TSTP Solution File: SWW220+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW220+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n031.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 : Fri Sep 1 00:13:11 EDT 2023
% Result : Theorem 19.29s 19.54s
% Output : CNFRefutation 19.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW220+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 17:58:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 19.29/19.47 %-------------------------------------------
% 19.29/19.47 % File :CSE---1.6
% 19.29/19.47 % Problem :theBenchmark
% 19.29/19.47 % Transform :cnf
% 19.29/19.47 % Format :tptp:raw
% 19.29/19.47 % Command :java -jar mcs_scs.jar %d %s
% 19.29/19.47
% 19.29/19.47 % Result :Theorem 18.120000s
% 19.29/19.47 % Output :CNFRefutation 18.120000s
% 19.29/19.47 %-------------------------------------------
% 19.29/19.48 %------------------------------------------------------------------------------
% 19.29/19.48 % File : SWW220+1 : TPTP v8.1.2. Released v5.2.0.
% 19.29/19.48 % Domain : Software Verification
% 19.29/19.48 % Problem : Fundamental Theorem of Algebra 437256, 1000 axioms selected
% 19.29/19.48 % Version : Especial.
% 19.29/19.48 % English :
% 19.29/19.48
% 19.29/19.48 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 19.29/19.48 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 19.29/19.48 % Source : [Bla11]
% 19.29/19.48 % Names : fta_437256.1000.p [Bla11]
% 19.29/19.48
% 19.29/19.48 % Status : Theorem
% 19.29/19.48 % Rating : 0.56 v8.1.0, 0.58 v7.5.0, 0.66 v7.4.0, 0.63 v7.3.0, 0.59 v7.1.0, 0.57 v7.0.0, 0.70 v6.4.0, 0.69 v6.3.0, 0.75 v6.2.0, 0.76 v6.1.0, 0.73 v6.0.0, 0.83 v5.5.0, 0.81 v5.4.0, 0.86 v5.3.0, 0.85 v5.2.0
% 19.29/19.48 % Syntax : Number of formulae : 1270 ( 387 unt; 0 def)
% 19.29/19.48 % Number of atoms : 2995 ( 737 equ)
% 19.29/19.48 % Maximal formula atoms : 13 ( 2 avg)
% 19.29/19.48 % Number of connectives : 1885 ( 160 ~; 59 |; 117 &)
% 19.29/19.48 % ( 243 <=>;1306 =>; 0 <=; 0 <~>)
% 19.29/19.48 % Maximal formula depth : 13 ( 5 avg)
% 19.29/19.48 % Maximal term depth : 8 ( 2 avg)
% 19.29/19.48 % Number of predicates : 82 ( 81 usr; 1 prp; 0-5 aty)
% 19.29/19.48 % Number of functors : 38 ( 38 usr; 8 con; 0-5 aty)
% 19.29/19.48 % Number of variables : 2745 (2706 !; 39 ?)
% 19.29/19.48 % SPC : FOF_THM_RFO_SEQ
% 19.29/19.48
% 19.29/19.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 19.29/19.48 % 2011-03-01 11:37:55
% 19.29/19.48 %------------------------------------------------------------------------------
% 19.29/19.48 %----Relevant facts (997)
% 19.29/19.48 fof(fact_ext,axiom,
% 19.29/19.48 ! [V_ga_2,V_f_2] :
% 19.29/19.48 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_ga_2,B_x)
% 19.29/19.48 => V_f_2 = V_ga_2 ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_zero__less__norm__iff,axiom,
% 19.29/19.48 ! [V_x_2,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => ( 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))
% 19.29/19.48 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact__096EX_Af_Az_O_Asubseq_Af_A_G_A_IALL_Ae_0620_O_AEX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_J_096,axiom,
% 19.29/19.48 ? [B_f] :
% 19.29/19.48 ( c_SEQ_Osubseq(B_f)
% 19.29/19.48 & ? [B_z] :
% 19.29/19.48 ! [B_e] :
% 19.29/19.48 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 19.29/19.48 => ? [B_N] :
% 19.29/19.48 ! [B_n] :
% 19.29/19.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n))
% 19.29/19.48 => 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_g____(hAPP(B_f,B_n)),B_z)),B_e) ) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__not__less__zero,axiom,
% 19.29/19.48 ! [V_x,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => ~ 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)) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__zero,axiom,
% 19.29/19.48 ! [T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__eq__zero,axiom,
% 19.29/19.48 ! [V_x_2,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 19.29/19.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_less__iff__diff__less__0,axiom,
% 19.29/19.48 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 19.29/19.48 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 19.29/19.48 <=> 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)) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_le__iff__diff__le__0,axiom,
% 19.29/19.48 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 19.29/19.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 19.29/19.48 <=> 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))) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_seq__suble,axiom,
% 19.29/19.48 ! [V_n_2,V_f_2] :
% 19.29/19.48 ( c_SEQ_Osubseq(V_f_2)
% 19.29/19.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_f_2,V_n_2))) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_order__refl,axiom,
% 19.29/19.48 ! [V_x,T_a] :
% 19.29/19.48 ( class_Orderings_Opreorder(T_a)
% 19.29/19.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__minus__commute,axiom,
% 19.29/19.48 ! [V_b,V_a,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => 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)) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_diff__eq__diff__less,axiom,
% 19.29/19.48 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 19.29/19.48 => ( 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)
% 19.29/19.48 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 19.29/19.48 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_diff__eq__diff__less__eq,axiom,
% 19.29/19.48 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 19.29/19.48 => ( 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)
% 19.29/19.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 19.29/19.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) ) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_rp,axiom,
% 19.29/19.48 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_g_I1_J,axiom,
% 19.29/19.48 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n))),v_r)) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_subseq__def,axiom,
% 19.29/19.48 ! [V_f_2] :
% 19.29/19.48 ( c_SEQ_Osubseq(V_f_2)
% 19.29/19.48 <=> ! [B_m,B_n] :
% 19.29/19.48 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
% 19.29/19.48 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_m),hAPP(V_f_2,B_n)) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__triangle__ineq2,axiom,
% 19.29/19.48 ! [V_b,V_a,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => 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)))) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__ge__zero,axiom,
% 19.29/19.48 ! [V_x,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => 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))) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_norm__le__zero__iff,axiom,
% 19.29/19.48 ! [V_x_2,T_a] :
% 19.29/19.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.48 => ( 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)))
% 19.29/19.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_zero__reorient,axiom,
% 19.29/19.48 ! [V_x_2,T_a] :
% 19.29/19.48 ( class_Groups_Ozero(T_a)
% 19.29/19.48 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 19.29/19.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_linorder__le__cases,axiom,
% 19.29/19.48 ! [V_y,V_x,T_a] :
% 19.29/19.48 ( class_Orderings_Olinorder(T_a)
% 19.29/19.48 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_le__funE,axiom,
% 19.29/19.48 ! [V_x_2,V_ga_2,V_f_2,T_a,T_b] :
% 19.29/19.48 ( class_Orderings_Oord(T_b)
% 19.29/19.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_ga_2))
% 19.29/19.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_ga_2,V_x_2))) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_xt1_I6_J,axiom,
% 19.29/19.48 ! [V_z,V_x,V_y,T_a] :
% 19.29/19.48 ( class_Orderings_Oorder(T_a)
% 19.29/19.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 19.29/19.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ).
% 19.29/19.48
% 19.29/19.48 fof(fact_xt1_I5_J,axiom,
% 19.29/19.48 ! [V_x,V_y,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 => V_x = V_y ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__trans,axiom,
% 19.29/19.49 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__antisym,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.49 => V_x = V_y ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I4_J,axiom,
% 19.29/19.49 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.49 => ( V_b = V_c
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_ord__le__eq__trans,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oord(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.49 => ( V_b = V_c
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I3_J,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( V_a = V_b
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_ord__eq__le__trans,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oord(T_a)
% 19.29/19.49 => ( V_a = V_b
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__antisym__conv,axiom,
% 19.29/19.49 ! [V_x_2,V_y_2,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.49 <=> V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_le__funD,axiom,
% 19.29/19.49 ! [V_x_2,V_ga_2,V_f_2,T_a,T_b] :
% 19.29/19.49 ( class_Orderings_Oord(T_b)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_ga_2))
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_ga_2,V_x_2))) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__eq__refl,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( V_x = V_y
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__eq__iff,axiom,
% 19.29/19.49 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( V_x_2 = V_y_2
% 19.29/19.49 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.49 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__linear,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_le__fun__def,axiom,
% 19.29/19.49 ! [V_ga_2,V_f_2,T_a,T_b] :
% 19.29/19.49 ( class_Orderings_Oord(T_b)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_ga_2))
% 19.29/19.49 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_ga_2,B_x))) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__cases,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ( V_x != V_y
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__asym,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I10_J,axiom,
% 19.29/19.49 ! [V_z,V_x,V_y,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__trans,axiom,
% 19.29/19.49 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I2_J,axiom,
% 19.29/19.49 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 19.29/19.49 => ( V_b = V_c
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_ord__less__eq__trans,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oord(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.49 => ( V_b = V_c
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I1_J,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( V_a = V_b
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_ord__eq__less__trans,axiom,
% 19.29/19.49 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oord(T_a)
% 19.29/19.49 => ( V_a = V_b
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I9_J,axiom,
% 19.29/19.49 ! [V_a,V_b,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__asym_H,axiom,
% 19.29/19.49 ! [V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__imp__not__eq2,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => V_y != V_x ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__imp__not__eq,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => V_x != V_y ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__imp__not__less,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__not__sym,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_less__imp__neq,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => V_x != V_y ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__neqE,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( V_x != V_y
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__antisym__conv3,axiom,
% 19.29/19.49 ! [V_x_2,V_y_2,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.49 <=> V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__less__linear,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 | V_x = V_y
% 19.29/19.49 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_not__less__iff__gr__or__eq,axiom,
% 19.29/19.49 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.49 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 19.29/19.49 | V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__neq__iff,axiom,
% 19.29/19.49 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( V_x_2 != V_y_2
% 19.29/19.49 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.49 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__irrefl,axiom,
% 19.29/19.49 ! [V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_diff__eq__diff__eq,axiom,
% 19.29/19.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.49 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.49 => ( 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)
% 19.29/19.49 => ( V_a_2 = V_b_2
% 19.29/19.49 <=> V_c_2 = V_d_2 ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I8_J,axiom,
% 19.29/19.49 ! [V_z,V_x,V_y,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__le__less__trans,axiom,
% 19.29/19.49 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I7_J,axiom,
% 19.29/19.49 ! [V_z,V_x,V_y,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__le__trans,axiom,
% 19.29/19.49 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I11_J,axiom,
% 19.29/19.49 ! [V_a,V_b,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.49 => ( V_a != V_b
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__le__neq__trans,axiom,
% 19.29/19.49 ! [V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.49 => ( V_a != V_b
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__le__imp__less__or__eq,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 | V_x = V_y ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__antisym__conv2,axiom,
% 19.29/19.49 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.49 <=> V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__less__imp__le,axiom,
% 19.29/19.49 ! [V_y,V_x,T_a] :
% 19.29/19.49 ( class_Orderings_Opreorder(T_a)
% 19.29/19.49 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_leD,axiom,
% 19.29/19.49 ! [V_x,V_y,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.49 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_xt1_I12_J,axiom,
% 19.29/19.49 ! [V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( V_a != V_b
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_order__neq__le__trans,axiom,
% 19.29/19.49 ! [V_b,V_a,T_a] :
% 19.29/19.49 ( class_Orderings_Oorder(T_a)
% 19.29/19.49 => ( V_a != V_b
% 19.29/19.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.49
% 19.29/19.49 fof(fact_linorder__antisym__conv1,axiom,
% 19.29/19.49 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.49 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_not__leE,axiom,
% 19.29/19.50 ! [V_x,V_y,T_a] :
% 19.29/19.50 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 19.29/19.50 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_leI,axiom,
% 19.29/19.50 ! [V_y,V_x,T_a] :
% 19.29/19.50 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_order__le__less,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.50 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.50 | V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__le__not__le,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.50 ( class_Orderings_Opreorder(T_a)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.50 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_order__less__le,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.50 & V_x_2 != V_y_2 ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_linorder__le__less__linear,axiom,
% 19.29/19.50 ! [V_y,V_x,T_a] :
% 19.29/19.50 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 19.29/19.50 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_linorder__not__le,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.50 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_linorder__not__less,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.50 ( class_Orderings_Olinorder(T_a)
% 19.29/19.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 19.29/19.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_right__minus__eq,axiom,
% 19.29/19.50 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.50 ( class_Groups_Ogroup__add(T_a)
% 19.29/19.50 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.50 <=> V_a_2 = V_b_2 ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_eq__iff__diff__eq__0,axiom,
% 19.29/19.50 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.50 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.50 => ( V_a_2 = V_b_2
% 19.29/19.50 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__self,axiom,
% 19.29/19.50 ! [V_a,T_a] :
% 19.29/19.50 ( class_Groups_Ogroup__add(T_a)
% 19.29/19.50 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__0__right,axiom,
% 19.29/19.50 ! [V_a,T_a] :
% 19.29/19.50 ( class_Groups_Ogroup__add(T_a)
% 19.29/19.50 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le0,axiom,
% 19.29/19.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_decseq__def,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 19.29/19.50 <=> ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_incseq__def,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 19.29/19.50 <=> ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_Bseq__def,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => ( c_SEQ_OBseq(T_a,V_X_2)
% 19.29/19.50 <=> ? [B_K] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.50 & ! [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)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_monoseq__def,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 19.29/19.50 <=> ( ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 19.29/19.50 | ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__is__0__eq,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2] :
% 19.29/19.50 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__is__0__eq_H,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__less__mono,axiom,
% 19.29/19.50 ! [V_c,V_b,V_a] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a))
% 19.29/19.50 => 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)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__diff__iff,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 19.29/19.50 => ( 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))
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__diff__iff,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 19.29/19.50 => ( 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)))
% 19.29/19.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_Nat_Odiff__diff__eq,axiom,
% 19.29/19.50 ! [V_n,V_m,V_k] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 19.29/19.50 => 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) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_eq__diff__iff,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 19.29/19.50 => ( 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)
% 19.29/19.50 <=> V_m_2 = V_n_2 ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__zeroE,axiom,
% 19.29/19.50 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_not__less0,axiom,
% 19.29/19.50 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__not__refl,axiom,
% 19.29/19.50 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_neq0__conv,axiom,
% 19.29/19.50 ! [V_n_2] :
% 19.29/19.50 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_nat__neq__iff,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2] :
% 19.29/19.50 ( V_m_2 != V_n_2
% 19.29/19.50 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__0__eq__0,axiom,
% 19.29/19.50 ! [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) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_zero__less__diff,axiom,
% 19.29/19.50 ! [V_m_2,V_n_2] :
% 19.29/19.50 ( 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))
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__nat__zero__code,axiom,
% 19.29/19.50 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_minus__nat_Odiff__0,axiom,
% 19.29/19.50 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__self__eq__0,axiom,
% 19.29/19.50 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__fun__def,axiom,
% 19.29/19.50 ! [V_ga_2,V_f_2,T_a,T_b] :
% 19.29/19.50 ( class_Orderings_Oord(T_b)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_ga_2)
% 19.29/19.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_ga_2))
% 19.29/19.50 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2),V_f_2)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__commute,axiom,
% 19.29/19.50 ! [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) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_decseq__imp__monoseq,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 19.29/19.50 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_incseq__imp__monoseq,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 19.29/19.50 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_linorder__neqE__nat,axiom,
% 19.29/19.50 ! [V_y,V_x] :
% 19.29/19.50 ( V_x != V_y
% 19.29/19.50 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 19.29/19.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__less,axiom,
% 19.29/19.50 ! [V_m,V_n] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 19.29/19.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__irrefl__nat,axiom,
% 19.29/19.50 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_gr__implies__not0,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.50 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__not__refl2,axiom,
% 19.29/19.50 ! [V_m,V_n] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 19.29/19.50 => V_m != V_n ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__not__refl3,axiom,
% 19.29/19.50 ! [V_t,V_s] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 19.29/19.50 => V_s != V_t ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__imp__diff__less,axiom,
% 19.29/19.50 ! [V_n,V_k,V_j] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 19.29/19.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__less__mono2,axiom,
% 19.29/19.50 ! [V_l,V_n,V_m] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 19.29/19.50 => 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)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diffs0__imp__equal,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 => V_m = V_n ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_gr0I,axiom,
% 19.29/19.50 ! [V_n] :
% 19.29/19.50 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_nat__less__cases,axiom,
% 19.29/19.50 ! [V_P_2,V_n_2,V_m_2] :
% 19.29/19.50 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 19.29/19.50 => ( ( V_m_2 = V_n_2
% 19.29/19.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 19.29/19.50 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 19.29/19.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 19.29/19.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__refl,axiom,
% 19.29/19.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_nat__le__linear,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_eq__imp__le,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( V_m = V_n
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__trans,axiom,
% 19.29/19.50 ! [V_k,V_j,V_i] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__antisym,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.50 => V_m = V_n ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 19.29/19.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__0__eq,axiom,
% 19.29/19.50 ! [V_n_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 19.29/19.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_nat__less__le,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.50 & V_m_2 != V_n_2 ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__eq__less__or__eq,axiom,
% 19.29/19.50 ! [V_n_2,V_m_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.50 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.50 | V_m_2 = V_n_2 ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__imp__le__nat,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_le__neq__implies__less,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 => ( V_m != V_n
% 19.29/19.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__or__eq__imp__le,axiom,
% 19.29/19.50 ! [V_n,V_m] :
% 19.29/19.50 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.50 | V_m = V_n )
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__le__self,axiom,
% 19.29/19.50 ! [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)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__le__mono2,axiom,
% 19.29/19.50 ! [V_l,V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 => 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))) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__le__mono,axiom,
% 19.29/19.50 ! [V_l,V_n,V_m] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.50 => 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))) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__diff__cancel,axiom,
% 19.29/19.50 ! [V_n,V_i] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n))
% 19.29/19.50 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__le__eq__diff,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 19.29/19.50 <=> 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))) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_termination__basic__simps_I5_J,axiom,
% 19.29/19.50 ! [V_y,V_x] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__less__def,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 19.29/19.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 19.29/19.50 & V_x_2 != V_y_2 ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__eq__real__def,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 19.29/19.50 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 19.29/19.50 | V_x_2 = V_y_2 ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_BseqD,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => ( c_SEQ_OBseq(T_a,V_X_2)
% 19.29/19.50 => ? [B_K] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.50 & ! [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)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_BseqI,axiom,
% 19.29/19.50 ! [V_X_2,V_K_2,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
% 19.29/19.50 => ( ! [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))
% 19.29/19.50 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_BseqI2_H,axiom,
% 19.29/19.50 ! [V_K_2,V_X_2,V_N_2,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => ( ! [B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n))
% 19.29/19.50 => 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)) )
% 19.29/19.50 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_psize__eq__0__iff,axiom,
% 19.29/19.50 ! [V_pa_2,T_a] :
% 19.29/19.50 ( class_Groups_Ozero(T_a)
% 19.29/19.50 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.50 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_BseqI_H,axiom,
% 19.29/19.50 ! [V_K_2,V_X_2,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => ( ! [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))
% 19.29/19.50 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_monoI2,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) )
% 19.29/19.50 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__le__antisym,axiom,
% 19.29/19.50 ! [V_w,V_z] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
% 19.29/19.50 => V_z = V_w ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__le__trans,axiom,
% 19.29/19.50 ! [V_k,V_j,V_i] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__le__linear,axiom,
% 19.29/19.50 ! [V_w,V_z] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 19.29/19.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__le__refl,axiom,
% 19.29/19.50 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_monoI1,axiom,
% 19.29/19.50 ! [V_X_2,T_a] :
% 19.29/19.50 ( class_Orderings_Oorder(T_a)
% 19.29/19.50 => ( ! [B_m,B_n] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 19.29/19.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 19.29/19.50 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_equal__real__def,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2] :
% 19.29/19.50 ( c_HOL_Oequal__class_Oequal(tc_RealDef_Oreal,V_x_2,V_y_2)
% 19.29/19.50 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_norm__triangle__ineq3,axiom,
% 19.29/19.50 ! [V_b,V_a,T_a] :
% 19.29/19.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.50 => 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)))) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_less__real__def,axiom,
% 19.29/19.50 ! [V_y_2,V_x_2] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 19.29/19.50 <=> c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_y_2,V_x_2)) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 19.29/19.50 ! [V_n_2] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_ex__least__nat__le,axiom,
% 19.29/19.50 ! [V_n_2,V_P_2] :
% 19.29/19.50 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 19.29/19.50 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 19.29/19.50 => ? [B_k] :
% 19.29/19.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_k),V_n_2))
% 19.29/19.50 & ! [B_i] :
% 19.29/19.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,B_k)
% 19.29/19.50 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 19.29/19.50 & hBOOL(hAPP(V_P_2,B_k)) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_of__nat__0__less__iff,axiom,
% 19.29/19.50 ! [V_n_2,T_a] :
% 19.29/19.50 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
% 19.29/19.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_diff__poly__code_I2_J,axiom,
% 19.29/19.50 ! [V_p,T_a] :
% 19.29/19.50 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.50 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_power__strict__mono,axiom,
% 19.29/19.50 ! [V_n,V_b,V_a,T_a] :
% 19.29/19.50 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.50 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.50 => 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)) ) ) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__of__nat__ge__zero,axiom,
% 19.29/19.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_field__power__not__zero,axiom,
% 19.29/19.50 ! [V_n,V_a,T_a] :
% 19.29/19.50 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 19.29/19.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__eq__of__nat,axiom,
% 19.29/19.50 c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_abs__real__of__nat__cancel,axiom,
% 19.29/19.50 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__of__nat__power,axiom,
% 19.29/19.50 ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_power__real__of__nat,axiom,
% 19.29/19.50 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__of__nat__inject,axiom,
% 19.29/19.50 ! [V_m_2,V_n_2] :
% 19.29/19.50 ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)
% 19.29/19.50 <=> V_n_2 = V_m_2 ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__of__nat__def,axiom,
% 19.29/19.50 c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_zero__le__power__abs,axiom,
% 19.29/19.50 ! [V_n,V_a,T_a] :
% 19.29/19.50 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.50 => 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))) ) ).
