320,1097,3,1527,1063,1543,1274,929,237,1088,1344,837,979,1882,1019,1100,1333,1669,1668,1346,1523,831,1671,1161,1481,1351,1277,227,1546,981,1166,246,1367,1099,1677,270,232,244,226,273,229,295,243,233,275,228,1296,1357,1519,1673,1624,1625,1090,1255,1696,1253,1049,1191,1251,1620,1250,1618,1135,1621,1248,1244,1469,1454,1896,1249,1254,1474,1170,1298,1697,1115,1310,1252,1695,1622,1045,1414,1455,1107,1202,1712,1283,1039,1694,1141,1347,1348,2003,1323,24,964]),
% 7.21/7.10 ['proof']).
% 7.21/7.10 % SZS output end Proof
% 7.21/7.10 % Total time :5.570000s
%------------------------------------------------------------------------------