% 19.29/19.50
% 19.29/19.50 fof(fact_real__norm__def,axiom,
% 19.29/19.50 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 19.29/19.50
% 19.29/19.51 fof(fact_abs__idempotent,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__power,axiom,
% 19.29/19.51 ! [V_n,V_m,T_a] :
% 19.29/19.51 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__abs,axiom,
% 19.29/19.51 ! [V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_norm__power,axiom,
% 19.29/19.51 ! [V_n,V_x,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_norm__of__nat,axiom,
% 19.29/19.51 ! [V_n,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 19.29/19.51 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__of__nat,axiom,
% 19.29/19.51 ! [V_n,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.51 => c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__eq__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2,T_a] :
% 19.29/19.51 ( class_Nat_Osemiring__char__0(T_a)
% 19.29/19.51 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
% 19.29/19.51 <=> V_m_2 = V_n_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_norm__power__ineq,axiom,
% 19.29/19.51 ! [V_n,V_x,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 19.29/19.51 => 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))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__zero,axiom,
% 19.29/19.51 ! [T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__eq__0,axiom,
% 19.29/19.51 ! [V_a_2,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__ge__self,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__le__D1,axiom,
% 19.29/19.51 ! [V_b,V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__minus__commute,axiom,
% 19.29/19.51 ! [V_b,V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__norm__cancel,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__le__power,axiom,
% 19.29/19.51 ! [V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__mono,axiom,
% 19.29/19.51 ! [V_n,V_b,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.51 => 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))) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__power,axiom,
% 19.29/19.51 ! [V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.51 => 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)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__eq__0__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_a_2,T_a] :
% 19.29/19.51 ( ( class_Power_Opower(T_a)
% 19.29/19.51 & class_Rings_Omult__zero(T_a)
% 19.29/19.51 & class_Rings_Ono__zero__divisors(T_a)
% 19.29/19.51 & class_Rings_Ozero__neq__one(T_a) )
% 19.29/19.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.51 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.51 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__zero__less__power__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_x_2] :
% 19.29/19.51 ( 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))
% 19.29/19.51 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 19.29/19.51 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__power__less__imp__less,axiom,
% 19.29/19.51 ! [V_n,V_m,V_i] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 19.29/19.51 => ( 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))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__ge__zero,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__le__zero__iff,axiom,
% 19.29/19.51 ! [V_a_2,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( 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)))
% 19.29/19.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__of__nonneg,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.51 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__not__less__zero,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__abs__iff,axiom,
% 19.29/19.51 ! [V_a_2,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 19.29/19.51 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__of__pos,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.51 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__triangle__ineq3,axiom,
% 19.29/19.51 ! [V_b,V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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)))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__triangle__ineq2,axiom,
% 19.29/19.51 ! [V_b,V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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)))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__triangle__ineq2__sym,axiom,
% 19.29/19.51 ! [V_b,V_a,T_a] :
% 19.29/19.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.51 => 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)))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__le__imp__of__nat,axiom,
% 19.29/19.51 ! [V_m,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__0__le__iff,axiom,
% 19.29/19.51 ! [V_n,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__less__0__iff,axiom,
% 19.29/19.51 ! [V_m,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__0,axiom,
% 19.29/19.51 ! [T_a] :
% 19.29/19.51 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__less__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__imp__of__nat__less,axiom,
% 19.29/19.51 ! [V_n,V_m,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__less__imp__less,axiom,
% 19.29/19.51 ! [V_n,V_m,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__less__imp__less__base,axiom,
% 19.29/19.51 ! [V_b,V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( 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))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__le__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__zero__iff,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 19.29/19.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__zero,axiom,
% 19.29/19.51 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_not__real__of__nat__less__zero,axiom,
% 19.29/19.51 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__less__iff,axiom,
% 19.29/19.51 ! [V_m_2,V_n_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__le__iff,axiom,
% 19.29/19.51 ! [V_m_2,V_n_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_positive__zero,axiom,
% 19.29/19.51 ~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__eq__imp__eq__base,axiom,
% 19.29/19.51 ! [V_b,V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( 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)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.51 => V_a = V_b ) ) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_of__nat__diff,axiom,
% 19.29/19.51 ! [V_m,V_n,T_a] :
% 19.29/19.51 ( class_Rings_Oring__1(T_a)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__diff,axiom,
% 19.29/19.51 ! [V_m,V_n] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.51 => hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiff__int__split,axiom,
% 19.29/19.51 ! [V_y_2,V_x_2,V_P_2] :
% 19.29/19.51 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2))))
% 19.29/19.51 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y_2),V_x_2))
% 19.29/19.51 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 19.29/19.51 & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
% 19.29/19.51 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiff__int,axiom,
% 19.29/19.51 ! [V_m,V_n] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.51 => c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__int__conv,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__power__nat__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_x_2] :
% 19.29/19.51 ( 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))
% 19.29/19.51 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_lemma__NBseq__def2,axiom,
% 19.29/19.51 ! [V_X_2,T_b] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__vector(T_b)
% 19.29/19.51 => ( ? [B_K] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.51 & ! [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)) )
% 19.29/19.51 <=> ? [B_N] :
% 19.29/19.51 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_lemma__NBseq__def,axiom,
% 19.29/19.51 ! [V_X_2,T_b] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__vector(T_b)
% 19.29/19.51 => ( ? [B_K] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.51 & ! [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)) )
% 19.29/19.51 <=> ? [B_N] :
% 19.29/19.51 ! [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))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N)))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_lemma__interval,axiom,
% 19.29/19.51 ! [V_b,V_x,V_a] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
% 19.29/19.51 => ? [B_d] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 19.29/19.51 & ! [B_y] :
% 19.29/19.51 ( 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)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y))
% 19.29/19.51 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b)) ) ) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Bseq__iff1a,axiom,
% 19.29/19.51 ! [V_X_2,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.51 => ( c_SEQ_OBseq(T_a,V_X_2)
% 19.29/19.51 <=> ? [B_N] :
% 19.29/19.51 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__mono,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_lessI,axiom,
% 19.29/19.51 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__Suc,axiom,
% 19.29/19.51 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__less__0__conv,axiom,
% 19.29/19.51 ! [V_k] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__zle__int,axiom,
% 19.29/19.51 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__le__zpower__abs,axiom,
% 19.29/19.51 ! [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))) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__zpower__abs__iff,axiom,
% 19.29/19.51 ! [V_n_2,V_x_2] :
% 19.29/19.51 ( 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))
% 19.29/19.51 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.51 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__bin__lemma,axiom,
% 19.29/19.51 ! [V_l_2,V_k_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 19.29/19.51 <=> 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)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__int__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
% 19.29/19.51 <=> V_m_2 = V_n_2 ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zpower__int,axiom,
% 19.29/19.51 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__power,axiom,
% 19.29/19.51 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_abs__int__eq,axiom,
% 19.29/19.51 ! [V_m] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__inject,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 19.29/19.51 => V_x = V_y ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat_Oinject,axiom,
% 19.29/19.51 ! [V_nat_H_2,V_nat_2] :
% 19.29/19.51 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 19.29/19.51 <=> V_nat_2 = V_nat_H_2 ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__n__not__n,axiom,
% 19.29/19.51 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 19.29/19.51
% 19.29/19.51 fof(fact_n__not__Suc__n,axiom,
% 19.29/19.51 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zless__linear,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 19.29/19.51 | V_x = V_y
% 19.29/19.51 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zless__le,axiom,
% 19.29/19.51 ! [V_w_2,V_z_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 19.29/19.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2))
% 19.29/19.51 & V_z_2 != V_w_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__neq__Zero,axiom,
% 19.29/19.51 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Zero__neq__Suc,axiom,
% 19.29/19.51 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat_Osimps_I3_J,axiom,
% 19.29/19.51 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__not__Zero,axiom,
% 19.29/19.51 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat_Osimps_I2_J,axiom,
% 19.29/19.51 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Zero__not__Suc,axiom,
% 19.29/19.51 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 19.29/19.51 ! [V_m_2,V_x_2] :
% 19.29/19.51 ( 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))
% 19.29/19.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.51 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__Suc__0,axiom,
% 19.29/19.51 ! [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)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__less__SucD,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__lessD,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__SucE,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 19.29/19.51 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => V_m = V_n ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__trans__Suc,axiom,
% 19.29/19.51 ! [V_k,V_j,V_i] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__lessI,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => ( c_Nat_OSuc(V_m) != V_n
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__SucI,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__antisym,axiom,
% 19.29/19.51 ! [V_m,V_n] :
% 19.29/19.51 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 19.29/19.51 => V_m = V_n ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_not__less__less__Suc__eq,axiom,
% 19.29/19.51 ! [V_m_2,V_n_2] :
% 19.29/19.51 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 19.29/19.51 <=> V_n_2 = V_m_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__less__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__Suc__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 19.29/19.51 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.51 | V_m_2 = V_n_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_not__less__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__leD,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__SucE,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
% 19.29/19.51 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.51 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__SucI,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__le__mono,axiom,
% 19.29/19.51 ! [V_m_2,V_n_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__Suc__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 19.29/19.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.51 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_not__less__eq__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__n__not__le__n,axiom,
% 19.29/19.51 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__diff__diff,axiom,
% 19.29/19.51 ! [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) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_diff__Suc__Suc,axiom,
% 19.29/19.51 ! [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) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 19.29/19.51 ! [V_x] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 19.29/19.51 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.51 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__0__Suc,axiom,
% 19.29/19.51 ! [V_n,T_a] :
% 19.29/19.51 ( ( class_Power_Opower(T_a)
% 19.29/19.51 & class_Rings_Osemiring__0(T_a) )
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__Suc__eq__0__disj,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 19.29/19.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.51 | ? [B_j] :
% 19.29/19.51 ( V_m_2 = c_Nat_OSuc(B_j)
% 19.29/19.51 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__Suc0,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 19.29/19.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_gr0__conv__Suc,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 19.29/19.51 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__one__le__power,axiom,
% 19.29/19.51 ! [V_n,V_i] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 19.29/19.51 => 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))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__eq__Suc__le,axiom,
% 19.29/19.51 ! [V_m_2,V_n_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_less__Suc__eq__le,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__le__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__imp__less__Suc,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__leI,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__less__Suc__eq,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 19.29/19.51 <=> V_n_2 = V_m_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__le__lessD,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 19.29/19.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_diff__less__Suc,axiom,
% 19.29/19.51 ! [V_n,V_m] : 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)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__diff__le,axiom,
% 19.29/19.51 ! [V_m,V_n] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.51 => 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)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_monoseq__Suc,axiom,
% 19.29/19.51 ! [V_X_2,T_a] :
% 19.29/19.51 ( class_Orderings_Oorder(T_a)
% 19.29/19.51 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 19.29/19.51 <=> ( ! [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))))
% 19.29/19.51 | ! [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))) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_subseq__Suc__iff,axiom,
% 19.29/19.51 ! [V_f_2] :
% 19.29/19.51 ( c_SEQ_Osubseq(V_f_2)
% 19.29/19.51 <=> ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_n),hAPP(V_f_2,c_Nat_OSuc(B_n))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__le__imp__le__base,axiom,
% 19.29/19.51 ! [V_b,V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( 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))))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_power__inject__base,axiom,
% 19.29/19.51 ! [V_b,V_n,V_a,T_a] :
% 19.29/19.51 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.51 => ( 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))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.51 => V_a = V_b ) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_diff__Suc__less,axiom,
% 19.29/19.51 ! [V_i,V_n] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.51 => 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) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Suc__pred,axiom,
% 19.29/19.51 ! [V_n] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.51 => 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 ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 19.29/19.51 ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__0,axiom,
% 19.29/19.51 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__eq__0__conv,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__le__0__conv,axiom,
% 19.29/19.51 ! [V_n_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zless__int,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zle__int,axiom,
% 19.29/19.51 ! [V_n_2,V_m_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Bseq__iff,axiom,
% 19.29/19.51 ! [V_X_2,T_a] :
% 19.29/19.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.51 => ( c_SEQ_OBseq(T_a,V_X_2)
% 19.29/19.51 <=> ? [B_N] :
% 19.29/19.51 ! [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))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N)))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
% 19.29/19.51 ! [V_y_2,V_x_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 19.29/19.51 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 19.29/19.51 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J,axiom,
% 19.29/19.51 ! [V_y_2,V_x_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 19.29/19.51 ! [V_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 19.29/19.51 ! [V_P_2] :
% 19.29/19.51 ( ? [B_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 19.29/19.51 & hBOOL(hAPP(V_P_2,B_x)) )
% 19.29/19.51 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zle__refl,axiom,
% 19.29/19.51 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zle__linear,axiom,
% 19.29/19.51 ! [V_w,V_z] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 19.29/19.51 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zle__trans,axiom,
% 19.29/19.51 ! [V_k,V_j,V_i] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k))
% 19.29/19.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zle__antisym,axiom,
% 19.29/19.51 ! [V_w,V_z] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
% 19.29/19.51 => V_z = V_w ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 19.29/19.51 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))) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 19.29/19.51 ! [V_n,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => 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))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
% 19.29/19.51 ! [V_y_2,V_x_2] :
% 19.29/19.51 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
% 19.29/19.51 <=> V_x_2 = V_y_2 ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 19.29/19.51 ! [V_P_2] :
% 19.29/19.51 ( ! [B_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 19.29/19.51 => hBOOL(hAPP(V_P_2,B_x)) )
% 19.29/19.51 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_tsub__def,axiom,
% 19.29/19.51 ! [V_x,V_y] :
% 19.29/19.51 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 19.29/19.51 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 19.29/19.51 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 19.29/19.51 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zero__less__imp__eq__int,axiom,
% 19.29/19.51 ! [V_k] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 19.29/19.51 => ? [B_n] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_n)
% 19.29/19.51 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_lemma__interval__lt,axiom,
% 19.29/19.51 ! [V_b,V_x,V_a] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
% 19.29/19.51 => ? [B_d] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 19.29/19.51 & ! [B_y] :
% 19.29/19.51 ( 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)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y)
% 19.29/19.51 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b) ) ) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_int__power__div__base,axiom,
% 19.29/19.51 ! [V_k,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 19.29/19.51 => 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)))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_tsub__eq,axiom,
% 19.29/19.51 ! [V_x,V_y] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 19.29/19.51 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 19.29/19.51 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__zero,axiom,
% 19.29/19.51 ! [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) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__by__0,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__0,axiom,
% 19.29/19.51 ! [V_a,T_a] :
% 19.29/19.51 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__neg__pos__less0,axiom,
% 19.29/19.51 ! [V_b,V_a] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 19.29/19.51 => 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)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 19.29/19.51 ! [V_a_2,V_b_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => ( 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))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 19.29/19.51 ! [V_a_2,V_b_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 19.29/19.51 => ( 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))
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__mono1__neg,axiom,
% 19.29/19.51 ! [V_b,V_a_H,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__mono1,axiom,
% 19.29/19.51 ! [V_b,V_a_H,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__neg__neg__trivial,axiom,
% 19.29/19.51 ! [V_b,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__mono2__neg,axiom,
% 19.29/19.51 ! [V_b,V_b_H,V_a] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 19.29/19.51 => 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))) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__nonpos__pos__le0,axiom,
% 19.29/19.51 ! [V_b,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 19.29/19.51 ! [V_a_2,V_b_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => ( 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)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__pos__pos__trivial,axiom,
% 19.29/19.51 ! [V_b,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__nonneg__neg__le0,axiom,
% 19.29/19.51 ! [V_b,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__mono2,axiom,
% 19.29/19.51 ! [V_b,V_b_H,V_a] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 19.29/19.51 => 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))) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 19.29/19.51 ! [V_b_2,V_a_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 19.29/19.51 => ( 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))
% 19.29/19.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2))
% 19.29/19.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 19.29/19.51 ! [V_i_2,V_k_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 19.29/19.51 => ( 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))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 19.29/19.51 ! [V_a_2,V_b_2] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 19.29/19.51 => ( 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)))
% 19.29/19.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__eq__0__iff,axiom,
% 19.29/19.51 ! [V_k_2,V_i_2] :
% 19.29/19.51 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.51 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.51 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 19.29/19.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 19.29/19.51 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.51 => 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))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__less__iff,axiom,
% 19.29/19.51 ! [V_m_2,V_w_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),V_m_2)
% 19.29/19.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_le__div__geq,axiom,
% 19.29/19.51 ! [V_m,V_n] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.51 => 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)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_incseq__SucI,axiom,
% 19.29/19.51 ! [V_X_2,T_a] :
% 19.29/19.51 ( class_Orderings_Oorder(T_a)
% 19.29/19.51 => ( ! [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))))
% 19.29/19.51 => c_SEQ_Oincseq(T_a,V_X_2) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.51 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_psize__def,axiom,
% 19.29/19.51 ! [V_p,T_a] :
% 19.29/19.51 ( class_Groups_Ozero(T_a)
% 19.29/19.51 => ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.51 => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 19.29/19.51 & ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.51 => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_poly__rec__0,axiom,
% 19.29/19.51 ! [T_a,V_z_2,V_f_2,T_b] :
% 19.29/19.51 ( class_Groups_Ozero(T_b)
% 19.29/19.51 => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
% 19.29/19.51 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__poly__less,axiom,
% 19.29/19.51 ! [V_y,V_x,T_a] :
% 19.29/19.51 ( class_Fields_Ofield(T_a)
% 19.29/19.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__le__dividend,axiom,
% 19.29/19.51 ! [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)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__le__mono,axiom,
% 19.29/19.51 ! [V_k,V_n,V_m] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.51 => 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))) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__int,axiom,
% 19.29/19.51 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__div__distrib,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 19.29/19.51 ! [V_y,V_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__1,axiom,
% 19.29/19.51 ! [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 ).
% 19.29/19.51
% 19.29/19.51 fof(fact_div__less,axiom,
% 19.29/19.51 ! [V_n,V_m] :
% 19.29/19.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.51 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_degree__0,axiom,
% 19.29/19.51 ! [T_a] :
% 19.29/19.51 ( class_Groups_Ozero(T_a)
% 19.29/19.51 => c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 19.29/19.51 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_nat__0,axiom,
% 19.29/19.51 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 19.29/19.51 ! [V_y_2,V_x_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 19.29/19.51 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 19.29/19.51 <=> V_x_2 = V_y_2 ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_all__nat,axiom,
% 19.29/19.51 ! [V_P_2] :
% 19.29/19.51 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 19.29/19.51 <=> ! [B_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 19.29/19.51 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_ex__nat,axiom,
% 19.29/19.51 ! [V_P_2] :
% 19.29/19.51 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 19.29/19.51 <=> ? [B_x] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 19.29/19.51 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_eq__nat__nat__iff,axiom,
% 19.29/19.51 ! [V_z_H_2,V_z_2] :
% 19.29/19.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 19.29/19.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 19.29/19.51 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 19.29/19.51 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 19.29/19.51 ! [V_y,V_x] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_zdiv__int,axiom,
% 19.29/19.51 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 19.29/19.51
% 19.29/19.51 fof(fact_degree__diff__less,axiom,
% 19.29/19.51 ! [V_q,V_n,V_p,T_a] :
% 19.29/19.52 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_degree__diff__le,axiom,
% 19.29/19.52 ! [V_q,V_n,V_p,T_a] :
% 19.29/19.52 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p)),V_n))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q)),V_n))
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))),V_n)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__le__mono2,axiom,
% 19.29/19.52 ! [V_k,V_n,V_m] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__le__0,axiom,
% 19.29/19.52 ! [V_z] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.52 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__0__iff,axiom,
% 19.29/19.52 ! [V_i_2] :
% 19.29/19.52 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mono__iff,axiom,
% 19.29/19.52 ! [V_w_2,V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zless__nat__conj,axiom,
% 19.29/19.52 ! [V_z_2,V_w_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2),V_y_2)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__0__le,axiom,
% 19.29/19.52 ! [V_z] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.52 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__eq__iff,axiom,
% 19.29/19.52 ! [V_z_2,V_m_2] :
% 19.29/19.52 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 19.29/19.52 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__nat__eq,axiom,
% 19.29/19.52 ! [V_z] :
% 19.29/19.52 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.52 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 19.29/19.52 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.52 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zless__nat__eq__int__zless,axiom,
% 19.29/19.52 ! [V_z_2,V_m_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),V_z_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__if,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 19.29/19.52 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__geq,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__less__nat__eq,axiom,
% 19.29/19.52 ! [V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_x_2),hAPP(c_Int_Onat,V_y_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__less__eq__zless,axiom,
% 19.29/19.52 ! [V_z_2,V_w_2] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__le__eq__zle,axiom,
% 19.29/19.52 ! [V_z_2,V_w_2] :
% 19.29/19.52 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_w_2)
% 19.29/19.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__eq__iff,axiom,
% 19.29/19.52 ! [V_m_2,V_w_2] :
% 19.29/19.52 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 19.29/19.52 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.52 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 19.29/19.52 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.52 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__eq__iff2,axiom,
% 19.29/19.52 ! [V_w_2,V_m_2] :
% 19.29/19.52 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 19.29/19.52 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.52 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 19.29/19.52 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 19.29/19.52 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_split__nat,axiom,
% 19.29/19.52 ! [V_i_2,V_P_2] :
% 19.29/19.52 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 19.29/19.52 <=> ( ! [B_n] :
% 19.29/19.52 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 19.29/19.52 => hBOOL(hAPP(V_P_2,B_n)) )
% 19.29/19.52 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__diff__distrib,axiom,
% 19.29/19.52 ! [V_z,V_z_H] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
% 19.29/19.52 => hAPP(c_Int_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_z_H)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 19.29/19.52 ! [V_n,V_x] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__power__eq,axiom,
% 19.29/19.52 ! [V_n,V_z] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.52 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_transfer__morphism__nat__int,axiom,
% 19.29/19.52 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_order__degree,axiom,
% 19.29/19.52 ! [V_a,V_p,T_a] :
% 19.29/19.52 ( class_Rings_Oidom(T_a)
% 19.29/19.52 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p)),c_Polynomial_Odegree(T_a,V_p))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_synthetic__div__eq__0__iff,axiom,
% 19.29/19.52 ! [V_c_2,V_pa_2,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.52 => ( c_Polynomial_Osynthetic__div(T_a,V_pa_2,V_c_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.52 <=> c_Polynomial_Odegree(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__less__nat__eq,axiom,
% 19.29/19.52 ! [V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_split__div_H,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_P_2] :
% 19.29/19.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
% 19.29/19.52 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 19.29/19.52 | ? [B_q] :
% 19.29/19.52 ( 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))
% 19.29/19.52 & 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)))
% 19.29/19.52 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__gt1__lemma,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__less__power__Suc,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__assoc,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__commute,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Groups_Oab__semigroup__mult(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult_Ocomm__neutral,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Groups_Ocomm__monoid__mult(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__1__right,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__reorient,axiom,
% 19.29/19.52 ! [V_x_2,T_a] :
% 19.29/19.52 ( class_Groups_Oone(T_a)
% 19.29/19.52 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 19.29/19.52 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__1,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Groups_Ocomm__monoid__mult(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__1__left,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_norm__one,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 19.29/19.52 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_norm__mult,axiom,
% 19.29/19.52 ! [V_y,V_x,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_of__nat__mult,axiom,
% 19.29/19.52 ! [V_n,V_m,T_a] :
% 19.29/19.52 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.52 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_of__nat__1,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.52 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_norm__mult__less,axiom,
% 19.29/19.52 ! [V_s,V_y,V_r,V_x,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_norm__mult__ineq,axiom,
% 19.29/19.52 ! [V_y,V_x,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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)))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__right_Ozero,axiom,
% 19.29/19.52 ! [V_x,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult_Ozero__right,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__left_Ozero,axiom,
% 19.29/19.52 ! [V_y,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult_Ozero__left,axiom,
% 19.29/19.52 ! [V_b,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__left_Odiff,axiom,
% 19.29/19.52 ! [V_ya,V_y,V_x,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult_Odiff__left,axiom,
% 19.29/19.52 ! [V_b,V_a_H,V_a,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__right_Odiff,axiom,
% 19.29/19.52 ! [V_y,V_x,V_xa,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult_Odiff__right,axiom,
% 19.29/19.52 ! [V_b_H,V_b,V_a,T_a] :
% 19.29/19.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__commutes,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__mult__distrib,axiom,
% 19.29/19.52 ! [V_n,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Groups_Ocomm__monoid__mult(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__cancel2,axiom,
% 19.29/19.52 ! [V_n_2,V_k_2,V_m_2] :
% 19.29/19.52 ( 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)
% 19.29/19.52 <=> ( V_m_2 = V_n_2
% 19.29/19.52 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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)
% 19.29/19.52 <=> ( V_m_2 = V_n_2
% 19.29/19.52 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__is__0,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__0__right,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__0,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__one,axiom,
% 19.29/19.52 ! [V_n,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__mult,axiom,
% 19.29/19.52 ! [V_n,V_m,V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Suc__mult__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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)
% 19.29/19.52 <=> V_m_2 = V_n_2 ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__mono,axiom,
% 19.29/19.52 ! [V_l,V_k,V_j,V_i] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__mono2,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.52 => 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))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__mono1,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.52 => 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))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_le__cube,axiom,
% 19.29/19.52 ! [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)))) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_le__square,axiom,
% 19.29/19.52 ! [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))) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__by__1,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__0__neq__1,axiom,
% 19.29/19.52 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_diff__mult__distrib,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_diff__mult__distrib2,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult2__eq,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zpower__zpower,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__Suc__less,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__le__power,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__inject__exp,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 19.29/19.52 => ( 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)
% 19.29/19.52 <=> V_m_2 = V_n_2 ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__mult1__if,axiom,
% 19.29/19.52 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => 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) )
% 19.29/19.52 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => 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) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__self2__is__id,axiom,
% 19.29/19.52 ! [V_a,V_b,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__self1__is__id,axiom,
% 19.29/19.52 ! [V_a,V_b,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__mult2,axiom,
% 19.29/19.52 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => 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) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__mult1,axiom,
% 19.29/19.52 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => 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) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__Suc2,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__Suc,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Power_Opower(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__self,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__0,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Power_Opower(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__eq__1__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 19.29/19.52 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__mono2,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__mono1,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel2,axiom,
% 19.29/19.52 ! [V_n_2,V_k_2,V_m_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__0__less__mult__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Suc__mult__less__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Suc__mult__le__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 19.29/19.52 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))) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__0__less__1,axiom,
% 19.29/19.52 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_degree__power__le,axiom,
% 19.29/19.52 ! [V_n,V_p,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),V_n))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_synthetic__div__0,axiom,
% 19.29/19.52 ! [V_c,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.52 => c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zdiv__self,axiom,
% 19.29/19.52 ! [V_a] :
% 19.29/19.52 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__0__left,axiom,
% 19.29/19.52 ! [V_n,T_a] :
% 19.29/19.52 ( ( class_Power_Opower(T_a)
% 19.29/19.52 & class_Rings_Osemiring__0(T_a) )
% 19.29/19.52 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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) )
% 19.29/19.52 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__gt1,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__strict__increasing,axiom,
% 19.29/19.52 ! [V_a,V_N,V_n,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__less__imp__less__exp,axiom,
% 19.29/19.52 ! [V_n,V_m,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => ( 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))
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__strict__increasing__iff,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__increasing,axiom,
% 19.29/19.52 ! [V_a,V_N,V_n,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__less__mult,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_n__less__n__mult__m,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_n__less__m__mult__n,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__le__mult__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( 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)))
% 19.29/19.52 <=> ( 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))
% 19.29/19.52 & 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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)))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__cancel2,axiom,
% 19.29/19.52 ! [V_n_2,V_k_2,V_m_2] :
% 19.29/19.52 ( 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)))
% 19.29/19.52 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__self__is__m,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => 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 ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__mult__self1__is__m,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => 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 ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__one__le__iff__zero__less,axiom,
% 19.29/19.52 ! [V_z_2] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__Suc0__eq__1,axiom,
% 19.29/19.52 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__1,axiom,
% 19.29/19.52 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__div__less__self,axiom,
% 19.29/19.52 ! [V_k,V_x] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zle__diff1__eq,axiom,
% 19.29/19.52 ! [V_z_2,V_w_2] :
% 19.29/19.52 ( 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))))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zabs__less__one__iff,axiom,
% 19.29/19.52 ! [V_z_2] :
% 19.29/19.52 ( 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))
% 19.29/19.52 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_realpow__Suc__le__self,axiom,
% 19.29/19.52 ! [V_n,V_r,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__Suc__less__one,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__strict__decreasing,axiom,
% 19.29/19.52 ! [V_a,V_N,V_n,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 19.29/19.52 => 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)) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__decreasing,axiom,
% 19.29/19.52 ! [V_a,V_N,V_n,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 19.29/19.52 => 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))) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__le__imp__le__exp,axiom,
% 19.29/19.52 ! [V_n,V_m,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__increasing__iff,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__less__power,axiom,
% 19.29/19.52 ! [V_n,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_split__div__lemma,axiom,
% 19.29/19.52 ! [V_m_2,V_q_2,V_n_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 19.29/19.52 => ( ( 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))
% 19.29/19.52 & 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))) )
% 19.29/19.52 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_lemma__realpow__diff,axiom,
% 19.29/19.52 ! [V_y,V_n,V_p,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p),V_n))
% 19.29/19.52 => 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) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_realpow__num__eq__if,axiom,
% 19.29/19.52 ! [V_m,V_n,T_a] :
% 19.29/19.52 ( class_Power_Opower(T_a)
% 19.29/19.52 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 19.29/19.52 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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)))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__div__cancel1,axiom,
% 19.29/19.52 ! [V_n,V_m,V_k] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__le__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__mult__pos,axiom,
% 19.29/19.52 ! [V_y,V_x,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__of__nat__1,axiom,
% 19.29/19.52 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__assoc,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__commute,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__1,axiom,
% 19.29/19.52 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__left__cancel,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2] :
% 19.29/19.52 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 19.29/19.52 => ( 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)
% 19.29/19.52 <=> V_a_2 = V_b_2 ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__right__cancel,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2] :
% 19.29/19.52 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 19.29/19.52 => ( 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)
% 19.29/19.52 <=> V_a_2 = V_b_2 ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__one__right,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zmult__1,axiom,
% 19.29/19.52 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zmult__1__right,axiom,
% 19.29/19.52 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__zero__not__eq__one,axiom,
% 19.29/19.52 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__poly__0__right,axiom,
% 19.29/19.52 ! [V_p,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__poly__0__left,axiom,
% 19.29/19.52 ! [V_q,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__1,axiom,
% 19.29/19.52 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__1__eq__mult__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 19.29/19.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 19.29/19.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__1__right,axiom,
% 19.29/19.52 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__eq__1__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 19.29/19.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 19.29/19.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zdiff__zmult__distrib2,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zdiff__zmult__distrib,axiom,
% 19.29/19.52 ! [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)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_poly__div__mult__right,axiom,
% 19.29/19.52 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.52 ( class_Fields_Ofield(T_a)
% 19.29/19.52 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_positive__mult,axiom,
% 19.29/19.52 ! [V_y,V_x] :
% 19.29/19.52 ( c_RealDef_Opositive(V_x)
% 19.29/19.52 => ( c_RealDef_Opositive(V_y)
% 19.29/19.52 => c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__less__iff1,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2,V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__order,axiom,
% 19.29/19.52 ! [V_y,V_x] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__less__mono2,axiom,
% 19.29/19.52 ! [V_y,V_x,V_z] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 19.29/19.52 ! [V_y,V_x] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zmult__zless__mono2,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 19.29/19.52 => 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)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_One__nat__def,axiom,
% 19.29/19.52 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__eq__self__implies__10,axiom,
% 19.29/19.52 ! [V_n,V_m] :
% 19.29/19.52 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 19.29/19.52 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 19.29/19.52 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zmult__int,axiom,
% 19.29/19.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__mult,axiom,
% 19.29/19.52 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 19.29/19.52 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_degree__1,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.52 => c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__of__nat__mult,axiom,
% 19.29/19.52 ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 19.29/19.52 ! [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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_diff__Suc__1,axiom,
% 19.29/19.52 ! [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 ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__zmult__eq__1,axiom,
% 19.29/19.52 ! [V_n,V_m] :
% 19.29/19.52 ( 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)
% 19.29/19.52 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_int__1,axiom,
% 19.29/19.52 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 19.29/19.52 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 19.29/19.52 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__le__cancel__iff1,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2,V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__mult__le__cancel__iff2,axiom,
% 19.29/19.52 ! [V_y_2,V_x_2,V_z_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_pos__zmult__eq__1__iff,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 19.29/19.52 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 19.29/19.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 19.29/19.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_linorder__neqE__linordered__idom,axiom,
% 19.29/19.52 ! [V_y,V_x,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => ( V_x != V_y
% 19.29/19.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zdiv__zmult2__eq,axiom,
% 19.29/19.52 ! [V_b,V_a,V_c] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_real__of__nat__one,axiom,
% 19.29/19.52 hAPP(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) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_div__less__dividend,axiom,
% 19.29/19.52 ! [V_m,V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__abs__mult__distrib,axiom,
% 19.29/19.52 ! [V_z,V_w] : hAPP(c_Int_Onat,c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_w))),hAPP(c_Int_Onat,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z))) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_degree__synthetic__div,axiom,
% 19.29/19.52 ! [V_c,V_p,T_a] :
% 19.29/19.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.52 => c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zmult__zless__mono2__lemma,axiom,
% 19.29/19.52 ! [V_k,V_j,V_i] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__distrib,axiom,
% 19.29/19.52 ! [V_z_H,V_z] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.52 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 19.29/19.52 ! [V_y,V_x] :
% 19.29/19.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Suc__pred_H,axiom,
% 19.29/19.52 ! [V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_Suc__diff__1,axiom,
% 19.29/19.52 ! [V_n] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_power__eq__if,axiom,
% 19.29/19.52 ! [V_p,V_m] :
% 19.29/19.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 19.29/19.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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)))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_realpow__minus__mult,axiom,
% 19.29/19.52 ! [V_x,V_n,T_a] :
% 19.29/19.52 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.52 => 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) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__zero__left,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Rings_Omult__zero(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__zero__right,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Rings_Omult__zero(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__eq__0__iff,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.52 ( class_Rings_Oring__no__zero__divisors(T_a)
% 19.29/19.52 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_no__zero__divisors,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Ono__zero__divisors(T_a)
% 19.29/19.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_divisors__zero,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Ono__zero__divisors(T_a)
% 19.29/19.52 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.52 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_one__neq__zero,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Ozero__neq__one(T_a)
% 19.29/19.52 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__neq__one,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Ozero__neq__one(T_a)
% 19.29/19.52 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__mult,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__mult__self,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => 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) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__one,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( 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)
% 19.29/19.52 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 | V_m_2 = V_n_2 ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__le__square,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring(T_a)
% 19.29/19.52 => 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))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__le__mult__iff,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 19.29/19.52 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__0__iff,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 19.29/19.52 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__nonneg__nonneg,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__cancel__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__nonneg__nonpos,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__cancel__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__nonneg__nonpos2,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__cancel__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__nonpos__nonneg,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__cancel__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__nonpos__nonpos,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__right__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__left__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_comm__mult__left__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__comm__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__right__mono__neg,axiom,
% 19.29/19.52 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__left__mono__neg,axiom,
% 19.29/19.52 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 => 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))) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__mono_H,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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))) ) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__mono,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__semiring(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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))) ) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_split__mult__pos__le,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.52 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 19.29/19.52 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_split__mult__neg__le,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Oordered__cancel__semiring(T_a)
% 19.29/19.52 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 19.29/19.52 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 19.29/19.52 => 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))) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_not__square__less__zero,axiom,
% 19.29/19.52 ! [V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring(T_a)
% 19.29/19.52 => ~ 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)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel__right__disj,axiom,
% 19.29/19.52 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 19.29/19.52 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel__left__disj,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.52 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 19.29/19.52 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel__left__pos,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__pos__pos,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__pos__neg,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__pos__neg2,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__less__mult__pos,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( 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))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__less__mult__pos2,axiom,
% 19.29/19.52 ! [V_a,V_b,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( 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))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__cancel__left__neg,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__neg__pos,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__neg__neg,axiom,
% 19.29/19.52 ! [V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__right__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__left__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_comm__mult__strict__left__mono,axiom,
% 19.29/19.52 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__right__mono__neg,axiom,
% 19.29/19.52 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__left__mono__neg,axiom,
% 19.29/19.52 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_not__one__le__zero,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__le__one,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_not__one__less__zero,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_zero__less__one,axiom,
% 19.29/19.52 ! [T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_less__1__mult,axiom,
% 19.29/19.52 ! [V_n,V_m,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_abs__mult__less,axiom,
% 19.29/19.52 ! [V_d,V_b,V_c,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 19.29/19.52 => 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)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__eq__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 => ( 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)
% 19.29/19.52 <=> V_m_2 = V_n_2 ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__less__cancel1,axiom,
% 19.29/19.52 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 19.29/19.52 => ( 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))
% 19.29/19.52 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_nat__mult__div__cancel__disj,axiom,
% 19.29/19.52 ! [V_n,V_m,V_k] :
% 19.29/19.52 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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) )
% 19.29/19.52 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.52 => 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) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__cancel__left__pos,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__cancel__left__neg,axiom,
% 19.29/19.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.52 => ( 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)))
% 19.29/19.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__mono,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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)) ) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__strict__mono_H,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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)) ) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__less__le__imp__less,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.52 => 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)) ) ) ) ) ) ).
% 19.29/19.52
% 19.29/19.52 fof(fact_mult__le__less__imp__less,axiom,
% 19.29/19.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.52 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 19.29/19.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.52 => 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)) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__right__less__imp__less,axiom,
% 19.29/19.53 ! [V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring(T_a)
% 19.29/19.53 => ( 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))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__less__imp__less__right,axiom,
% 19.29/19.53 ! [V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.53 => ( 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))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__left__less__imp__less,axiom,
% 19.29/19.53 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring(T_a)
% 19.29/19.53 => ( 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))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__less__imp__less__left,axiom,
% 19.29/19.53 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.53 => ( 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))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__right__le__imp__le,axiom,
% 19.29/19.53 ! [V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.53 => ( 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)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__left__le__imp__le,axiom,
% 19.29/19.53 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 19.29/19.53 => ( 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)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__left__le__one__le,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 19.29/19.53 => 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)) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__right__le__one__le,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 19.29/19.53 => 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)) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__eq__mult,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Oordered__ring__abs(T_a)
% 19.29/19.53 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 19.29/19.53 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 19.29/19.53 => 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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__ratiotest__lemma,axiom,
% 19.29/19.53 ! [V_y,V_x,V_c,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.53 => ( 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))))
% 19.29/19.53 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_rabs__ratiotest__lemma,axiom,
% 19.29/19.53 ! [V_y,V_x,V_c] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.53 => ( 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))))
% 19.29/19.53 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_not__real__square__gt__zero,axiom,
% 19.29/19.53 ! [V_x_2] :
% 19.29/19.53 ( ~ 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))
% 19.29/19.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 19.29/19.53 ! [V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zmult__assoc,axiom,
% 19.29/19.53 ! [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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zmult__commute,axiom,
% 19.29/19.53 ! [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) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 19.29/19.53 ! [V_ry,V_rx,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 19.29/19.53 ! [V_ry,V_rx,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 19.29/19.53 ! [V_rx,V_ly,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 19.29/19.53 ! [V_rx,V_ly,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 19.29/19.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 19.29/19.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 19.29/19.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 19.29/19.53 ! [V_q,V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 19.29/19.53 ! [V_q,V_p,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 19.29/19.53 ! [V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 19.29/19.53 ! [V_q,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 19.29/19.53 ! [V_q,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 19.29/19.53 ! [V_q,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_power__power__power,axiom,
% 19.29/19.53 ! [T_a] :
% 19.29/19.53 ( class_Power_Opower(T_a)
% 19.29/19.53 => 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_reals__Archimedean4,axiom,
% 19.29/19.53 ! [V_x,V_y] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.53 => ? [B_n] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_y)),V_x))
% 19.29/19.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n))),V_y)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__left_Opos__bounded,axiom,
% 19.29/19.53 ! [V_y,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => ? [B_K] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.53 & ! [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))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_power_Opower_Opower__0,axiom,
% 19.29/19.53 ! [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 ).
% 19.29/19.53
% 19.29/19.53 fof(fact_power_Opower_Opower__Suc,axiom,
% 19.29/19.53 ! [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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult_Opos__bounded,axiom,
% 19.29/19.53 ! [T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => ? [B_K] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.53 & ! [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))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__right_Opos__bounded,axiom,
% 19.29/19.53 ! [V_x,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => ? [B_K] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 19.29/19.53 & ! [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))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__pcompose__le,axiom,
% 19.29/19.53 ! [V_q,V_p,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_pcompose__0,axiom,
% 19.29/19.53 ! [V_q,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.53 => c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_decr__mult__lemma,axiom,
% 19.29/19.53 ! [V_k_2,V_P_2,V_d_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
% 19.29/19.53 => ( ! [B_x] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,B_x))
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2))) )
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 19.29/19.53 => ! [B_x] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,B_x))
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_incr__lemma,axiom,
% 19.29/19.53 ! [V_x,V_z,V_d] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),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))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_decr__lemma,axiom,
% 19.29/19.53 ! [V_z,V_x,V_d] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 19.29/19.53 => 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),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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_crossproduct__noteq,axiom,
% 19.29/19.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 19.29/19.53 => ( ( V_a_2 != V_b_2
% 19.29/19.53 & V_c_2 != V_d_2 )
% 19.29/19.53 <=> 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)) != 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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__class_Odistrib,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 19.29/19.53 ! [V_b,V_m,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_combine__common__factor,axiom,
% 19.29/19.53 ! [V_c,V_b,V_e,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Osemiring(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_crossproduct__eq,axiom,
% 19.29/19.53 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 19.29/19.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 19.29/19.53 => ( 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)) = 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))
% 19.29/19.53 <=> ( V_w_2 = V_x_2
% 19.29/19.53 | V_y_2 = V_z_2 ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__left_Oadd,axiom,
% 19.29/19.53 ! [V_ya,V_y,V_x,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult_Oadd__left,axiom,
% 19.29/19.53 ! [V_b,V_a_H,V_a,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__right_Oadd,axiom,
% 19.29/19.53 ! [V_y,V_x,V_xa,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult_Oadd__right,axiom,
% 19.29/19.53 ! [V_b_H,V_b,V_a,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__zmult__distrib,axiom,
% 19.29/19.53 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = 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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__zmult__distrib2,axiom,
% 19.29/19.53 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = 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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 19.29/19.53 ! [V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 19.29/19.53 ! [V_d,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 19.29/19.53 ! [V_d,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__0__iff,axiom,
% 19.29/19.53 ! [V_a_2,V_b_2,T_a] :
% 19.29/19.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 19.29/19.53 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 19.29/19.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_double__eq__0__iff,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add_Ocomm__neutral,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__0__right,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Groups_Omonoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_double__zero__sym,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 19.29/19.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__0,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__0__left,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Groups_Omonoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__imp__le__left,axiom,
% 19.29/19.53 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__imp__le__right,axiom,
% 19.29/19.53 ! [V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__mono,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__left__mono,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__right__mono,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__cancel__left,axiom,
% 19.29/19.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__cancel__right,axiom,
% 19.29/19.53 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__imp__less__left,axiom,
% 19.29/19.53 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__imp__less__right,axiom,
% 19.29/19.53 ! [V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__strict__mono,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__strict__left__mono,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__strict__right__mono,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__cancel__left,axiom,
% 19.29/19.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__cancel__right,axiom,
% 19.29/19.53 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Deriv_Oadd__diff__add,axiom,
% 19.29/19.53 ! [V_d,V_b,V_c,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oab__group__add(T_a)
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__diff__cancel,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ogroup__add(T_a)
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__cancel,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ogroup__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__0__right,axiom,
% 19.29/19.53 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__0,axiom,
% 19.29/19.53 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__add__abs,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.53 => c_Groups_Oabs__class_Oabs(T_a,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))) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__left__mono,axiom,
% 19.29/19.53 ! [V_k,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__strict__right__mono,axiom,
% 19.29/19.53 ! [V_k,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__triangle__ineq,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))),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)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__add__less,axiom,
% 19.29/19.53 ! [V_s,V_y,V_r,V_x,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_of__nat__add,axiom,
% 19.29/19.53 ! [V_n,V_m,T_a] :
% 19.29/19.53 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__commute,axiom,
% 19.29/19.53 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__left__commute,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__assoc,axiom,
% 19.29/19.53 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oab__semigroup__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__left__cancel,axiom,
% 19.29/19.53 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 19.29/19.53 <=> V_b_2 = V_c_2 ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__right__cancel,axiom,
% 19.29/19.53 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 19.29/19.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 19.29/19.53 <=> V_b_2 = V_c_2 ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__left__imp__eq,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 19.29/19.53 => V_b = V_c ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__imp__eq,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 19.29/19.53 => V_b = V_c ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__right__imp__eq,axiom,
% 19.29/19.53 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 19.29/19.53 => V_b = V_c ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__diff__triangle__ineq,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)))),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))))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__nonneg__nonneg,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__nonneg__eq__0__iff,axiom,
% 19.29/19.53 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__increasing,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__increasing2,axiom,
% 19.29/19.53 ! [V_a,V_b,V_c,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__nonpos__nonpos,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_pos__add__strict,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__pos__pos,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__neg__neg,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_even__less__0__iff,axiom,
% 19.29/19.53 ! [V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__le__mono,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__less__mono,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_sum__squares__eq__zero__iff,axiom,
% 19.29/19.53 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.53 => ( 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)
% 19.29/19.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__scale__eq__noteq,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 19.29/19.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 19.29/19.53 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 => ( ( V_a = V_b
% 19.29/19.53 & V_c != V_d )
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__one,axiom,
% 19.29/19.53 ! [V_a,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_eq__add__iff1,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oring(T_a)
% 19.29/19.53 => ( 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) = 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)
% 19.29/19.53 <=> 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 ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_eq__add__iff2,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oring(T_a)
% 19.29/19.53 => ( 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) = 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)
% 19.29/19.53 <=> V_c_2 = 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) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__diff__mult,axiom,
% 19.29/19.53 ! [V_b,V_a,V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Oring(T_a)
% 19.29/19.53 => 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)) = 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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult_Oprod__diff__prod,axiom,
% 19.29/19.53 ! [V_b,V_a,V_y,V_x,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__algebra(T_a)
% 19.29/19.53 => 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)) = c_Groups_Oplus__class_Oplus(T_a,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))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 19.29/19.53 ! [V_m,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 19.29/19.53 ! [V_a,V_m,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 19.29/19.53 ! [V_m,V_a,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__triangle__ineq,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),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)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 19.29/19.53 ! [V_y,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_odd__nonzero,axiom,
% 19.29/19.53 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,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) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__zless__mono,axiom,
% 19.29/19.53 ! [V_z,V_z_H,V_w,V_w_H] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zless__add1__eq,axiom,
% 19.29/19.53 ! [V_z_2,V_w_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 19.29/19.53 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 19.29/19.53 | V_w_2 = V_z_2 ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zle__iff__zadd,axiom,
% 19.29/19.53 ! [V_z_2,V_w_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2))
% 19.29/19.53 <=> ? [B_n] : V_z_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__pos__nonneg,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__nonneg__pos,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__strict__increasing,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__strict__increasing2,axiom,
% 19.29/19.53 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__neg__nonpos,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__nonpos__neg,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_sum__squares__le__zero__iff,axiom,
% 19.29/19.53 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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)))
% 19.29/19.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_sum__squares__ge__zero,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__ring(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),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)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_sum__squares__gt__zero__iff,axiom,
% 19.29/19.53 ! [V_y_2,V_x_2,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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)))
% 19.29/19.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_not__sum__squares__lt__zero,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__ring(T_a)
% 19.29/19.53 => ~ c_Orderings_Oord__class_Oless(T_a,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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zero__less__two,axiom,
% 19.29/19.53 ! [T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semidom(T_a)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add__iff1,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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)),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)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add__iff2,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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)),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)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),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))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__iff2,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,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),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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__iff1,axiom,
% 19.29/19.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 19.29/19.53 ( class_Rings_Oordered__ring(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,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),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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(T_a,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) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__squared__diff__one__factored,axiom,
% 19.29/19.53 ! [V_x,T_a] :
% 19.29/19.53 ( class_Rings_Oring__1(T_a)
% 19.29/19.53 => 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),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))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_div__mult__self1,axiom,
% 19.29/19.53 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.53 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_div__mult__self2,axiom,
% 19.29/19.53 ! [V_c,V_a,V_b,T_a] :
% 19.29/19.53 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_div__add__self1,axiom,
% 19.29/19.53 ! [V_a,V_b,T_a] :
% 19.29/19.53 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = 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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_div__add__self2,axiom,
% 19.29/19.53 ! [V_a,V_b,T_a] :
% 19.29/19.53 ( class_Divides_Osemiring__div(T_a)
% 19.29/19.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.53 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = 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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__triangle__ineq4,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.53 => 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))),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)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__diff__triangle__ineq,axiom,
% 19.29/19.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 19.29/19.53 => 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_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)))),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))))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_of__nat__Suc,axiom,
% 19.29/19.53 ! [V_m,T_a] :
% 19.29/19.53 ( class_Rings_Osemiring__1(T_a)
% 19.29/19.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__diff__ineq,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => 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_Oplus__class_Oplus(T_a,V_a,V_b)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_odd__less__0,axiom,
% 19.29/19.53 ! [V_z_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zle__add1__eq__le,axiom,
% 19.29/19.53 ! [V_z_2,V_w_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add1__zle__eq,axiom,
% 19.29/19.53 ! [V_z_2,V_w_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zless__imp__add1__zle,axiom,
% 19.29/19.53 ! [V_z,V_w] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zless__iff__Suc__zadd,axiom,
% 19.29/19.53 ! [V_z_2,V_w_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 19.29/19.53 <=> ? [B_n] : V_z_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_int__Suc,axiom,
% 19.29/19.53 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_convex__bound__le,axiom,
% 19.29/19.53 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__1(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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)) ) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__imp__0__less,axiom,
% 19.29/19.53 ! [V_z] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 19.29/19.53 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = 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)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_unique__quotient__lemma__neg,axiom,
% 19.29/19.53 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zdiv__mono2__lemma,axiom,
% 19.29/19.53 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = 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)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_unique__quotient__lemma,axiom,
% 19.29/19.53 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_q__neg__lemma,axiom,
% 19.29/19.53 ! [V_r_H,V_q_H,V_b_H] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_q__pos__lemma,axiom,
% 19.29/19.53 ! [V_r_H,V_q_H,V_b_H] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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)))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_convex__bound__lt,axiom,
% 19.29/19.53 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(T_a,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) ) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_realpow__two__diff,axiom,
% 19.29/19.53 ! [V_y,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__ring__1(T_a)
% 19.29/19.53 => 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)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 19.29/19.53 ! [V_z] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.53 => c_Nat_OSuc(hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_self__quotient__aux1,axiom,
% 19.29/19.53 ! [V_q,V_r,V_a] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 19.29/19.53 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_self__quotient__aux2,axiom,
% 19.29/19.53 ! [V_q,V_r,V_a] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 19.29/19.53 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_split__zdiv,axiom,
% 19.29/19.53 ! [V_k_2,V_n_2,V_P_2] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
% 19.29/19.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 19.29/19.53 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 19.29/19.53 => ! [B_i] :
% 19.29/19.53 ( ? [B_j] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 19.29/19.53 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 19.29/19.53 & V_n_2 = 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) )
% 19.29/19.53 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 19.29/19.53 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 19.29/19.53 => ! [B_i] :
% 19.29/19.53 ( ? [B_j] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 19.29/19.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 19.29/19.53 & V_n_2 = 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) )
% 19.29/19.53 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_divmod__int__rel__div__eq,axiom,
% 19.29/19.53 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 19.29/19.53 ( V_a_1 = 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)
% 19.29/19.53 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 19.29/19.53 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1) ) )
% 19.29/19.53 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1)
% 19.29/19.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 19.29/19.53 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 19.29/19.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__diff__less__iff,axiom,
% 19.29/19.53 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 19.29/19.53 ( class_Rings_Olinordered__idom(T_a)
% 19.29/19.53 => ( 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)
% 19.29/19.53 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)
% 19.29/19.53 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_incr__mult__lemma,axiom,
% 19.29/19.53 ! [V_k_2,V_P_2,V_d_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
% 19.29/19.53 => ( ! [B_x] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,B_x))
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 19.29/19.53 => ! [B_x] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,B_x))
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_realpow__pos__nth__unique,axiom,
% 19.29/19.53 ! [V_a,V_n] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 19.29/19.53 => ? [B_x] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)
% 19.29/19.53 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 19.29/19.53 & ! [B_y] :
% 19.29/19.53 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)
% 19.29/19.53 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 19.29/19.53 => B_y = B_x ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__poly__add__left,axiom,
% 19.29/19.53 ! [V_r,V_q,V_p,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_left__add__mult__distrib,axiom,
% 19.29/19.53 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__add__mult__distrib,axiom,
% 19.29/19.53 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = 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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__mult__distrib2,axiom,
% 19.29/19.53 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = 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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__mult__distrib,axiom,
% 19.29/19.53 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = 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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__Suc__ex__iff,axiom,
% 19.29/19.53 ! [V_l_2,V_k_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2))
% 19.29/19.53 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_positive__add,axiom,
% 19.29/19.53 ! [V_y,V_x] :
% 19.29/19.53 ( c_RealDef_Opositive(V_x)
% 19.29/19.53 => ( c_RealDef_Opositive(V_y)
% 19.29/19.53 => c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__add__left__mono,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__eq__self__zero,axiom,
% 19.29/19.53 ! [V_n,V_m] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 19.29/19.53 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__is__0,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Nat_Oadd__0__right,axiom,
% 19.29/19.53 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 19.29/19.53
% 19.29/19.53 fof(fact_plus__nat_Oadd__0,axiom,
% 19.29/19.53 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__Suc__shift,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__Suc,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__Suc__right,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_termination__basic__simps_I2_J,axiom,
% 19.29/19.53 ! [V_y,V_z,V_x] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_termination__basic__simps_I1_J,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__lessD1,axiom,
% 19.29/19.53 ! [V_k,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__eq__less,axiom,
% 19.29/19.53 ! [V_n,V_m,V_l,V_k] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 19.29/19.53 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__mono,axiom,
% 19.29/19.53 ! [V_l,V_k,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__less__mono1,axiom,
% 19.29/19.53 ! [V_k,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_trans__less__add2,axiom,
% 19.29/19.53 ! [V_m,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_trans__less__add1,axiom,
% 19.29/19.53 ! [V_m,V_j,V_i] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__left__cancel__less,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_not__add__less2,axiom,
% 19.29/19.53 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_not__add__less1,axiom,
% 19.29/19.53 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__commute,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__left__commute,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__assoc,axiom,
% 19.29/19.53 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__left__cancel,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 19.29/19.53 <=> V_m_2 = V_n_2 ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__right__cancel,axiom,
% 19.29/19.53 ! [V_n_2,V_k_2,V_m_2] :
% 19.29/19.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 19.29/19.53 <=> V_m_2 = V_n_2 ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__of__nat__add,axiom,
% 19.29/19.53 ! [V_n,V_m] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_complex__mod__triangle__sub,axiom,
% 19.29/19.53 ! [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)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__poly__code_I1_J,axiom,
% 19.29/19.53 ! [V_q,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__poly__code_I2_J,axiom,
% 19.29/19.53 ! [V_p,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__cancel2,axiom,
% 19.29/19.53 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__cancel,axiom,
% 19.29/19.53 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__diff__left,axiom,
% 19.29/19.53 ! [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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__inverse,axiom,
% 19.29/19.53 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__inverse2,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ).
% 19.29/19.53
% 19.29/19.53 fof(fact_termination__basic__simps_I4_J,axiom,
% 19.29/19.53 ! [V_y,V_z,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_termination__basic__simps_I3_J,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__leE,axiom,
% 19.29/19.53 ! [V_n,V_k,V_m] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k)),V_n))
% 19.29/19.53 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 19.29/19.53 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__leD1,axiom,
% 19.29/19.53 ! [V_n,V_k,V_m] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k)),V_n))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__leD2,axiom,
% 19.29/19.53 ! [V_n,V_k,V_m] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k)),V_n))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__mono,axiom,
% 19.29/19.53 ! [V_l,V_k,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__le__mono1,axiom,
% 19.29/19.53 ! [V_k,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_trans__le__add2,axiom,
% 19.29/19.53 ! [V_m,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_trans__le__add1,axiom,
% 19.29/19.53 ! [V_m,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__left__cancel__le,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_k_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__iff__add,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 19.29/19.53 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add1,axiom,
% 19.29/19.53 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add2,axiom,
% 19.29/19.53 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 19.29/19.53 ! [V_q,V_p,V_x,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 19.29/19.53 => 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_power__add,axiom,
% 19.29/19.53 ! [V_n,V_m,V_a,T_a] :
% 19.29/19.53 ( class_Groups_Omonoid__mult(T_a)
% 19.29/19.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__is__1,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( 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))
% 19.29/19.53 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 19.29/19.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 19.29/19.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_one__is__add,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.53 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 19.29/19.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 19.29/19.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__gr__0,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
% 19.29/19.53 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 19.29/19.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__two__squares__add__zero__iff,axiom,
% 19.29/19.53 ! [V_y_2,V_x_2] :
% 19.29/19.53 ( 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)
% 19.29/19.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 19.29/19.53 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__iff__Suc__add,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 19.29/19.53 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__Suc2,axiom,
% 19.29/19.53 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__add__Suc1,axiom,
% 19.29/19.53 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__0,axiom,
% 19.29/19.53 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__Suc__right,axiom,
% 19.29/19.53 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__Suc,axiom,
% 19.29/19.53 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__diff__inverse,axiom,
% 19.29/19.53 ! [V_n,V_m] :
% 19.29/19.53 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_less__diff__conv,axiom,
% 19.29/19.53 ! [V_k_2,V_j_2,V_i_2] :
% 19.29/19.53 ( 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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Suc__eq__plus1,axiom,
% 19.29/19.53 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Suc__eq__plus1__left,axiom,
% 19.29/19.53 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__add__eq__left,axiom,
% 19.29/19.53 ! [V_p,V_q,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))
% 19.29/19.53 => c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_p) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__add__eq__right,axiom,
% 19.29/19.53 ! [V_q,V_p,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
% 19.29/19.53 => c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_q) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__add__less,axiom,
% 19.29/19.53 ! [V_q,V_n,V_p,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 19.29/19.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__diff__right,axiom,
% 19.29/19.53 ! [V_i,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__diff__conv,axiom,
% 19.29/19.53 ! [V_i_2,V_k_2,V_j_2] :
% 19.29/19.53 ( 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))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add__diff,axiom,
% 19.29/19.53 ! [V_m,V_n,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add__diff__inverse,axiom,
% 19.29/19.53 ! [V_m,V_n] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__diff__assoc,axiom,
% 19.29/19.53 ! [V_i,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__diff__conv2,axiom,
% 19.29/19.53 ! [V_i_2,V_j_2,V_k_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2))
% 19.29/19.53 => ( 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)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)),V_j_2)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__add__diff__inverse2,axiom,
% 19.29/19.53 ! [V_m,V_n] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_le__imp__diff__is__add,axiom,
% 19.29/19.53 ! [V_k_2,V_j_2,V_i_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 19.29/19.53 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 19.29/19.53 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__assoc,axiom,
% 19.29/19.53 ! [V_i,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__diff__assoc2,axiom,
% 19.29/19.53 ! [V_i,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__add__assoc2,axiom,
% 19.29/19.53 ! [V_i,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__add__le,axiom,
% 19.29/19.53 ! [V_q,V_n,V_p,T_a] :
% 19.29/19.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p)),V_n))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q)),V_n))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))),V_n)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 19.29/19.53 ! [V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__int,axiom,
% 19.29/19.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zadd__int__left,axiom,
% 19.29/19.53 ! [V_z,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_zpower__zadd__distrib,axiom,
% 19.29/19.53 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),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)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_norm__triangle__ineq4,axiom,
% 19.29/19.53 ! [V_b,V_a,T_a] :
% 19.29/19.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 19.29/19.53 => 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))),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)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__diff__split,axiom,
% 19.29/19.53 ! [V_b_2,V_a_2,V_P_2] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 19.29/19.53 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 19.29/19.53 & ! [B_d] :
% 19.29/19.53 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 19.29/19.53 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__diff__split__asm,axiom,
% 19.29/19.53 ! [V_b_2,V_a_2,V_P_2] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 19.29/19.53 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 19.29/19.53 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 19.29/19.53 | ? [B_d] :
% 19.29/19.53 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 19.29/19.53 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__Suc__diff__eq2,axiom,
% 19.29/19.53 ! [V_m,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_diff__Suc__diff__eq1,axiom,
% 19.29/19.53 ! [V_m,V_j,V_k] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 19.29/19.53 => 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_real__of__nat__Suc,axiom,
% 19.29/19.53 ! [V_n] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__le__add__iff1,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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)),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)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__diff__add__eq1,axiom,
% 19.29/19.53 ! [V_n,V_m,V_u,V_i,V_j] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i))
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__eq__add__iff1,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 19.29/19.53 => ( 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) = 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)
% 19.29/19.53 <=> 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 ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__le__add__iff2,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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)),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)))
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),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))) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__diff__add__eq2,axiom,
% 19.29/19.53 ! [V_n,V_m,V_u,V_j,V_i] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 19.29/19.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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)) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__eq__add__iff2,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 19.29/19.53 => ( 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) = 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)
% 19.29/19.53 <=> V_m_2 = 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) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__add__one__not__less__self,axiom,
% 19.29/19.53 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__mult__le,axiom,
% 19.29/19.53 ! [V_q,V_p,T_a] :
% 19.29/19.53 ( class_Rings_Ocomm__semiring__0(T_a)
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_degree__mult__eq,axiom,
% 19.29/19.53 ! [V_q,V_p,T_a] :
% 19.29/19.53 ( class_Rings_Oidom(T_a)
% 19.29/19.53 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.53 => ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.53 => c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__less__real__le,axiom,
% 19.29/19.53 ! [V_m_2,V_n_2] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 19.29/19.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_add__eq__if,axiom,
% 19.29/19.53 ! [V_n,V_m] :
% 19.29/19.53 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 19.29/19.53 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__le__real__less,axiom,
% 19.29/19.53 ! [V_m_2,V_n_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__less__add__iff1,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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),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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__less__add__iff2,axiom,
% 19.29/19.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 19.29/19.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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),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))
% 19.29/19.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_abs__add__one__gt__zero,axiom,
% 19.29/19.53 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_mult__eq__if,axiom,
% 19.29/19.53 ! [V_n,V_m] :
% 19.29/19.53 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 19.29/19.53 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = 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)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__add__distrib,axiom,
% 19.29/19.53 ! [V_z_H,V_z] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 19.29/19.53 => hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_z_H)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 19.29/19.53 ! [V_y,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 19.29/19.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_split__div,axiom,
% 19.29/19.53 ! [V_k_2,V_n_2,V_P_2] :
% 19.29/19.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
% 19.29/19.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 19.29/19.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.53 => ! [B_i,B_j] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
% 19.29/19.53 => ( V_n_2 = 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)
% 19.29/19.53 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 19.29/19.53 ! [V_n,V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(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),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_nat__aux__def,axiom,
% 19.29/19.53 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_i),V_n) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_complex__mod__triangle__ineq2,axiom,
% 19.29/19.53 ! [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,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))) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_natceiling__eq,axiom,
% 19.29/19.53 ! [V_x,V_n] :
% 19.29/19.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x)
% 19.29/19.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 19.29/19.53 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 19.29/19.53
% 19.29/19.53 fof(fact_natceiling__add__one,axiom,
% 19.29/19.53 ! [V_x] :
% 19.29/19.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__zero,axiom,
% 19.29/19.54 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_zero__le__natceiling,axiom,
% 19.29/19.54 ! [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))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__mono,axiom,
% 19.29/19.54 ! [V_y,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__natceiling__ge,axiom,
% 19.29/19.54 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__one,axiom,
% 19.29/19.54 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__real__of__nat,axiom,
% 19.29/19.54 ! [V_n] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__neg,axiom,
% 19.29/19.54 ! [V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.54 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__le,axiom,
% 19.29/19.54 ! [V_a,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__le__eq,axiom,
% 19.29/19.54 ! [V_a_2,V_x_2] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 19.29/19.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))
% 19.29/19.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2))) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__le__eq__one,axiom,
% 19.29/19.54 ! [V_x_2] :
% 19.29/19.54 ( 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)))
% 19.29/19.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__subtract,axiom,
% 19.29/19.54 ! [V_x,V_a] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))
% 19.29/19.54 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natceiling__add,axiom,
% 19.29/19.54 ! [V_a,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_reals__Archimedean6,axiom,
% 19.29/19.54 ! [V_r] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
% 19.29/19.54 => ? [B_n] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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))
% 19.29/19.54 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_unimodular__reduce__norm,axiom,
% 19.29/19.54 ! [V_z] :
% 19.29/19.54 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 19.29/19.54 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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))
% 19.29/19.54 | 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))
% 19.29/19.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 19.29/19.54 | 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)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_complex__i__not__zero,axiom,
% 19.29/19.54 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_complex__i__not__one,axiom,
% 19.29/19.54 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_reduce__poly__simple,axiom,
% 19.29/19.54 ! [V_n,V_b] :
% 19.29/19.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 19.29/19.54 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 19.29/19.54 => ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_lemmaCauchy,axiom,
% 19.29/19.54 ! [V_X_2,V_M_2,T_a,T_b] :
% 19.29/19.54 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 19.29/19.54 & class_Orderings_Oord(T_a) )
% 19.29/19.54 => ( ! [B_n] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 19.29/19.54 => 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)) )
% 19.29/19.54 => ! [B_n] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 19.29/19.54 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),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)))) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__add__one,axiom,
% 19.29/19.54 ! [V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__def,axiom,
% 19.29/19.54 ! [V_ra_2,V_q_2,V_y_2,V_x_2,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_ra_2)
% 19.29/19.54 <=> ( V_x_2 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q_2),V_y_2),V_ra_2)
% 19.29/19.54 & ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.54 => V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 19.29/19.54 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.54 => ( V_ra_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_ra_2),c_Polynomial_Odegree(T_a,V_y_2)) ) ) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__by__0,axiom,
% 19.29/19.54 ! [V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__0,axiom,
% 19.29/19.54 ! [V_y,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__by__0__iff,axiom,
% 19.29/19.54 ! [V_ra_2,V_q_2,V_x_2,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_ra_2)
% 19.29/19.54 <=> ( V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.54 & V_ra_2 = V_x_2 ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__0__iff,axiom,
% 19.29/19.54 ! [V_ra_2,V_q_2,V_y_2,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_ra_2)
% 19.29/19.54 <=> ( V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 19.29/19.54 & V_ra_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__zero,axiom,
% 19.29/19.54 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_zero__le__natfloor,axiom,
% 19.29/19.54 ! [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))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__mult,axiom,
% 19.29/19.54 ! [V_r_H,V_q_H,V_z,V_r,V_q,V_y,V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)
% 19.29/19.54 => c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H),V_r)) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__real__of__nat,axiom,
% 19.29/19.54 ! [V_n] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__mono,axiom,
% 19.29/19.54 ! [V_y,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_div__poly__eq,axiom,
% 19.29/19.54 ! [V_r,V_q,V_y,V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
% 19.29/19.54 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_q ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__unique__div,axiom,
% 19.29/19.54 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 19.29/19.54 => V_q1 = V_q2 ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__unique__mod,axiom,
% 19.29/19.54 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 19.29/19.54 => V_r1 = V_r2 ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_pdivmod__rel__unique,axiom,
% 19.29/19.54 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 19.29/19.54 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 19.29/19.54 => ( V_q1 = V_q2
% 19.29/19.54 & V_r1 = V_r2 ) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__one,axiom,
% 19.29/19.54 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__neg,axiom,
% 19.29/19.54 ! [V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.54 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__natfloor__le,axiom,
% 19.29/19.54 ! [V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))),V_x)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_le__natfloor,axiom,
% 19.29/19.54 ! [V_a,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)),V_a))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__power,axiom,
% 19.29/19.54 ! [V_n,V_x] :
% 19.29/19.54 ( V_x = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))
% 19.29/19.54 => 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) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_le__natfloor__eq,axiom,
% 19.29/19.54 ! [V_a_2,V_x_2] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 19.29/19.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))
% 19.29/19.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)),V_x_2)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_le__natfloor__eq__one,axiom,
% 19.29/19.54 ! [V_x_2] :
% 19.29/19.54 ( 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)))
% 19.29/19.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__natfloor__add__one__gt,axiom,
% 19.29/19.54 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__subtract,axiom,
% 19.29/19.54 ! [V_x,V_a] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))
% 19.29/19.54 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__natfloor__gt__diff__one,axiom,
% 19.29/19.54 ! [V_x] : 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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_less__natfloor,axiom,
% 19.29/19.54 ! [V_n,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
% 19.29/19.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_le__mult__natfloor,axiom,
% 19.29/19.54 ! [V_b,V_a] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 19.29/19.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))
% 19.29/19.54 => 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)))) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__add,axiom,
% 19.29/19.54 ! [V_a,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 19.29/19.54 ! [V_n,V_z] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
% 19.29/19.54 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__eq,axiom,
% 19.29/19.54 ! [V_x,V_n] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x))
% 19.29/19.54 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 19.29/19.54 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_natfloor__div__nat,axiom,
% 19.29/19.54 ! [V_y,V_x] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 19.29/19.54 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
% 19.29/19.54 => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_DeMoivre2,axiom,
% 19.29/19.54 ! [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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__1,axiom,
% 19.29/19.54 ! [V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__of__nat__div4,axiom,
% 19.29/19.54 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide_Oadd,axiom,
% 19.29/19.54 ! [V_ya,V_y,V_x,T_a] :
% 19.29/19.54 ( class_RealVector_Oreal__normed__field(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_add__divide__distrib,axiom,
% 19.29/19.54 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_diff__divide__distrib,axiom,
% 19.29/19.54 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => 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,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_norm__divide,axiom,
% 19.29/19.54 ! [V_b,V_a,T_a] :
% 19.29/19.54 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 19.29/19.54 & class_RealVector_Oreal__normed__field(T_a) )
% 19.29/19.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = 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)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide_Odiff,axiom,
% 19.29/19.54 ! [V_ya,V_y,V_x,T_a] :
% 19.29/19.54 ( class_RealVector_Oreal__normed__field(T_a)
% 19.29/19.54 => 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,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__0__le__divide__iff,axiom,
% 19.29/19.54 ! [V_y_2,V_x_2] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))
% 19.29/19.54 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 19.29/19.54 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) )
% 19.29/19.54 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 19.29/19.54 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_lemma__MVT,axiom,
% 19.29/19.54 ! [V_b_2,V_a_2,V_f_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_b_2),hAPP(V_f_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_f_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_b_2),hAPP(V_f_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_times__divide__eq__right,axiom,
% 19.29/19.54 ! [V_c,V_b,V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__divide__square__eq,axiom,
% 19.29/19.54 ! [V_a,V_r] : 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)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_nonzero__norm__divide,axiom,
% 19.29/19.54 ! [V_a,V_b,T_a] :
% 19.29/19.54 ( class_RealVector_Oreal__normed__field(T_a)
% 19.29/19.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = 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)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide_Ozero,axiom,
% 19.29/19.54 ! [V_y,T_a] :
% 19.29/19.54 ( class_RealVector_Oreal__normed__field(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__zero__left,axiom,
% 19.29/19.54 ! [V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__zero,axiom,
% 19.29/19.54 ! [V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_power__divide,axiom,
% 19.29/19.54 ! [V_n,V_b,V_a,T_a] :
% 19.29/19.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 19.29/19.54 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = 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)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_nonzero__power__divide,axiom,
% 19.29/19.54 ! [V_n,V_a,V_b,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = 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)) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_nonzero__eq__divide__eq,axiom,
% 19.29/19.54 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 19.29/19.54 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_nonzero__divide__eq__eq,axiom,
% 19.29/19.54 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 19.29/19.54 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__eq__imp,axiom,
% 19.29/19.54 ! [V_a,V_b,V_c,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_eq__divide__imp,axiom,
% 19.29/19.54 ! [V_b,V_a,V_c,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 19.29/19.54 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_DERIV__mult__lemma,axiom,
% 19.29/19.54 ! [V_h,V_d,V_c,V_b,V_a,T_a] :
% 19.29/19.54 ( class_RealVector_Oreal__field(T_a)
% 19.29/19.54 => 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) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),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),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h)),V_d)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_power__one__over,axiom,
% 19.29/19.54 ! [V_n,V_a,T_a] :
% 19.29/19.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 19.29/19.54 => 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),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)),V_n) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_right__inverse__eq,axiom,
% 19.29/19.54 ! [V_a_2,V_b_2,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 19.29/19.54 <=> V_a_2 = V_b_2 ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__self,axiom,
% 19.29/19.54 ! [V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring(T_a)
% 19.29/19.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_divide__self__if,axiom,
% 19.29/19.54 ! [V_a,T_a] :
% 19.29/19.54 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 19.29/19.54 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 19.29/19.54 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_complex__mod__rcis,axiom,
% 19.29/19.54 ! [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) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_rcis__zero__mod,axiom,
% 19.29/19.54 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_power__diff,axiom,
% 19.29/19.54 ! [V_m,V_n,V_a,T_a] :
% 19.29/19.54 ( class_Fields_Ofield(T_a)
% 19.29/19.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 19.29/19.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 19.29/19.54 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = 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)) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_rcis__mult,axiom,
% 19.29/19.54 ! [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),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__of__nat__div2,axiom,
% 19.29/19.54 ! [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,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_real__of__nat__div3,axiom,
% 19.29/19.54 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)),hAPP(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))) ).
% 19.29/19.54
% 19.29/19.54 fof(fact_le__divide__eq,axiom,
% 19.29/19.54 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 19.29/19.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 19.29/19.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))
% 19.29/19.54 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 19.29/19.54 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 19.29/19.54 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
% 19.29/19.54 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 19.29/19.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 19.29/19.54
% 19.29/19.54 %----Arity declarations (271)
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__ring(T_1)
% 19.29/19.54 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_fun__Orderings_Opreorder,axiom,
% 19.29/19.54 ! [T_2,T_1] :
% 19.29/19.54 ( class_Orderings_Opreorder(T_1)
% 19.29/19.54 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_fun__Orderings_Oorder,axiom,
% 19.29/19.54 ! [T_2,T_1] :
% 19.29/19.54 ( class_Orderings_Oorder(T_1)
% 19.29/19.54 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_fun__Orderings_Oord,axiom,
% 19.29/19.54 ! [T_2,T_1] :
% 19.29/19.54 ( class_Orderings_Oord(T_1)
% 19.29/19.54 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 19.29/19.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 19.29/19.54 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 19.29/19.54 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 19.29/19.54 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 19.29/19.54 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 19.29/19.54 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 19.29/19.54 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 19.29/19.54 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 19.29/19.54 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 19.29/19.54 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 19.29/19.54 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 19.29/19.54 class_Orderings_Opreorder(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 19.29/19.54 class_Orderings_Olinorder(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 19.29/19.54 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 19.29/19.54 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 19.29/19.54 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 19.29/19.54 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 19.29/19.54 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 19.29/19.54 class_Rings_Omult__zero(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 19.29/19.54 class_Orderings_Oorder(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 19.29/19.54 class_Rings_Osemiring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 19.29/19.54 class_Orderings_Oord(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 19.29/19.54 class_Rings_Oring__1(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Power_Opower,axiom,
% 19.29/19.54 class_Power_Opower(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 19.29/19.54 class_Groups_Ozero(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oring,axiom,
% 19.29/19.54 class_Rings_Oring(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 19.29/19.54 class_Rings_Oidom(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Int__Oint__Groups_Oone,axiom,
% 19.29/19.54 class_Groups_Oone(tc_Int_Oint) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 19.29/19.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 19.29/19.54 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 19.29/19.54 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 19.29/19.54 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 19.29/19.54 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 19.29/19.54 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 19.29/19.54 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 19.29/19.54 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 19.29/19.54 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 19.29/19.54 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 19.29/19.54 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 19.29/19.54 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 19.29/19.54 class_Orderings_Oorder(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 19.29/19.54 class_Rings_Osemiring(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 19.29/19.54 class_Orderings_Oord(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Power_Opower,axiom,
% 19.29/19.54 class_Power_Opower(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 19.29/19.54 class_Groups_Ozero(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 19.29/19.54 class_Groups_Oone(tc_Nat_Onat) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 19.29/19.54 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 19.29/19.54 class_Orderings_Oorder(tc_HOL_Obool) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 19.29/19.54 class_Orderings_Oord(tc_HOL_Obool) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 19.29/19.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 19.29/19.54 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 19.29/19.54 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 19.29/19.54 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 19.29/19.54 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 19.29/19.54 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 19.29/19.54 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 19.29/19.54 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 19.29/19.54 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 19.29/19.54 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 19.29/19.54 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 19.29/19.54 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 19.29/19.54 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__RealVector_Oreal__field,axiom,
% 19.29/19.54 class_RealVector_Oreal__field(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 19.29/19.54 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
% 19.29/19.54 class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 19.29/19.54 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 19.29/19.54 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 19.29/19.54 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 19.29/19.54 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 19.29/19.54 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 19.29/19.54 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 19.29/19.54 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 19.29/19.54 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 19.29/19.54 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 19.29/19.54 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 19.29/19.54 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 19.29/19.54 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 19.29/19.54 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 19.29/19.54 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 19.29/19.54 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 19.29/19.54 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 19.29/19.54 class_Power_Opower(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 19.29/19.54 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 19.29/19.54 class_Rings_Oring(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 19.29/19.54 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 19.29/19.54 class_Groups_Oone(tc_RealDef_Oreal) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 19.29/19.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 19.29/19.54 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 19.29/19.54 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 19.29/19.54 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 19.29/19.54 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 19.29/19.54 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 19.29/19.54 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
% 19.29/19.54 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 19.29/19.54 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 19.29/19.54 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
% 19.29/19.54 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 19.29/19.54 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 19.29/19.54 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 19.29/19.54 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 19.29/19.54 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 19.29/19.54 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 19.29/19.54 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 19.29/19.54 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 19.29/19.54 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 19.29/19.54 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 19.29/19.54 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 19.29/19.54 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 19.29/19.54 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 19.29/19.54 class_Power_Opower(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 19.29/19.54 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 19.29/19.54 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 19.29/19.54 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 19.29/19.54 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Oidom(T_1)
% 19.29/19.54 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Oidom(T_1)
% 19.29/19.54 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Oidom(T_1)
% 19.29/19.54 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocomm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Oidom(T_1)
% 19.29/19.54 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocomm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Fields_Ofield(T_1)
% 19.29/19.54 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Nat_Osemiring__char__0,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Oab__group__add(T_1)
% 19.29/19.54 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__ring__1(T_1)
% 19.29/19.54 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ocomm__monoid__add(T_1)
% 19.29/19.54 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Osemiring__1,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Oab__group__add(T_1)
% 19.29/19.54 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__0(T_1)
% 19.29/19.54 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Olinordered__idom(T_1)
% 19.29/19.54 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__ring__1(T_1)
% 19.29/19.54 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Groups_Ozero(T_1)
% 19.29/19.54 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__ring(T_1)
% 19.29/19.54 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Oidom(T_1)
% 19.29/19.54 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 19.29/19.54 ! [T_1] :
% 19.29/19.54 ( class_Rings_Ocomm__semiring__1(T_1)
% 19.29/19.54 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 19.29/19.54
% 19.29/19.54 %----Conjectures (2)
% 19.29/19.54 fof(conj_0,hypothesis,
% 19.29/19.54 ! [B_f] :
% 19.29/19.54 ( c_SEQ_Osubseq(B_f)
% 19.29/19.54 => ( ? [B_z] :
% 19.29/19.54 ! [B_e] :
% 19.29/19.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 19.29/19.54 => ? [B_N] :
% 19.29/19.54 ! [B_n] :
% 19.29/19.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n))
% 19.29/19.54 => 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_g____(hAPP(B_f,B_n)),B_z)),B_e) ) )
% 19.29/19.54 => v_thesis____ ) ) ).
% 19.29/19.54
% 19.29/19.54 fof(conj_1,conjecture,
% 19.29/19.54 v_thesis____ ).
% 19.29/19.54
% 19.29/19.54 %------------------------------------------------------------------------------
% 19.29/19.54 %-------------------------------------------
% 19.29/19.54 % Proof found
% 19.29/19.54 % SZS status Theorem for theBenchmark
% 19.29/19.54 % SZS output start Proof
% 19.29/19.54 %ClaNum:2058(EqnAxiom:332)
% 19.29/19.54 %VarNum:9484(SingletonVarNum:3350)
% 19.29/19.54 %MaxLitNum:7
% 19.29/19.54 %MaxfuncDepth:6
% 19.29/19.54 %SharedTerms:293
% 19.29/19.54 %goalClause: 693
% 19.29/19.54 %singleGoalClaCount:1
% 19.29/19.54 [333]P1(a1)
% 19.29/19.54 [334]P1(a2)
% 19.29/19.54 [335]P2(a3)
% 19.29/19.54 [336]P12(a1)
% 19.29/19.54 [337]P12(a112)
% 19.29/19.54 [338]P30(a1)
% 19.29/19.54 [339]P30(a114)
% 19.29/19.54 [340]P30(a112)
% 19.29/19.54 [341]P30(a113)
% 19.29/19.54 [342]P31(a1)
% 19.29/19.54 [343]P31(a114)
% 19.29/19.54 [344]P31(a2)
% 19.29/19.54 [345]P31(a112)
% 19.29/19.54 [346]P37(a1)
% 19.29/19.54 [347]P37(a114)
% 19.29/19.54 [348]P37(a112)
% 19.29/19.54 [349]P39(a1)
% 19.29/19.54 [350]P39(a114)
% 19.29/19.54 [351]P39(a112)
% 19.29/19.54 [352]P39(a113)
% 19.29/19.54 [353]P40(a1)
% 19.29/19.54 [354]P40(a114)
% 19.29/19.54 [355]P40(a112)
% 19.29/19.54 [356]P40(a113)
% 19.29/19.54 [357]P13(a1)
% 19.29/19.54 [358]P13(a2)
% 19.29/19.54 [359]P13(a112)
% 19.29/19.54 [360]P18(a1)
% 19.29/19.54 [361]P18(a2)
% 19.29/19.54 [362]P18(a112)
% 19.29/19.54 [363]P47(a1)
% 19.29/19.54 [364]P47(a114)
% 19.29/19.54 [365]P47(a112)
% 19.29/19.54 [366]P60(a1)
% 19.29/19.54 [367]P60(a2)
% 19.29/19.54 [368]P60(a112)
% 19.29/19.54 [369]P48(a1)
% 19.29/19.54 [370]P48(a112)
% 19.29/19.54 [371]P32(a1)
% 19.29/19.54 [372]P32(a112)
% 19.29/19.54 [373]P74(a1)
% 19.29/19.54 [374]P74(a114)
% 19.29/19.54 [375]P74(a2)
% 19.29/19.54 [376]P74(a112)
% 19.29/19.54 [377]P41(a1)
% 19.29/19.54 [378]P41(a2)
% 19.29/19.54 [379]P42(a1)
% 19.29/19.54 [380]P42(a2)
% 19.29/19.54 [381]P38(a1)
% 19.29/19.54 [382]P38(a114)
% 19.29/19.54 [383]P38(a2)
% 19.29/19.54 [384]P38(a112)
% 19.29/19.54 [385]P43(a1)
% 19.29/19.54 [386]P43(a114)
% 19.29/19.54 [387]P43(a2)
% 19.29/19.54 [388]P43(a112)
% 19.29/19.54 [389]P61(a1)
% 19.29/19.54 [390]P61(a114)
% 19.29/19.54 [391]P61(a2)
% 19.29/19.54 [392]P61(a112)
% 19.29/19.54 [393]P66(a1)
% 19.29/19.54 [394]P66(a114)
% 19.29/19.54 [395]P66(a2)
% 19.29/19.54 [396]P66(a112)
% 19.29/19.54 [397]P78(a1)
% 19.29/19.54 [398]P78(a114)
% 19.29/19.54 [399]P78(a2)
% 19.29/19.54 [400]P78(a112)
% 19.29/19.54 [401]P67(a1)
% 19.29/19.54 [402]P67(a2)
% 19.29/19.54 [403]P67(a112)
% 19.29/19.54 [404]P75(a1)
% 19.29/19.54 [405]P75(a114)
% 19.29/19.54 [406]P75(a2)
% 19.29/19.54 [407]P75(a112)
% 19.29/19.54 [408]P14(a114)
% 19.29/19.54 [409]P14(a112)
% 19.29/19.54 [410]P15(a1)
% 19.29/19.54 [411]P15(a2)
% 19.29/19.54 [412]P49(a1)
% 19.29/19.54 [413]P49(a2)
% 19.29/19.54 [414]P49(a112)
% 19.29/19.54 [415]P50(a1)
% 19.29/19.54 [416]P50(a114)
% 19.29/19.54 [417]P50(a2)
% 19.29/19.54 [418]P50(a112)
% 19.29/19.54 [419]P19(a1)
% 19.29/19.54 [420]P19(a114)
% 19.29/19.54 [421]P19(a2)
% 19.29/19.54 [422]P19(a112)
% 19.29/19.54 [423]P21(a1)
% 19.29/19.54 [424]P21(a114)
% 19.29/19.54 [425]P21(a2)
% 19.29/19.54 [426]P21(a112)
% 19.29/19.54 [427]P26(a1)
% 19.29/19.54 [428]P26(a114)
% 19.29/19.54 [429]P26(a2)
% 19.29/19.54 [430]P26(a112)
% 19.29/19.54 [431]P29(a1)
% 19.29/19.54 [432]P29(a114)
% 19.29/19.54 [433]P29(a2)
% 19.29/19.54 [434]P29(a112)
% 19.29/19.54 [435]P44(a1)
% 19.29/19.54 [436]P44(a2)
% 19.29/19.54 [437]P54(a1)
% 19.29/19.54 [438]P54(a114)
% 19.29/19.54 [439]P54(a2)
% 19.29/19.54 [440]P54(a112)
% 19.29/19.54 [441]P76(a1)
% 19.29/19.54 [442]P76(a2)
% 19.29/19.54 [443]P76(a112)
% 19.29/19.54 [444]P58(a1)
% 19.29/19.54 [445]P58(a112)
% 19.29/19.54 [446]P59(a1)
% 19.29/19.54 [447]P59(a112)
% 19.29/19.54 [448]P68(a1)
% 19.29/19.54 [449]P68(a114)
% 19.29/19.54 [450]P68(a112)
% 19.29/19.54 [451]P69(a1)
% 19.29/19.54 [452]P69(a112)
% 19.29/19.54 [453]P71(a1)
% 19.29/19.54 [454]P71(a114)
% 19.29/19.54 [455]P71(a112)
% 19.29/19.54 [456]P70(a1)
% 19.29/19.54 [457]P70(a114)
% 19.29/19.54 [458]P70(a112)
% 19.29/19.54 [459]P62(a1)
% 19.29/19.54 [460]P62(a114)
% 19.29/19.54 [461]P62(a112)
% 19.29/19.54 [462]P57(a1)
% 19.29/19.54 [463]P57(a114)
% 19.29/19.54 [464]P57(a112)
% 19.29/19.54 [465]P63(a1)
% 19.29/19.54 [466]P63(a114)
% 19.29/19.54 [467]P63(a112)
% 19.29/19.54 [468]P72(a1)
% 19.29/19.54 [469]P72(a112)
% 19.29/19.54 [470]P79(a1)
% 19.29/19.54 [471]P79(a114)
% 19.29/19.54 [472]P79(a2)
% 19.29/19.54 [473]P79(a112)
% 19.29/19.54 [474]P51(a1)
% 19.29/19.54 [475]P51(a114)
% 19.29/19.54 [476]P51(a2)
% 19.29/19.54 [477]P51(a112)
% 19.29/19.54 [478]P77(a1)
% 19.29/19.54 [479]P77(a114)
% 19.29/19.54 [480]P77(a2)
% 19.29/19.54 [481]P77(a112)
% 19.29/19.54 [482]P27(a1)
% 19.29/19.54 [483]P27(a112)
% 19.29/19.54 [484]P22(a1)
% 19.29/19.54 [485]P22(a114)
% 19.29/19.54 [486]P22(a2)
% 19.29/19.54 [487]P22(a112)
% 19.29/19.54 [488]P28(a1)
% 19.29/19.54 [489]P28(a114)
% 19.29/19.54 [490]P28(a2)
% 19.29/19.54 [491]P28(a112)
% 19.29/19.54 [492]P33(a1)
% 19.29/19.54 [493]P33(a114)
% 19.29/19.54 [494]P33(a112)
% 19.29/19.54 [495]P34(a1)
% 19.29/19.54 [496]P34(a114)
% 19.29/19.54 [497]P34(a112)
% 19.29/19.54 [498]P35(a1)
% 19.29/19.54 [499]P35(a114)
% 19.29/19.54 [500]P35(a112)
% 19.29/19.54 [501]P20(a1)
% 19.29/19.54 [502]P20(a114)
% 19.29/19.54 [503]P20(a2)
% 19.29/19.54 [504]P20(a112)
% 19.29/19.54 [505]P23(a1)
% 19.29/19.54 [506]P23(a114)
% 19.29/19.54 [507]P23(a2)
% 19.29/19.54 [508]P23(a112)
% 19.29/19.54 [509]P24(a1)
% 19.29/19.54 [510]P24(a114)
% 19.29/19.54 [511]P24(a2)
% 19.29/19.54 [512]P24(a112)
% 19.29/19.54 [513]P36(a1)
% 19.29/19.54 [514]P36(a114)
% 19.29/19.54 [515]P36(a112)
% 19.29/19.54 [516]P73(a1)
% 19.29/19.54 [517]P73(a2)
% 19.29/19.54 [518]P73(a112)
% 19.29/19.54 [519]P64(a1)
% 19.29/19.54 [520]P64(a112)
% 19.29/19.54 [521]P65(a1)
% 19.29/19.54 [522]P65(a112)
% 19.29/19.54 [523]P52(a1)
% 19.29/19.54 [524]P52(a2)
% 19.29/19.54 [525]P52(a112)
% 19.29/19.54 [526]P55(a1)
% 19.29/19.54 [527]P55(a2)
% 19.29/19.54 [528]P46(a1)
% 19.29/19.54 [529]P46(a2)
% 19.29/19.54 [530]P16(a1)
% 19.29/19.54 [531]P16(a2)
% 19.29/19.54 [532]P56(a1)
% 19.29/19.54 [533]P56(a2)
% 19.29/19.54 [534]P45(a1)
% 19.29/19.54 [535]P45(a2)
% 19.29/19.54 [536]P17(a1)
% 19.29/19.54 [537]P25(a1)
% 19.29/19.54 [538]P25(a114)
% 19.29/19.54 [539]P25(a2)
% 19.29/19.54 [540]P25(a112)
% 19.29/19.54 [541]P53(a1)
% 19.29/19.54 [542]P53(a2)
% 19.29/19.54 [543]P53(a112)
% 19.29/19.54 [693]~P82(a500)
% 19.29/19.54 [545]E(f4(a114),f5(a1))
% 19.29/19.54 [580]P3(a112,f6(a112),f7(a112))
% 19.29/19.54 [694]~E(f6(a2),a9)
% 19.29/19.54 [695]~E(f7(a2),a9)
% 19.29/19.54 [696]~E(f7(a1),f6(a1))
% 19.29/19.54 [697]~E(f7(a112),f6(a112))
% 19.29/19.54 [698]~P6(f6(a1))
% 19.29/19.54 [546]E(f17(f6(a1)),f6(a114))
% 19.29/19.54 [547]E(f17(f7(a1)),f7(a114))
% 19.29/19.54 [548]E(f27(f6(a1)),f6(a114))
% 19.29/19.54 [549]E(f27(f7(a1)),f7(a114))
% 19.29/19.54 [551]E(f51(a16,f7(a112)),f7(a114))
% 19.29/19.54 [552]E(f51(a16,f6(a112)),f6(a114))
% 19.29/19.54 [556]E(f51(f4(a114),f6(a114)),f6(a1))
% 19.29/19.54 [557]E(f51(f4(a114),f7(a114)),f7(a1))
% 19.29/19.54 [558]E(f51(f5(a112),f6(a114)),f6(a112))
% 19.29/19.54 [559]E(f51(f5(a112),f7(a114)),f7(a112))
% 19.29/19.54 [584]E(f15(a114,f6(a114),f7(a114)),f51(a16,f7(a112)))
% 19.29/19.54 [595]P80(f51(f18(a112,f6(a112)),f7(a112)))
% 19.29/19.54 [638]P4(a112,a114,a16,f18(a112,f6(a112)))
% 19.29/19.54 [588]P80(f51(f18(a1,f6(a1)),a116))
% 19.29/19.54 [601]E(f51(f4(a114),f15(a114,f6(a114),f7(a114))),f7(a1))
% 19.29/19.54 [602]E(f51(f5(a112),f15(a114,f6(a114),f7(a114))),f7(a112))
% 19.29/19.54 [700]~P3(a114,x7001,x7001)
% 19.29/19.54 [560]E(f28(a1,x5601),f10(a1,x5601))
% 19.29/19.54 [572]E(f13(a114,x5721,x5721),f6(a114))
% 19.29/19.54 [703]~P3(a114,x7031,f6(a114))
% 19.29/19.54 [553]E(f8(f6(a1),x5531),f6(a2))
% 19.29/19.54 [564]E(f51(f51(f14(a114),x5641),f7(a114)),x5641)
% 19.29/19.54 [565]E(f51(f51(f14(a112),x5651),f7(a112)),x5651)
% 19.29/19.54 [567]E(f51(f51(f14(a114),x5671),f6(a114)),f6(a114))
% 19.29/19.54 [573]E(f13(a114,x5731,f6(a114)),x5731)
% 19.29/19.54 [574]E(f15(a114,x5741,f6(a114)),x5741)
% 19.29/19.54 [575]E(f15(a112,x5751,f6(a112)),x5751)
% 19.29/19.54 [576]E(f15(a114,f6(a114),x5761),x5761)
% 19.29/19.54 [577]E(f15(a112,f6(a112),x5771),x5771)
% 19.29/19.54 [578]E(f13(a114,f6(a114),x5781),f6(a114))
% 19.29/19.54 [579]E(f11(a112,f6(a112),x5791),f6(a112))
% 19.29/19.54 [585]P80(f51(f18(a1,x5851),x5851))
% 19.29/19.54 [586]P80(f51(f18(a114,x5861),x5861))
% 19.29/19.54 [587]P80(f51(f18(a112,x5871),x5871))
% 19.29/19.54 [609]P3(a114,x6091,f15(a114,x6091,f7(a114)))
% 19.29/19.54 [611]P3(a114,f6(a114),f15(a114,x6111,f7(a114)))
% 19.29/19.54 [615]P3(a1,f13(a1,x6151,f7(a1)),f51(f4(a114),f27(x6151)))
% 19.29/19.54 [616]P3(a1,f6(a1),f15(a1,f7(a1),f10(a1,x6161)))
% 19.29/19.54 [634]P3(a1,x6341,f15(a1,f51(f4(a114),f27(x6341)),f7(a1)))
% 19.29/19.54 [705]~E(f15(a114,x7051,f7(a114)),x7051)
% 19.29/19.54 [711]~E(f15(a114,x7111,f7(a114)),f6(a114))
% 19.29/19.54 [712]~P3(a1,f51(f4(a114),x7121),f6(a1))
% 19.29/19.54 [713]~P3(a112,f51(f5(a112),x7131),f6(a112))
% 19.29/19.54 [717]~P3(a1,f15(a1,f10(a1,x7171),f7(a1)),x7171)
% 19.29/19.54 [561]E(f17(f51(f4(a114),x5611)),x5611)
% 19.29/19.54 [562]E(f27(f51(f4(a114),x5621)),x5621)
% 19.29/19.54 [563]E(f51(a16,f51(f5(a112),x5631)),x5631)
% 19.29/19.54 [568]E(f51(f51(f14(a1),f7(a1)),x5681),x5681)
% 19.29/19.54 [569]E(f51(f51(f14(a114),f7(a114)),x5691),x5691)
% 19.29/19.54 [570]E(f51(f51(f14(a112),f7(a112)),x5701),x5701)
% 19.29/19.54 [571]E(f51(f51(f14(a114),f6(a114)),x5711),f6(a114))
% 19.29/19.54 [582]E(f10(a1,f51(f4(a114),x5821)),f51(f4(a114),x5821))
% 19.29/19.54 [583]E(f10(a112,f51(f5(a112),x5831)),f51(f5(a112),x5831))
% 19.29/19.54 [590]P80(f51(f18(a114,f6(a114)),x5901))
% 19.29/19.54 [603]P80(f51(f18(a1,f6(a1)),f51(f4(a114),x6031)))
% 19.29/19.54 [605]P80(f51(f18(a112,f6(a112)),f51(f5(a112),x6051)))
% 19.29/19.54 [610]P80(f51(f18(a1,x6101),f51(f4(a114),f17(x6101))))
% 19.29/19.54 [613]E(f11(a114,x6131,f15(a114,f6(a114),f7(a114))),x6131)
% 19.29/19.54 [618]E(f15(a112,f7(a112),f51(f5(a112),x6181)),f51(f5(a112),f15(a114,x6181,f7(a114))))
% 19.29/19.54 [619]E(f15(a1,f51(f4(a114),x6191),f7(a1)),f51(f4(a114),f15(a114,x6191,f7(a114))))
% 19.29/19.54 [644]P3(a1,f6(a1),f51(f4(a114),f15(a114,x6441,f7(a114))))
% 19.29/19.54 [716]~E(f15(a112,f15(a112,f7(a112),x7161),x7161),f6(a112))
% 19.29/19.54 [617]P80(f51(f18(a1,f28(a2,f117(x6171))),a116))
% 19.29/19.54 [635]P80(f51(f18(a114,x6351),f51(f51(f14(a114),x6351),x6351)))
% 19.29/19.54 [659]E(f51(f51(f20(a114),f15(a114,f6(a114),f7(a114))),x6591),f15(a114,f6(a114),f7(a114)))
% 19.29/19.54 [718]~P80(f51(f18(a114,f15(a114,x7181,f7(a114))),x7181))
% 19.29/19.54 [683]P80(f51(f18(a114,x6831),f51(f51(f14(a114),x6831),f51(f51(f14(a114),x6831),x6831))))
% 19.29/19.54 [598]E(f15(a114,x5981,x5982),f15(a114,x5982,x5981))
% 19.29/19.54 [599]E(f15(a112,x5991,x5992),f15(a112,x5992,x5991))
% 19.29/19.54 [714]~P3(a114,f15(a114,x7141,x7142),x7142)
% 19.29/19.54 [715]~P3(a114,f15(a114,x7151,x7152),x7151)
% 19.29/19.54 [566]E(f28(a2,f8(x5661,x5662)),f10(a1,x5661))
% 19.29/19.54 [606]E(f13(a114,f15(a114,x6061,x6062),x6062),x6061)
% 19.29/19.54 [607]E(f13(a114,f15(a114,x6071,x6072),x6071),x6072)
% 19.29/19.54 [608]E(f13(a114,x6081,f15(a114,x6081,x6082)),f6(a114))
% 19.29/19.54 [637]P3(a114,f13(a114,x6371,x6372),f15(a114,x6371,f7(a114)))
% 19.29/19.54 [639]P80(f51(f18(a114,x6391),f15(a114,x6392,x6391)))
% 19.29/19.54 [640]P80(f51(f18(a114,x6401),f15(a114,x6401,x6402)))
% 19.29/19.54 [664]P3(a114,x6641,f15(a114,f15(a114,x6642,x6641),f7(a114)))
% 19.29/19.54 [665]P3(a114,x6651,f15(a114,f15(a114,x6651,x6652),f7(a114)))
% 19.29/19.54 [690]P80(f51(f18(a1,f13(a1,f28(a2,f15(a2,x6901,x6902)),f28(a2,x6901))),f28(a2,x6902)))
% 19.29/19.54 [691]P80(f51(f18(a1,f13(a1,f29(a1,f51(f4(a114),x6911),f51(f4(a114),x6912)),f51(f4(a114),f11(a114,x6911,x6912)))),f7(a1)))
% 19.29/19.54 [591]E(f51(f51(f14(a1),x5911),x5912),f51(f51(f14(a1),x5912),x5911))
% 19.29/19.54 [592]E(f51(f51(f14(a114),x5921),x5922),f51(f51(f14(a114),x5922),x5921))
% 19.29/19.54 [593]E(f51(f51(f14(a112),x5931),x5932),f51(f51(f14(a112),x5932),x5931))
% 19.29/19.54 [614]E(f19(f51(f5(a112),x6141),f51(f5(a112),x6142)),f51(f5(a112),f13(a114,x6141,x6142)))
% 19.29/19.54 [625]E(f15(a1,f51(f4(a114),x6251),f51(f4(a114),x6252)),f51(f4(a114),f15(a114,x6251,x6252)))
% 19.29/19.54 [627]E(f11(a112,f51(f5(a112),x6271),f51(f5(a112),x6272)),f51(f5(a112),f11(a114,x6271,x6272)))
% 19.29/19.54 [629]E(f15(a112,f51(f5(a112),x6291),f51(f5(a112),x6292)),f51(f5(a112),f15(a114,x6291,x6292)))
% 19.29/19.54 [654]E(f15(a114,f15(a114,x6541,f7(a114)),x6542),f15(a114,f15(a114,x6541,x6542),f7(a114)))
% 19.29/19.54 [655]E(f13(a114,f13(a114,x6551,f7(a114)),x6552),f13(a114,x6551,f15(a114,x6552,f7(a114))))
% 19.29/19.54 [656]E(f15(a114,f15(a114,x6561,f7(a114)),x6562),f15(a114,x6561,f15(a114,x6562,f7(a114))))
% 19.29/19.54 [680]P80(f51(f18(a114,f13(a114,x6801,x6802)),x6801))
% 19.29/19.54 [681]P80(f51(f18(a114,f11(a114,x6811,x6812)),x6811))
% 19.29/19.54 [687]P80(f51(f18(a1,f28(a2,x6871)),f15(a1,f28(a2,f15(a2,x6871,x6872)),f28(a2,x6872))))
% 19.29/19.54 [622]E(f51(f51(f20(a1),f51(f4(a114),x6221)),x6222),f51(f4(a114),f51(f51(f20(a114),x6221),x6222)))
% 19.29/19.54 [624]E(f51(f51(f20(a112),f51(f5(a112),x6241)),x6242),f51(f5(a112),f51(f51(f20(a114),x6241),x6242)))
% 19.29/19.54 [630]E(f51(f51(f14(a1),f51(f4(a114),x6301)),f51(f4(a114),x6302)),f51(f4(a114),f51(f51(f14(a114),x6301),x6302)))
% 19.29/19.54 [633]E(f51(f51(f14(a112),f51(f5(a112),x6331)),f51(f5(a112),x6332)),f51(f5(a112),f51(f51(f14(a114),x6331),x6332)))
% 19.29/19.54 [641]E(f29(a1,f51(f51(f14(a1),x6411),x6412),f51(f51(f14(a1),x6411),x6411)),f29(a1,x6412,x6411))
% 19.29/19.54 [642]E(f51(f51(f14(a114),x6421),f15(a114,x6422,f7(a114))),f15(a114,x6421,f51(f51(f14(a114),x6421),x6422)))
% 19.29/19.54 [670]E(f51(f51(f14(a114),f15(a114,x6701,f7(a114))),x6702),f15(a114,x6702,f51(f51(f14(a114),x6701),x6702)))
% 19.29/19.54 [672]P80(f51(f18(a112,f6(a112)),f51(f51(f20(a112),f10(a112,x6721)),x6722)))
% 19.29/19.54 [688]P80(f51(f18(a1,f51(f4(a114),f11(a114,x6881,x6882))),f29(a1,f51(f4(a114),x6881),f51(f4(a114),x6882))))
% 19.29/19.54 [689]P80(f51(f18(a1,f6(a1)),f13(a1,f29(a1,f51(f4(a114),x6891),f51(f4(a114),x6892)),f51(f4(a114),f11(a114,x6891,x6892)))))
% 19.29/19.54 [674]E(f51(f51(f14(a114),f51(a16,f10(a112,x6741))),f51(a16,f10(a112,x6742))),f51(a16,f10(a112,f51(f51(f14(a112),x6741),x6742))))
% 19.29/19.54 [645]E(f15(a114,x6451,f15(a114,x6452,x6453)),f15(a114,x6452,f15(a114,x6451,x6453)))
% 19.29/19.54 [646]E(f15(a112,x6461,f15(a112,x6462,x6463)),f15(a112,x6462,f15(a112,x6461,x6463)))
% 19.29/19.54 [647]E(f13(a114,f13(a114,x6471,x6472),x6473),f13(a114,x6471,f15(a114,x6472,x6473)))
% 19.29/19.54 [648]E(f15(a114,f15(a114,x6481,x6482),x6483),f15(a114,x6481,f15(a114,x6482,x6483)))
% 19.29/19.54 [649]E(f15(a112,f15(a112,x6491,x6492),x6493),f15(a112,x6491,f15(a112,x6492,x6493)))
% 19.29/19.54 [650]E(f13(a114,f13(a114,x6501,x6502),x6503),f13(a114,f13(a114,x6501,x6503),x6502))
% 19.29/19.54 [651]E(f13(a114,f15(a114,x6511,x6512),f15(a114,x6513,x6512)),f13(a114,x6511,x6513))
% 19.29/19.54 [652]E(f13(a114,f15(a114,x6521,x6522),f15(a114,x6521,x6523)),f13(a114,x6522,x6523))
% 19.29/19.54 [684]E(f13(a114,f13(a114,f15(a114,x6841,f7(a114)),x6842),f15(a114,x6843,f7(a114))),f13(a114,f13(a114,x6841,x6842),x6843))
% 19.29/19.54 [643]E(f11(a114,x6431,f51(f51(f14(a114),x6432),x6433)),f11(a114,f11(a114,x6431,x6432),x6433))
% 19.29/19.54 [666]E(f13(a114,f51(f51(f14(a114),x6661),x6662),f51(f51(f14(a114),x6661),x6663)),f51(f51(f14(a114),x6661),f13(a114,x6662,x6663)))
% 19.29/19.54 [667]E(f15(a114,f51(f51(f14(a114),x6671),x6672),f51(f51(f14(a114),x6671),x6673)),f51(f51(f14(a114),x6671),f15(a114,x6672,x6673)))
% 19.29/19.54 [668]E(f13(a112,f51(f51(f14(a112),x6681),x6682),f51(f51(f14(a112),x6681),x6683)),f51(f51(f14(a112),x6681),f13(a112,x6682,x6683)))
% 19.29/19.54 [669]E(f15(a112,f51(f51(f14(a112),x6691),x6692),f51(f51(f14(a112),x6691),x6693)),f51(f51(f14(a112),x6691),f15(a112,x6692,x6693)))
% 19.29/19.54 [673]E(f51(f51(f14(a112),f51(f51(f20(a112),x6731),x6732)),f51(f51(f20(a112),x6731),x6733)),f51(f51(f20(a112),x6731),f15(a114,x6732,x6733)))
% 19.29/19.54 [675]E(f15(a1,f51(f51(f14(a1),x6751),x6752),f51(f51(f14(a1),x6753),x6752)),f51(f51(f14(a1),f15(a1,x6751,x6753)),x6752))
% 19.29/19.54 [676]E(f13(a114,f51(f51(f14(a114),x6761),x6762),f51(f51(f14(a114),x6763),x6762)),f51(f51(f14(a114),f13(a114,x6761,x6763)),x6762))
% 19.29/19.54 [677]E(f15(a114,f51(f51(f14(a114),x6771),x6772),f51(f51(f14(a114),x6773),x6772)),f51(f51(f14(a114),f15(a114,x6771,x6773)),x6772))
% 19.29/19.54 [678]E(f13(a112,f51(f51(f14(a112),x6781),x6782),f51(f51(f14(a112),x6783),x6782)),f51(f51(f14(a112),f13(a112,x6781,x6783)),x6782))
% 19.29/19.54 [679]E(f15(a112,f51(f51(f14(a112),x6791),x6792),f51(f51(f14(a112),x6793),x6792)),f51(f51(f14(a112),f15(a112,x6791,x6793)),x6792))
% 19.29/19.54 [682]E(f15(a112,f51(f5(a112),x6821),f15(a112,f51(f5(a112),x6822),x6823)),f15(a112,f51(f5(a112),f15(a114,x6821,x6822)),x6823))
% 19.29/19.54 [660]E(f51(f51(f20(a112),f51(f51(f20(a112),x6601),x6602)),x6603),f51(f51(f20(a112),x6601),f51(f51(f14(a114),x6602),x6603)))
% 19.29/19.54 [661]E(f51(f51(f14(a1),f51(f51(f14(a1),x6611),x6612)),x6613),f51(f51(f14(a1),x6611),f51(f51(f14(a1),x6612),x6613)))
% 19.29/19.54 [662]E(f51(f51(f14(a114),f51(f51(f14(a114),x6621),x6622)),x6623),f51(f51(f14(a114),x6621),f51(f51(f14(a114),x6622),x6623)))
% 19.29/19.54 [663]E(f51(f51(f14(a112),f51(f51(f14(a112),x6631),x6632)),x6633),f51(f51(f14(a112),x6631),f51(f51(f14(a112),x6632),x6633)))
% 19.29/19.54 [671]E(f8(f51(f51(f20(a1),x6711),x6712),f51(f51(f14(a1),f51(f4(a114),x6712)),x6713)),f51(f51(f20(a2),f8(x6711,x6713)),x6712))
% 19.29/19.54 [692]E(f13(a1,f51(x6921,x6922),f51(f51(f14(a1),f29(a1,f13(a1,f51(x6921,x6923),f51(x6921,x6922)),f13(a1,x6923,x6922))),x6922)),f13(a1,f51(x6921,x6923),f51(f51(f14(a1),f29(a1,f13(a1,f51(x6921,x6923),f51(x6921,x6922)),f13(a1,x6923,x6922))),x6923)))
% 19.29/19.54 [636]E(f51(f51(f21(x6361,x6362,x6363),x6364),f6(a114)),x6362)
% 19.29/19.54 [658]E(f8(f51(f51(f14(a1),x6581),x6582),f15(a1,x6583,x6584)),f51(f51(f14(a2),f8(x6581,x6583)),f8(x6582,x6584)))
% 19.29/19.54 [686]E(f15(a114,f51(f51(f14(a114),x6861),x6862),f15(a114,f51(f51(f14(a114),x6863),x6862),x6864)),f15(a114,f51(f51(f14(a114),f15(a114,x6861,x6863)),x6862),x6864))
% 19.29/19.54 [685]E(f51(f51(f21(x6851,x6852,x6853),x6854),f15(a114,x6855,f7(a114))),f51(f51(x6853,x6854),f51(f51(f21(x6851,x6852,x6853),x6854),x6855)))
% 19.29/19.54 [719]~P48(x7191)+P12(f115(x7191))
% 19.29/19.54 [720]~P48(x7201)+P30(f115(x7201))
% 19.29/19.54 [721]~P31(x7211)+P31(f115(x7211))
% 19.29/19.54 [722]~P48(x7221)+P37(f115(x7221))
% 19.29/19.54 [723]~P48(x7231)+P39(f115(x7231))
% 19.29/19.54 [724]~P48(x7241)+P40(f115(x7241))
% 19.29/19.54 [725]~P13(x7251)+P13(f115(x7251))
% 19.29/19.54 [726]~P13(x7261)+P18(f115(x7261))
% 19.29/19.54 [727]~P48(x7271)+P47(f115(x7271))
% 19.29/19.54 [728]~P49(x7281)+P60(f115(x7281))
% 19.29/19.54 [729]~P48(x7291)+P48(f115(x7291))
% 19.29/19.54 [730]~P48(x7301)+P32(f115(x7301))
% 19.29/19.54 [731]~P54(x7311)+P74(f115(x7311))
% 19.29/19.54 [732]~P48(x7321)+P38(f115(x7321))
% 19.29/19.54 [733]~P54(x7331)+P43(f115(x7331))
% 19.29/19.54 [734]~P50(x7341)+P61(f115(x7341))
% 19.29/19.54 [735]~P49(x7351)+P66(f115(x7351))
% 19.29/19.54 [736]~P54(x7361)+P78(f115(x7361))
% 19.29/19.54 [737]~P52(x7371)+P67(f115(x7371))
% 19.29/19.54 [738]~P50(x7381)+P75(f115(x7381))
% 19.29/19.54 [739]~P15(x7391)+P14(f115(x7391))
% 19.29/19.54 [740]~P49(x7401)+P49(f115(x7401))
% 19.29/19.54 [741]~P50(x7411)+P50(f115(x7411))
% 19.29/19.54 [742]~P50(x7421)+P19(f115(x7421))
% 19.29/19.54 [743]~P54(x7431)+P21(f115(x7431))
% 19.29/19.54 [744]~P54(x7441)+P26(f115(x7441))
% 19.29/19.54 [745]~P54(x7451)+P29(f115(x7451))
% 19.29/19.54 [746]~P54(x7461)+P54(f115(x7461))
% 19.29/19.54 [747]~P49(x7471)+P76(f115(x7471))
% 19.29/19.54 [748]~P48(x7481)+P58(f115(x7481))
% 19.29/19.54 [749]~P48(x7491)+P59(f115(x7491))
% 19.29/19.54 [750]~P48(x7501)+P68(f115(x7501))
% 19.29/19.54 [751]~P48(x7511)+P69(f115(x7511))
% 19.29/19.54 [752]~P48(x7521)+P71(f115(x7521))
% 19.29/19.54 [753]~P48(x7531)+P70(f115(x7531))
% 19.29/19.54 [754]~P48(x7541)+P62(f115(x7541))
% 19.29/19.54 [755]~P48(x7551)+P57(f115(x7551))
% 19.29/19.54 [756]~P48(x7561)+P63(f115(x7561))
% 19.29/19.54 [757]~P48(x7571)+P72(f115(x7571))
% 19.29/19.54 [758]~P49(x7581)+P79(f115(x7581))
% 19.29/19.54 [759]~P50(x7591)+P51(f115(x7591))
% 19.29/19.54 [760]~P50(x7601)+P77(f115(x7601))
% 19.29/19.54 [761]~P48(x7611)+P27(f115(x7611))
% 19.29/19.54 [762]~P22(x7621)+P22(f115(x7621))
% 19.29/19.54 [763]~P22(x7631)+P28(f115(x7631))
% 19.29/19.54 [764]~P48(x7641)+P33(f115(x7641))
% 19.29/19.54 [765]~P48(x7651)+P34(f115(x7651))
% 19.29/19.54 [766]~P48(x7661)+P35(f115(x7661))
% 19.29/19.54 [767]~P22(x7671)+P20(f115(x7671))
% 19.29/19.54 [768]~P25(x7681)+P23(f115(x7681))
% 19.29/19.54 [769]~P25(x7691)+P24(f115(x7691))
% 19.29/19.54 [770]~P48(x7701)+P36(f115(x7701))
% 19.29/19.54 [771]~P53(x7711)+P73(f115(x7711))
% 19.29/19.54 [772]~P48(x7721)+P64(f115(x7721))
% 19.29/19.54 [773]~P48(x7731)+P65(f115(x7731))
% 19.29/19.54 [774]~P52(x7741)+P52(f115(x7741))
% 19.29/19.54 [775]~P25(x7751)+P25(f115(x7751))
% 19.29/19.54 [776]~P53(x7761)+P53(f115(x7761))
% 19.29/19.54 [778]~P78(x7781)+~E(f7(x7781),f6(x7781))
% 19.29/19.54 [813]E(x8131,f6(a112))+E(f11(a112,x8131,x8131),f7(a112))
% 19.29/19.54 [817]E(x8171,f6(a114))+P3(a114,f6(a114),x8171)
% 19.29/19.54 [843]~P44(x8431)+P3(a1,f6(a1),f52(x8431))
% 19.29/19.54 [848]P2(x8481)+P3(a114,f53(x8481),f86(x8481))
% 19.29/19.54 [864]~P47(x8641)+P3(x8641,f6(x8641),f7(x8641))
% 19.29/19.54 [887]~E(x8871,f6(a112))+P3(a112,f10(a112,x8871),f7(a112))
% 19.29/19.54 [954]~P47(x9541)+~P3(x9541,f7(x9541),f6(x9541))
% 19.29/19.54 [975]E(x9751,f6(a112))+~P3(a112,f10(a112,x9751),f7(a112))
% 19.29/19.54 [1010]~P3(a112,f6(a112),x10101)+P3(a114,f6(a114),f55(x10101))
% 19.29/19.54 [1041]~P3(a112,f6(a112),x10411)+P3(a114,f6(a114),f51(a16,x10411))
% 19.29/19.54 [1094]P3(a112,f6(a112),x10941)+~P3(a114,f6(a114),f51(a16,x10941))
% 19.29/19.54 [779]~E(x7791,f6(a114))+E(f51(f4(a114),x7791),f6(a1))
% 19.29/19.54 [780]~E(x7801,f6(a114))+E(f51(f5(a112),x7801),f6(a112))
% 19.29/19.54 [781]~P1(x7811)+E(f28(x7811,f6(x7811)),f6(a1))
% 19.29/19.54 [782]~P42(x7821)+E(f28(x7821,f7(x7821)),f7(a1))
% 19.29/19.54 [783]~P32(x7831)+E(f10(x7831,f6(x7831)),f6(x7831))
% 19.29/19.54 [784]~P48(x7841)+E(f10(x7841,f7(x7841)),f7(x7841))
% 19.29/19.54 [787]~P74(x7871)+E(f51(f5(x7871),f6(a114)),f6(x7871))
% 19.29/19.54 [788]~P74(x7881)+E(f51(f5(x7881),f7(a114)),f7(x7881))
% 19.29/19.54 [789]E(x7891,f6(a114))+~E(f51(f4(a114),x7891),f6(a1))
% 19.29/19.54 [790]E(x7901,f6(a114))+~E(f51(f5(a112),x7901),f6(a112))
% 19.29/19.54 [875]~P43(x8751)+E(f21(x8751,f7(x8751),f14(x8751)),f20(x8751))
% 19.29/19.54 [938]~E(f51(a16,x9381),f6(a114))+P80(f51(f18(a112,x9381),f6(a112)))
% 19.29/19.54 [955]~P3(a112,f6(a112),x9551)+E(f51(f5(a112),f55(x9551)),x9551)
% 19.29/19.54 [973]~P47(x9731)+P80(f51(f18(x9731,f6(x9731)),f7(x9731)))
% 19.29/19.54 [980]E(x9801,f6(a114))+~P80(f51(f18(a114,x9801),f6(a114)))
% 19.29/19.54 [982]E(f17(x9821),f6(a114))+~P80(f51(f18(a1,x9821),f6(a1)))
% 19.29/19.54 [983]E(f27(x9831),f6(a114))+~P80(f51(f18(a1,x9831),f6(a1)))
% 19.29/19.54 [996]E(f51(a16,x9961),f6(a114))+~P80(f51(f18(a112,x9961),f6(a112)))
% 19.29/19.54 [1011]~P3(a114,f6(a114),x10111)+E(f15(a114,f56(x10111),f7(a114)),x10111)
% 19.29/19.54 [1069]~P3(a114,f6(a114),x10691)+P3(a1,f6(a1),f51(f4(a114),x10691))
% 19.29/19.54 [1070]~P3(a114,f6(a114),x10701)+P3(a112,f6(a112),f51(f5(a112),x10701))
% 19.29/19.54 [1122]~P47(x11221)+~P80(f51(f18(x11221,f7(x11221)),f6(x11221)))
% 19.29/19.54 [1126]P3(a114,f6(a114),x11261)+~P3(a1,f6(a1),f51(f4(a114),x11261))
% 19.29/19.54 [1127]P3(a114,f6(a114),x11271)+~P3(a112,f6(a112),f51(f5(a112),x11271))
% 19.29/19.54 [1130]~P47(x11301)+P3(x11301,f6(x11301),f15(x11301,f7(x11301),f7(x11301)))
% 19.29/19.54 [1139]P2(x11391)+~P3(a114,f51(x11391,f53(x11391)),f51(x11391,f86(x11391)))
% 19.29/19.54 [1151]~E(x11511,f6(a114))+P80(f51(f18(a1,f51(f4(a114),x11511)),f6(a1)))
% 19.29/19.54 [1152]~E(x11521,f6(a114))+P80(f51(f18(a112,f51(f5(a112),x11521)),f6(a112)))
% 19.29/19.54 [1184]~P80(f51(f18(a1,x11841),f7(a1)))+P80(f51(f18(a114,f17(x11841)),f7(a114)))
% 19.29/19.54 [1223]~P80(f51(f18(a114,f17(x12231)),f7(a114)))+P80(f51(f18(a1,x12231),f7(a1)))
% 19.29/19.54 [1232]~P3(a114,f6(a114),x12321)+E(f15(a114,f13(a114,x12321,f7(a114)),f7(a114)),x12321)
% 19.29/19.54 [1255]E(x12551,f6(a114))+~P3(a114,x12551,f15(a114,f6(a114),f7(a114)))
% 19.29/19.54 [1275]~P3(a112,f7(a112),x12751)+P3(a114,f15(a114,f6(a114),f7(a114)),f51(a16,x12751))
% 19.29/19.54 [1363]E(x13631,f6(a114))+~P80(f51(f18(a1,f51(f4(a114),x13631)),f6(a1)))
% 19.29/19.54 [1364]E(x13641,f6(a114))+~P80(f51(f18(a112,f51(f5(a112),x13641)),f6(a112)))
% 19.29/19.54 [1394]P3(a112,f7(a112),x13941)+~P3(a114,f15(a114,f6(a114),f7(a114)),f51(a16,x13941))
% 19.29/19.54 [1550]~P3(a114,f6(a114),x15501)+E(f15(a114,f13(a114,x15501,f15(a114,f6(a114),f7(a114))),f7(a114)),x15501)
% 19.29/19.54 [798]~P31(x7981)+E(f22(x7981,f6(f115(x7981))),f6(a114))
% 19.29/19.54 [799]~P54(x7991)+E(f22(x7991,f7(f115(x7991))),f6(a114))
% 19.29/19.54 [979]E(f51(f5(a112),f51(a16,x9791)),f6(a112))+P80(f51(f18(a112,f6(a112)),x9791))
% 19.29/19.54 [1004]E(x10041,f6(a1))+P3(a1,f6(a1),f51(f51(f14(a1),x10041),x10041))
% 19.29/19.54 [1068]~P3(a112,f6(a112),x10681)+P80(f51(f18(a112,f7(a112)),x10681))
% 19.29/19.54 [1086]E(f51(f5(a112),f51(a16,x10861)),x10861)+~P80(f51(f18(a112,f6(a112)),x10861))
% 19.29/19.54 [1125]P3(a112,f6(a112),x11251)+~P80(f51(f18(a112,f7(a112)),x11251))
% 19.29/19.54 [1183]~E(x11831,f6(a1))+~P3(a1,f6(a1),f51(f51(f14(a1),x11831),x11831))
% 19.29/19.54 [1185]P3(a1,x11851,f51(f4(a114),f97(x11851)))+~P80(f51(f18(a1,f6(a1)),x11851))
% 19.29/19.54 [1190]P80(f51(f18(a114,f7(a114)),f27(x11901)))+~P80(f51(f18(a1,f7(a1)),x11901))
% 19.29/19.54 [1212]~P80(f51(f18(a114,f7(a114)),f27(x12121)))+P80(f51(f18(a1,f7(a1)),x12121))
% 19.29/19.54 [1304]P3(a112,f6(a112),f15(a112,f7(a112),x13041))+~P80(f51(f18(a112,f6(a112)),x13041))
% 19.29/19.54 [1313]E(f17(f15(a1,x13131,f7(a1))),f15(a114,f17(x13131),f7(a114)))+~P80(f51(f18(a1,f6(a1)),x13131))
% 19.29/19.54 [1314]E(f27(f15(a1,x13141,f7(a1))),f15(a114,f27(x13141),f7(a114)))+~P80(f51(f18(a1,f6(a1)),x13141))
% 19.29/19.54 [1371]E(f15(a114,f51(a16,x13711),f7(a114)),f51(a16,f15(a112,f7(a112),x13711)))+~P80(f51(f18(a112,f6(a112)),x13711))
% 19.29/19.54 [1543]~P3(a112,x15431,f6(a112))+P3(a112,f15(a112,f15(a112,f7(a112),x15431),x15431),f6(a112))
% 19.29/19.54 [1651]P2(x16511)+~P3(a114,f51(x16511,f69(x16511)),f51(x16511,f15(a114,f69(x16511),f7(a114))))
% 19.29/19.54 [1715]P3(a112,x17151,f6(a112))+~P3(a112,f15(a112,f15(a112,f7(a112),x17151),x17151),f6(a112))
% 19.29/19.54 [1431]~P80(f51(f18(a1,f6(a1)),x14311))+P80(f51(f18(a1,f51(f4(a114),f27(x14311))),x14311))
% 19.29/19.54 [1941]~P80(f51(f18(a1,f6(a1)),x19411))+P80(f51(f18(a1,f51(f4(a114),f13(a114,f97(x19411),f7(a114)))),x19411))
% 19.29/19.54 [892]~E(x8921,x8922)+~P3(a1,x8921,x8922)
% 19.29/19.54 [897]~E(x8971,x8972)+~P3(a114,x8971,x8972)
% 19.29/19.54 [898]~E(x8981,x8982)+~P3(a112,x8981,x8982)
% 19.29/19.54 [916]~P3(x9161,x9162,x9162)+~P30(x9161)
% 19.29/19.54 [791]~P30(x7912)+P30(f118(x7911,x7912))
% 19.29/19.54 [792]~P39(x7922)+P39(f118(x7921,x7922))
% 19.29/19.54 [793]~P40(x7932)+P40(f118(x7931,x7932))
% 19.29/19.54 [815]E(f15(a114,x8151,x8152),x8152)+~E(x8151,f6(a114))
% 19.29/19.54 [821]~E(x8212,f6(a112))+E(f11(a112,x8211,x8212),f6(a112))
% 19.29/19.54 [824]~P18(x8241)+E(f13(x8241,x8242,x8242),f6(x8241))
% 19.29/19.54 [900]~E(f15(a114,x9002,x9001),x9002)+E(x9001,f6(a114))
% 19.29/19.54 [903]~P44(x9032)+P3(a1,f6(a1),f54(x9031,x9032))
% 19.29/19.54 [904]~P44(x9042)+P3(a1,f6(a1),f87(x9041,x9042))
% 19.29/19.54 [905]~P3(a114,x9052,x9051)+~E(x9051,f6(a114))
% 19.29/19.54 [909]E(x9091,f6(a114))+~E(f15(a114,x9092,x9091),f6(a114))
% 19.29/19.54 [910]E(x9101,f6(a114))+~E(f15(a114,x9101,x9102),f6(a114))
% 19.29/19.54 [984]~P1(x9841)+~P3(a1,f28(x9841,x9842),f6(a1))
% 19.29/19.54 [985]~P5(a1,x9851,x9852)+E(f13(a1,x9851,x9852),f6(a1))
% 19.29/19.54 [986]~P3(a114,x9861,x9862)+E(f11(a114,x9861,x9862),f6(a114))
% 19.29/19.54 [987]P5(a1,x9871,x9872)+~E(f13(a1,x9871,x9872),f6(a1))
% 19.29/19.54 [989]~P32(x9891)+~P3(x9891,f10(x9891,x9892),f6(x9891))
% 19.29/19.54 [1111]~P3(a1,x11112,x11111)+P6(f13(a1,x11111,x11112))
% 19.29/19.54 [1140]P3(a112,x11401,x11402)+~P3(a114,f51(a16,x11401),f51(a16,x11402))
% 19.29/19.54 [1145]P3(a112,f6(a112),x11451)+~P3(a114,f51(a16,x11452),f51(a16,x11451))
% 19.29/19.54 [1163]P3(a1,x11631,x11632)+~P6(f13(a1,x11632,x11631))
% 19.29/19.54 [1208]~P3(a114,x12082,x12081)+P3(a114,f6(a114),f13(a114,x12081,x12082))
% 19.29/19.54 [1209]~P3(a112,x12091,x12092)+P3(a112,f13(a112,x12091,x12092),f6(a112))
% 19.29/19.54 [1302]P3(a114,x13021,x13022)+~P3(a114,f6(a114),f13(a114,x13022,x13021))
% 19.29/19.54 [1303]P3(a112,x13031,x13032)+~P3(a112,f13(a112,x13031,x13032),f6(a112))
% 19.29/19.54 [800]E(x8001,f51(a16,x8002))+~E(f51(f5(a112),x8001),x8002)
% 19.29/19.54 [810]E(x8101,x8102)+~E(f51(f4(a114),x8101),f51(f4(a114),x8102))
% 19.29/19.54 [812]E(x8121,x8122)+~E(f51(f5(a112),x8121),f51(f5(a112),x8122))
% 19.29/19.54 [814]~P1(x8141)+E(f10(a1,f28(x8141,x8142)),f28(x8141,x8142))
% 19.29/19.54 [820]~P32(x8201)+E(f10(x8201,f10(x8201,x8202)),f10(x8201,x8202))
% 19.29/19.54 [822]~P26(x8221)+E(f51(f51(f20(x8221),x8222),f7(a114)),x8222)
% 19.29/19.54 [823]~P54(x8231)+E(f51(f51(f20(x8231),x8232),f7(a114)),x8232)
% 19.29/19.54 [825]~P21(x8251)+E(f51(f51(f14(x8251),x8252),f7(x8251)),x8252)
% 19.29/19.54 [826]~P26(x8261)+E(f51(f51(f14(x8261),x8262),f7(x8261)),x8262)
% 19.29/19.54 [827]~P54(x8271)+E(f51(f51(f14(x8271),x8272),f7(x8271)),x8272)
% 19.29/19.54 [828]~P43(x8281)+E(f51(f51(f20(x8281),x8282),f6(a114)),f7(x8281))
% 19.29/19.54 [829]~P54(x8291)+E(f51(f51(f20(x8291),x8292),f6(a114)),f7(x8291))
% 19.29/19.54 [831]~P18(x8311)+E(f13(x8311,x8312,f6(x8311)),x8312)
% 19.29/19.54 [832]~P14(x8321)+E(f11(x8321,x8322,f7(x8321)),x8322)
% 19.29/19.54 [833]~P54(x8331)+E(f15(x8331,x8332,f6(x8331)),x8332)
% 19.29/19.54 [834]~P22(x8341)+E(f15(x8341,x8342,f6(x8341)),x8342)
% 19.29/19.54 [835]~P28(x8351)+E(f15(x8351,x8352,f6(x8351)),x8352)
% 19.29/19.54 [836]~P55(x8361)+E(f29(x8361,x8362,f7(x8361)),x8362)
% 19.29/19.54 [837]~P54(x8371)+E(f15(x8371,f6(x8371),x8372),x8372)
% 19.29/19.54 [838]~P22(x8381)+E(f15(x8381,f6(x8381),x8382),x8382)
% 19.29/19.54 [839]~P28(x8391)+E(f15(x8391,f6(x8391),x8392),x8392)
% 19.29/19.54 [844]~P61(x8441)+E(f51(f51(f14(x8441),x8442),f6(x8441)),f6(x8441))
% 19.29/19.54 [846]~P44(x8461)+E(f51(f51(f14(x8461),x8462),f6(x8461)),f6(x8461))
% 19.29/19.54 [847]~P54(x8471)+E(f51(f51(f14(x8471),x8472),f6(x8471)),f6(x8471))
% 19.29/19.54 [853]~P14(x8531)+E(f11(x8531,x8532,f6(x8531)),f6(x8531))
% 19.29/19.54 [854]~P56(x8541)+E(f29(x8541,x8542,f6(x8541)),f6(x8541))
% 19.29/19.54 [855]~P14(x8551)+E(f11(x8551,f6(x8551),x8552),f6(x8551))
% 19.29/19.54 [856]~P55(x8561)+E(f29(x8561,f6(x8561),x8562),f6(x8561))
% 19.29/19.54 [857]~P46(x8571)+E(f29(x8571,f6(x8571),x8572),f6(x8571))
% 19.29/19.54 [877]~E(x8771,x8772)+P80(f51(f18(a1,x8771),x8772))
% 19.29/19.54 [880]~E(x8801,x8802)+P80(f51(f18(a114,x8801),x8802))
% 19.29/19.54 [902]~P30(x9021)+P80(f51(f18(x9021,x9022),x9022))
% 19.29/19.54 [911]E(f19(x9111,x9112),f6(a112))+P80(f51(f18(a112,x9112),x9111))
% 19.29/19.54 [974]E(x9741,x9742)+~E(f51(x9741,f39(x9742,x9741)),f51(x9742,f39(x9742,x9741)))
% 19.29/19.55 [978]P80(f51(x9781,x9782))+P80(f51(f18(a112,f6(a112)),f76(x9781)))
% 19.29/19.55 [981]~P2(x9812)+P80(f51(f18(a114,x9811),f51(x9812,x9811)))
% 19.29/19.55 [988]~P32(x9881)+P80(f51(f18(x9881,x9882),f10(x9881,x9882)))
% 19.29/19.55 [998]P3(a114,f6(a114),x9981)+~E(x9981,f15(a114,x9982,f7(a114)))
% 19.29/19.55 [999]~P1(x9991)+P80(f51(f18(a1,f6(a1)),f28(x9991,x9992)))
% 19.29/19.55 [1002]~P80(f51(x10021,x10022))+P80(f51(f18(a112,f6(a112)),f81(x10021)))
% 19.29/19.55 [1019]P80(f51(f18(a1,x10192),x10191))+P80(f51(f18(a1,x10191),x10192))
% 19.29/19.55 [1020]P80(f51(f18(a114,x10202),x10201))+P80(f51(f18(a114,x10201),x10202))
% 19.29/19.55 [1021]P80(f51(f18(a112,x10212),x10211))+P80(f51(f18(a112,x10211),x10212))
% 19.29/19.55 [1025]~P3(a1,x10251,x10252)+P80(f51(f18(a1,x10251),x10252))
% 19.29/19.55 [1030]~P3(a114,x10301,x10302)+P80(f51(f18(a114,x10301),x10302))
% 19.29/19.55 [1031]~P3(a112,x10311,x10312)+P80(f51(f18(a112,x10311),x10312))
% 19.29/19.55 [1035]~P47(x10351)+~P3(x10351,f51(f5(x10351),x10352),f6(x10351))
% 19.29/19.55 [1036]~E(f13(a114,x10361,x10362),f6(a114))+P80(f51(f18(a114,x10361),x10362))
% 19.29/19.55 [1037]~P32(x10371)+P80(f51(f18(x10371,f6(x10371)),f10(x10371,x10372)))
% 19.29/19.55 [1038]~E(x10381,x10382)+P3(a114,x10381,f15(a114,x10382,f7(a114)))
% 19.29/19.55 [1039]~E(x10391,x10392)+P3(a112,x10391,f15(a112,x10392,f7(a112)))
% 19.29/19.55 [1044]~E(x10441,f6(a114))+P3(a114,x10441,f15(a114,x10442,f7(a114)))
% 19.29/19.55 [1056]E(f13(a114,x10561,x10562),f6(a114))+~P80(f51(f18(a114,x10561),x10562))
% 19.29/19.55 [1093]~P47(x10931)+P3(x10931,x10932,f15(x10931,x10932,f7(x10931)))
% 19.29/19.55 [1102]E(f13(a112,x11021,x11022),f19(x11021,x11022))+~P80(f51(f18(a112,x11022),x11021))
% 19.29/19.55 [1131]E(f15(a114,x11311,f88(x11312,x11311)),x11312)+~P80(f51(f18(a114,x11311),x11312))
% 19.29/19.55 [1132]E(f15(a114,x11321,f94(x11322,x11321)),x11322)+~P80(f51(f18(a114,x11321),x11322))
% 19.29/19.55 [1134]~P3(a114,x11341,x11342)+P3(a1,f51(f4(a114),x11341),f51(f4(a114),x11342))
% 19.29/19.55 [1136]~P3(a114,x11361,x11362)+P3(a112,f51(f5(a112),x11361),f51(f5(a112),x11362))
% 19.29/19.55 [1138]~P3(a114,x11381,f51(a16,x11382))+P3(a112,f51(f5(a112),x11381),x11382)
% 19.29/19.55 [1142]P3(a114,x11421,f51(a16,x11422))+~P3(a112,f51(f5(a112),x11421),x11422)
% 19.29/19.55 [1143]P3(a114,x11432,x11431)+E(f15(a114,x11431,f13(a114,x11432,x11431)),x11432)
% 19.29/19.55 [1153]P3(a114,x11531,x11532)+P3(a114,x11532,f15(a114,x11531,f7(a114)))
% 19.29/19.55 [1172]~P80(f51(f18(a1,x11721),x11722))+P80(f51(f18(a114,f17(x11721)),f17(x11722)))
% 19.29/19.55 [1173]~P80(f51(f18(a1,x11731),x11732))+P80(f51(f18(a114,f27(x11731)),f27(x11732)))
% 19.29/19.55 [1186]P3(a114,x11861,x11862)+~P3(a1,f51(f4(a114),x11861),f51(f4(a114),x11862))
% 19.29/19.55 [1188]P3(a114,x11881,x11882)+~P3(a112,f51(f5(a112),x11881),f51(f5(a112),x11882))
% 19.29/19.55 [1215]~P3(a112,x12151,x12152)+P3(a112,x12151,f15(a112,x12152,f7(a112)))
% 19.29/19.55 [1265]E(f13(a114,x12651,f13(a114,x12651,x12652)),x12652)+~P80(f51(f18(a114,x12652),x12651))
% 19.29/19.55 [1266]E(f15(a114,x12661,f13(a114,x12662,x12661)),x12662)+~P80(f51(f18(a114,x12661),x12662))
% 19.29/19.55 [1267]E(f15(a114,f13(a114,x12671,x12672),x12672),x12671)+~P80(f51(f18(a114,x12672),x12671))
% 19.29/19.55 [1278]P3(a114,x12781,f15(a114,x12782,f7(a114)))+~P80(f51(f18(a114,x12781),x12782))
% 19.29/19.55 [1279]P3(a112,x12791,f15(a112,x12792,f7(a112)))+~P80(f51(f18(a112,x12791),x12792))
% 19.29/19.55 [1289]~P3(a114,x12891,x12892)+E(f15(a114,f15(a114,x12891,f95(x12892,x12891)),f7(a114)),x12892)
% 19.29/19.55 [1355]~P3(a114,x13551,f15(a114,x13552,f7(a114)))+P80(f51(f18(a114,x13551),x13552))
% 19.29/19.55 [1356]~P3(a112,x13561,f15(a112,x13562,f7(a112)))+P80(f51(f18(a112,x13561),x13562))
% 19.29/19.55 [1372]~P3(a114,x13721,x13722)+~P3(a114,x13722,f15(a114,x13721,f7(a114)))
% 19.29/19.55 [1417]P3(a1,f51(f4(a114),x14171),f15(a1,f51(f4(a114),x14172),f7(a1)))+~P80(f51(f18(a114,x14171),x14172))
% 19.29/19.55 [1499]E(x14991,f6(a114))+E(f15(a114,f15(a114,f13(a114,x14991,f7(a114)),x14992),f7(a114)),f15(a114,x14991,x14992))
% 19.29/19.55 [1552]P3(a114,x15521,x15522)+~P3(a114,f15(a114,x15521,f7(a114)),f15(a114,x15522,f7(a114)))
% 19.29/19.55 [1554]~P3(a1,f51(f4(a114),x15541),f15(a1,f51(f4(a114),x15542),f7(a1)))+P80(f51(f18(a114,x15541),x15542))
% 19.29/19.55 [1688]~P80(f51(f18(a1,x16881),x16882))+P80(f51(f18(a1,f13(a1,x16881,x16882)),f6(a1)))
% 19.29/19.55 [1816]P80(f51(f18(a1,x18161),x18162))+~P80(f51(f18(a1,f13(a1,x18161,x18162)),f6(a1)))
% 19.29/19.55 [1924]~P15(x19241)+P7(x19241,x19242,f6(f115(x19241)),f6(f115(x19241)),x19242)
% 19.29/19.55 [1927]~P15(x19271)+P7(x19271,f6(f115(x19271)),x19272,f6(f115(x19271)),f6(f115(x19271)))
% 19.29/19.55 [806]~E(x8062,f6(a114))+E(f51(f51(f20(a114),x8061),x8062),f7(a114))
% 19.29/19.55 [807]~E(x8072,f6(a114))+E(f51(f51(f14(a114),x8071),x8072),f6(a114))
% 19.29/19.55 [809]~E(x8091,f6(a114))+E(f51(f51(f14(a114),x8091),x8092),f6(a114))
% 19.29/19.55 [860]~P21(x8601)+E(f51(f51(f14(x8601),f7(x8601)),x8602),x8602)
% 19.29/19.55 [861]~P26(x8611)+E(f51(f51(f14(x8611),f7(x8611)),x8612),x8612)
% 19.29/19.55 [862]~P54(x8621)+E(f51(f51(f14(x8621),f7(x8621)),x8622),x8622)
% 19.29/19.55 [869]~P26(x8691)+E(f51(f51(f20(x8691),f7(x8691)),x8692),f7(x8691))
% 19.29/19.55 [870]~P61(x8701)+E(f51(f51(f14(x8701),f6(x8701)),x8702),f6(x8701))
% 19.29/19.55 [872]~P44(x8721)+E(f51(f51(f14(x8721),f6(x8721)),x8722),f6(x8721))
% 19.29/19.55 [873]~P54(x8731)+E(f51(f51(f14(x8731),f6(x8731)),x8732),f6(x8731))
% 19.29/19.55 [874]~P42(x8741)+E(f28(x8741,f51(f5(x8741),x8742)),f51(f5(a1),x8742))
% 19.29/19.55 [876]~P48(x8761)+E(f10(x8761,f51(f5(x8761),x8762)),f51(f5(x8761),x8762))
% 19.29/19.55 [883]E(x8831,f7(a114))+~E(f51(f51(f14(a114),x8832),x8831),f7(a114))
% 19.29/19.55 [884]E(x8841,f7(a114))+~E(f51(f51(f14(a114),x8841),x8842),f7(a114))
% 19.29/19.55 [889]~P13(x8891)+E(f13(f115(x8891),x8892,f6(f115(x8891))),x8892)
% 19.29/19.55 [890]~P22(x8901)+E(f15(f115(x8901),x8902,f6(f115(x8901))),x8902)
% 19.29/19.55 [891]~P22(x8911)+E(f15(f115(x8911),f6(f115(x8911)),x8912),x8912)
% 19.29/19.55 [906]~P50(x9061)+E(f23(x9061,f6(f115(x9061)),x9062),f6(f115(x9061)))
% 19.29/19.55 [907]~P50(x9071)+E(f24(x9071,f6(f115(x9071)),x9072),f6(f115(x9071)))
% 19.29/19.55 [949]~E(x9492,f6(a114))+E(f51(f51(f20(a114),x9491),x9492),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [953]~P50(x9531)+E(f51(f51(f14(f115(x9531)),x9532),f6(f115(x9531))),f6(f115(x9531)))
% 19.29/19.55 [960]~E(f51(f5(a112),x9602),x9601)+P80(f51(f18(a112,f6(a112)),x9601))
% 19.29/19.55 [1001]~P80(f51(x10011,x10012))+P80(f51(x10011,f51(a16,f81(x10011))))
% 19.29/19.55 [1018]~E(x10182,f6(a114))+P3(a114,f6(a114),f51(f51(f20(a114),x10181),x10182))
% 19.29/19.55 [1034]~P80(f51(x10341,f66(x10341)))+P80(f51(x10341,f51(f5(a112),x10342)))
% 19.29/19.55 [1103]P80(f51(x11031,x11032))+~P80(f51(x11031,f51(a16,f76(x11031))))
% 19.29/19.55 [1104]~P48(x11041)+E(f51(f51(f14(x11041),f10(x11041,x11042)),f10(x11041,x11042)),f51(f51(f14(x11041),x11042),x11042))
% 19.29/19.55 [1106]~P47(x11061)+P80(f51(f18(x11061,f6(x11061)),f51(f5(x11061),x11062)))
% 19.29/19.55 [1109]P80(f51(x11091,f67(x11091)))+~P80(f51(x11091,f51(f5(a112),x11092)))
% 19.29/19.55 [1124]P80(f51(f18(a112,f6(a112)),f66(x11241)))+P80(f51(x11241,f51(f5(a112),x11242)))
% 19.29/19.55 [1133]~E(x11331,f15(a114,f6(a114),f7(a114)))+E(f51(f51(f20(a114),x11331),x11332),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1165]E(x11651,f15(a114,f6(a114),f7(a114)))+~E(f51(f51(f14(a114),x11652),x11651),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1166]E(x11661,f15(a114,f6(a114),f7(a114)))+~E(f51(f51(f14(a114),x11661),x11662),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1180]~P3(a114,f6(a114),x11801)+P3(a114,f6(a114),f51(f51(f20(a114),x11801),x11802))
% 19.29/19.55 [1181]~P74(x11811)+E(f15(x11811,f7(x11811),f51(f5(x11811),x11812)),f51(f5(x11811),f15(a114,x11812,f7(a114))))
% 19.29/19.55 [1202]E(x12021,f6(a112))+P3(a112,f6(a112),f51(f51(f20(a112),f10(a112,x12021)),x12022))
% 19.29/19.55 [1207]~E(x12072,f6(a114))+P3(a112,f6(a112),f51(f51(f20(a112),f10(a112,x12071)),x12072))
% 19.29/19.55 [1222]P80(f51(f18(a112,f6(a112)),f67(x12221)))+~P80(f51(x12221,f51(f5(a112),x12222)))
% 19.29/19.55 [1234]E(f15(a112,x12341,f51(f5(a112),f89(x12342,x12341))),x12342)+~P80(f51(f18(a112,x12341),x12342))
% 19.29/19.55 [1243]~P58(x12431)+~P3(x12431,f51(f51(f14(x12431),x12432),x12432),f6(x12431))
% 19.29/19.55 [1281]P3(a114,f6(a114),x12811)+~P3(a114,f6(a114),f51(f51(f14(a114),x12812),x12811))
% 19.29/19.55 [1282]P3(a114,f6(a114),x12821)+~P3(a114,f6(a114),f51(f51(f14(a114),x12821),x12822))
% 19.29/19.55 [1327]P80(f51(f18(a114,f17(x13271)),x13272))+~P80(f51(f18(a1,x13271),f51(f4(a114),x13272)))
% 19.29/19.55 [1354]~P2(x13541)+P3(a114,f51(x13541,x13542),f51(x13541,f15(a114,x13542,f7(a114))))
% 19.29/19.55 [1385]E(f11(a114,f51(a16,x13851),f51(a16,x13852)),f51(a16,f11(a112,x13851,x13852)))+~P80(f51(f18(a112,f6(a112)),x13851))
% 19.29/19.55 [1392]E(f13(a1,f51(f4(a114),x13921),f51(f4(a114),x13922)),f51(f4(a114),f13(a114,x13921,x13922)))+~P80(f51(f18(a114,x13922),x13921))
% 19.29/19.55 [1393]E(f13(a112,f51(f5(a112),x13931),f51(f5(a112),x13932)),f51(f5(a112),f13(a114,x13931,x13932)))+~P80(f51(f18(a114,x13932),x13931))
% 19.29/19.55 [1418]~P3(a112,x14181,x14182)+P80(f51(f18(a112,x14181),f13(a112,x14182,f7(a112))))
% 19.29/19.55 [1425]~P80(f51(f18(a114,x14251),x14252))+P80(f51(f18(a1,f51(f4(a114),x14251)),f51(f4(a114),x14252)))
% 19.29/19.55 [1427]~P80(f51(f18(a114,x14271),x14272))+P80(f51(f18(a112,f51(f5(a112),x14271)),f51(f5(a112),x14272)))
% 19.29/19.55 [1541]~P3(a114,f6(a114),x15411)+P3(a114,f13(a114,x15411,f15(a114,x15412,f7(a114))),x15411)
% 19.29/19.55 [1576]P80(f51(f18(a114,x15761),x15762))+~P80(f51(f18(a1,f51(f4(a114),x15761)),f51(f4(a114),x15762)))
% 19.29/19.55 [1578]P80(f51(f18(a114,x15781),x15782))+~P80(f51(f18(a112,f51(f5(a112),x15781)),f51(f5(a112),x15782)))
% 19.29/19.55 [1589]P3(a112,x15891,x15892)+~P80(f51(f18(a112,x15891),f13(a112,x15892,f7(a112))))
% 19.29/19.55 [1660]~P67(x16601)+E(f51(f51(f14(x16601),f15(x16601,x16602,f7(x16601))),f13(x16601,x16602,f7(x16601))),f13(x16601,f51(f51(f14(x16601),x16602),x16602),f7(x16601)))
% 19.29/19.55 [1849]~P3(a114,x18491,x18492)+P80(f51(f18(a1,f15(a1,f51(f4(a114),x18491),f7(a1))),f51(f4(a114),x18492)))
% 19.29/19.55 [1920]P80(f51(f18(a114,x19201),x19202))+~P80(f51(f18(a114,f15(a114,x19201,f7(a114))),f15(a114,x19202,f7(a114))))
% 19.29/19.55 [1945]P3(a114,x19451,x19452)+~P80(f51(f18(a1,f15(a1,f51(f4(a114),x19451),f7(a1))),f51(f4(a114),x19452)))
% 19.29/19.55 [977]~P50(x9771)+E(f51(f51(f14(f115(x9771)),f6(f115(x9771))),x9772),f6(f115(x9771)))
% 19.29/19.55 [1087]E(f10(a112,x10871),f7(a112))+~E(f10(a112,f51(f51(f14(a112),x10871),x10872)),f7(a112))
% 19.29/19.55 [1108]~E(f51(f4(a114),f27(x11081)),x11081)+E(f27(f51(f51(f20(a1),x11081),x11082)),f51(f51(f20(a114),f27(x11081)),x11082))
% 19.29/19.55 [1174]~P3(a114,f6(a114),x11742)+E(f11(a114,f51(f51(f14(a114),x11741),x11742),x11742),x11741)
% 19.29/19.55 [1175]~P3(a114,f6(a114),x11751)+E(f11(a114,f51(f51(f14(a114),x11751),x11752),x11751),x11752)
% 19.29/19.55 [1319]~P58(x13191)+P80(f51(f18(x13191,f6(x13191)),f51(f51(f14(x13191),x13192),x13192)))
% 19.29/19.55 [1359]E(f51(f51(f20(a114),f51(a16,x13591)),x13592),f51(a16,f51(f51(f20(a112),x13591),x13592)))+~P80(f51(f18(a112,f6(a112)),x13591))
% 19.29/19.55 [1388]E(f51(f51(f14(a114),f51(a16,x13881)),f51(a16,x13882)),f51(a16,f51(f51(f14(a112),x13881),x13882)))+~P80(f51(f18(a112,f6(a112)),x13881))
% 19.29/19.55 [1409]E(f17(f15(a1,x14091,f51(f4(a114),x14092))),f15(a114,f17(x14091),x14092))+~P80(f51(f18(a1,f6(a1)),x14091))
% 19.29/19.55 [1410]E(f27(f15(a1,x14101,f51(f4(a114),x14102))),f15(a114,f27(x14101),x14102))+~P80(f51(f18(a1,f6(a1)),x14101))
% 19.29/19.55 [1411]E(x14111,f6(a1))+~E(f15(a1,f51(f51(f14(a1),x14112),x14112),f51(f51(f14(a1),x14111),x14111)),f6(a1))
% 19.29/19.55 [1412]E(x14121,f6(a1))+~E(f15(a1,f51(f51(f14(a1),x14121),x14121),f51(f51(f14(a1),x14122),x14122)),f6(a1))
% 19.29/19.55 [1414]~P54(x14141)+E(f15(x14141,x14142,x14142),f51(f51(f14(x14141),f15(x14141,f7(x14141),f7(x14141))),x14142))
% 19.29/19.55 [1444]E(x14441,f6(a114))+E(f51(f51(f14(a114),x14442),f51(f51(f20(a114),x14442),f13(a114,x14441,f7(a114)))),f51(f51(f20(a114),x14442),x14441))
% 19.29/19.55 [1455]~P80(f51(f18(a112,f6(a112)),x14551))+P80(f51(f18(a112,f6(a112)),f51(f51(f20(a112),x14551),x14552)))
% 19.29/19.55 [1457]P80(f51(f18(a114,x14571),f27(x14572)))+~P80(f51(f18(a1,f51(f4(a114),x14571)),x14572))
% 19.29/19.55 [1571]~P3(a112,x15711,x15712)+E(f15(a112,x15711,f51(f5(a112),f15(a114,f92(x15712,x15711),f7(a114)))),x15712)
% 19.29/19.55 [1631]E(f17(f13(a1,x16311,f51(f4(a114),x16312))),f13(a114,f17(x16311),x16312))+~P80(f51(f18(a1,f51(f4(a114),x16312)),x16311))
% 19.29/19.55 [1632]E(f27(f13(a1,x16321,f51(f4(a114),x16322))),f13(a114,f27(x16321),x16322))+~P80(f51(f18(a1,f51(f4(a114),x16322)),x16321))
% 19.29/19.55 [1668]P80(f51(f18(a114,x16681),x16682))+P80(f51(f18(a114,f15(a114,x16682,f7(a114))),x16681))
% 19.29/19.55 [1675]~P3(a114,x16751,x16752)+P80(f51(f18(a114,f15(a114,x16751,f7(a114))),x16752))
% 19.29/19.55 [1677]~P3(a112,x16771,x16772)+P80(f51(f18(a112,f15(a112,x16771,f7(a112))),x16772))
% 19.29/19.55 [1826]P3(a114,x18261,x18262)+~P80(f51(f18(a114,f15(a114,x18261,f7(a114))),x18262))
% 19.29/19.55 [1827]P3(a112,x18271,x18272)+~P80(f51(f18(a112,f15(a112,x18271,f7(a112))),x18272))
% 19.29/19.55 [1856]~P80(f51(f18(a114,x18561),x18562))+~P80(f51(f18(a114,f15(a114,x18562,f7(a114))),x18561))
% 19.29/19.55 [1864]P3(a1,x18641,f51(f4(a114),x18642))+~P80(f51(f18(a114,f15(a114,f27(x18641),f7(a114))),x18642))
% 19.29/19.55 [1965]~P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),x19651))+P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),f51(f51(f20(a114),x19651),x19652)))
% 19.29/19.55 [1972]P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),x19721))+~P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),f51(f51(f14(a114),x19722),x19721)))
% 19.29/19.55 [1973]P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),x19731))+~P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),f51(f51(f14(a114),x19731),x19732)))
% 19.29/19.55 [1699]E(x16991,f6(a114))+E(f15(a114,x16992,f51(f51(f14(a114),f13(a114,x16991,f7(a114))),x16992)),f51(f51(f14(a114),x16991),x16992))
% 19.29/19.55 [2031]~P80(f51(f18(a1,f6(a1)),x20312))+P80(f51(f18(a1,f15(a1,f51(f51(f14(a1),f51(f4(a114),x20311)),x20312),f7(a1))),f51(f51(f20(a1),f15(a1,x20312,f7(a1))),x20311)))
% 19.29/19.55 [959]~P54(x9591)+E(f15(x9591,x9592,x9593),f15(x9591,x9593,x9592))
% 19.29/19.55 [1042]E(x10421,x10422)+~E(f15(a114,x10423,x10421),f15(a114,x10423,x10422))
% 19.29/19.55 [1043]E(x10431,x10432)+~E(f15(a114,x10431,x10433),f15(a114,x10432,x10433))
% 19.29/19.55 [1197]~P3(a114,x11971,x11973)+P3(a114,x11971,f15(a114,x11972,x11973))
% 19.29/19.55 [1199]~P3(a114,x11991,x11992)+P3(a114,x11991,f15(a114,x11992,x11993))
% 19.29/19.55 [1200]~P3(a114,x12001,x12003)+P3(a114,f13(a114,x12001,x12002),x12003)
% 19.29/19.55 [1295]P3(a114,x12951,x12952)+~P3(a114,f15(a114,x12951,x12953),x12952)
% 19.29/19.55 [1377]~P3(a114,x13772,x13773)+P3(a114,f15(a114,x13771,x13772),f15(a114,x13771,x13773))
% 19.29/19.55 [1378]~P3(a114,x13781,x13783)+P3(a114,f15(a114,x13781,x13782),f15(a114,x13783,x13782))
% 19.29/19.55 [1379]~P3(a112,x13791,x13793)+P3(a112,f15(a112,x13791,x13792),f15(a112,x13793,x13792))
% 19.29/19.55 [1442]~P3(a114,f15(a114,x14421,x14423),x14422)+P3(a114,x14421,f13(a114,x14422,x14423))
% 19.29/19.55 [1443]~P3(a114,x14431,f13(a114,x14433,x14432))+P3(a114,f15(a114,x14431,x14432),x14433)
% 19.29/19.55 [1538]P3(a114,x15381,x15382)+~P3(a114,f15(a114,x15383,x15381),f15(a114,x15383,x15382))
% 19.29/19.55 [1033]~E(x10332,f15(a114,x10331,x10333))+P80(f51(f18(a114,x10331),x10332))
% 19.29/19.55 [1047]~P18(x10471)+E(f13(x10471,f15(x10471,x10472,x10473),x10473),x10472)
% 19.29/19.55 [1048]~P18(x10481)+E(f15(x10481,f13(x10481,x10482,x10483),x10483),x10482)
% 19.29/19.55 [1141]~P50(x11411)+E(f22(x11411,f23(x11411,x11412,x11413)),f13(a114,f22(x11411,x11412),f7(a114)))
% 19.29/19.55 [1220]~P1(x12201)+E(f28(x12201,f13(x12201,x12202,x12203)),f28(x12201,f13(x12201,x12203,x12202)))
% 19.29/19.55 [1221]~P32(x12211)+E(f10(x12211,f13(x12211,x12212,x12213)),f10(x12211,f13(x12211,x12213,x12212)))
% 19.29/19.55 [1306]P3(a114,x13061,x13062)+~E(x13062,f15(a114,f15(a114,x13061,x13063),f7(a114)))
% 19.29/19.55 [1336]~P81(x13361,x13363,x13362)+P80(f51(x13361,f11(a112,x13362,x13363)))
% 19.29/19.55 [1439]~P80(f51(f18(a114,x14391),x14393))+P80(f51(f18(a114,x14391),f15(a114,x14392,x14393)))
% 19.29/19.55 [1441]~P80(f51(f18(a114,x14411),x14412))+P80(f51(f18(a114,x14411),f15(a114,x14412,x14413)))
% 19.29/19.55 [1492]P81(x14921,x14922,x14923)+~P80(f51(x14921,f11(a112,x14923,x14922)))
% 19.29/19.55 [1494]E(f13(a114,f15(a114,x14941,x14942),x14943),f13(a114,x14941,f13(a114,x14943,x14942)))+~P80(f51(f18(a114,x14942),x14943))
% 19.29/19.55 [1496]E(f15(a114,x14961,f13(a114,x14962,x14963)),f13(a114,f15(a114,x14961,x14962),x14963))+~P80(f51(f18(a114,x14963),x14962))
% 19.29/19.55 [1498]E(f15(a114,f13(a114,x14981,x14982),x14983),f13(a114,f15(a114,x14981,x14983),x14982))+~P80(f51(f18(a114,x14982),x14981))
% 19.29/19.55 [1781]~P80(f51(f18(a1,x17812),x17813))+P80(f51(f18(a1,f15(a1,x17811,x17812)),f15(a1,x17811,x17813)))
% 19.29/19.55 [1782]~P80(f51(f18(a114,x17823),x17822))+P80(f51(f18(a114,f13(a114,x17821,x17822)),f13(a114,x17821,x17823)))
% 19.29/19.55 [1783]~P80(f51(f18(a114,x17831),x17833))+P80(f51(f18(a114,f13(a114,x17831,x17832)),f13(a114,x17833,x17832)))
% 19.29/19.55 [1784]~P80(f51(f18(a114,x17841),x17843))+P80(f51(f18(a114,f11(a114,x17841,x17842)),f11(a114,x17843,x17842)))
% 19.29/19.55 [1785]~P80(f51(f18(a114,x17852),x17853))+P80(f51(f18(a114,f15(a114,x17851,x17852)),f15(a114,x17851,x17853)))
% 19.29/19.55 [1786]~P80(f51(f18(a114,x17861),x17863))+P80(f51(f18(a114,f15(a114,x17861,x17862)),f15(a114,x17863,x17862)))
% 19.29/19.55 [1787]~P80(f51(f18(a112,x17872),x17873))+P80(f51(f18(a112,f15(a112,x17871,x17872)),f15(a112,x17871,x17873)))
% 19.29/19.55 [1909]P80(f51(f18(a114,x19091),x19092))+~P80(f51(f18(a114,f15(a114,x19093,x19091)),f15(a114,x19093,x19092)))
% 19.29/19.55 [927]~E(x9272,f6(a114))+E(f51(f51(f14(a114),x9271),x9272),f51(f51(f14(a114),x9273),x9272))
% 19.29/19.55 [929]~E(x9291,f6(a114))+E(f51(f51(f14(a114),x9291),x9292),f51(f51(f14(a114),x9291),x9293))
% 19.29/19.55 [950]~P54(x9501)+E(f51(f51(f14(x9501),x9502),x9503),f51(f51(f14(x9501),x9503),x9502))
% 19.29/19.55 [1144]~E(x11442,f15(a112,x11441,f51(f5(a112),x11443)))+P80(f51(f18(a112,x11441),x11442))
% 19.29/19.55 [1239]~P74(x12391)+E(f15(x12391,f51(f5(x12391),x12392),f51(f5(x12391),x12393)),f51(f5(x12391),f15(a114,x12392,x12393)))
% 19.29/19.55 [1369]~P32(x13691)+E(f10(x13691,f15(x13691,f10(x13691,x13692),f10(x13691,x13693))),f15(x13691,f10(x13691,x13692),f10(x13691,x13693)))
% 19.29/19.55 [1472]P3(a114,x14721,x14722)+~P3(a114,f51(f51(f14(a114),x14723),x14721),f51(f51(f14(a114),x14723),x14722))
% 19.29/19.55 [1473]P3(a114,x14731,x14732)+~P3(a114,f51(f51(f14(a114),x14731),x14733),f51(f51(f14(a114),x14732),x14733))
% 19.29/19.55 [1478]P3(a114,f6(a114),x14781)+~P3(a114,f51(f51(f14(a114),x14782),x14781),f51(f51(f14(a114),x14783),x14781))
% 19.29/19.55 [1479]P3(a114,f6(a114),x14791)+~P3(a114,f51(f51(f14(a114),x14791),x14792),f51(f51(f14(a114),x14791),x14793))
% 19.29/19.55 [1772]E(f13(a114,f15(a114,x17721,x17722),f15(a114,x17723,f7(a114))),f13(a114,x17721,f15(a114,f13(a114,x17723,x17722),f7(a114))))+~P80(f51(f18(a114,x17722),x17723))
% 19.29/19.55 [1773]E(f13(a114,f15(a114,f13(a114,x17731,x17732),f7(a114)),x17733),f13(a114,f15(a114,x17731,f7(a114)),f15(a114,x17732,x17733)))+~P80(f51(f18(a114,x17732),x17731))
% 19.29/19.55 [1780]~P80(f51(f18(a114,x17803),x17802))+P80(f51(f18(a114,x17801),f13(a114,f15(a114,x17802,x17801),x17803)))
% 19.29/19.55 [1811]P80(f51(f18(a114,x18111),x18112))+~P80(f51(f18(a114,f15(a114,x18113,x18111)),x18112))
% 19.29/19.55 [1812]P80(f51(f18(a114,x18121),x18122))+~P80(f51(f18(a114,f15(a114,x18121,x18123)),x18122))
% 19.29/19.55 [1858]~P80(f51(f18(a114,x18581),f15(a114,x18583,x18582)))+P80(f51(f18(a114,f13(a114,x18581,x18582)),x18583))
% 19.29/19.55 [1885]P80(f51(f18(a114,x18851),f15(a114,x18852,x18853)))+~P80(f51(f18(a114,f13(a114,x18851,x18853)),x18852))
% 19.29/19.55 [1946]~P1(x19461)+P80(f51(f18(a1,f13(a1,f28(x19461,x19462),f28(x19461,x19463))),f28(x19461,f13(x19461,x19462,x19463))))
% 19.29/19.55 [1947]~P1(x19471)+P80(f51(f18(a1,f13(a1,f28(x19471,x19472),f28(x19471,x19473))),f28(x19471,f15(x19471,x19472,x19473))))
% 19.29/19.55 [1950]~P32(x19501)+P80(f51(f18(x19501,f13(x19501,f10(x19501,x19502),f10(x19501,x19503))),f10(x19501,f13(x19501,x19503,x19502))))
% 19.29/19.55 [1951]~P32(x19511)+P80(f51(f18(x19511,f13(x19511,f10(x19511,x19512),f10(x19511,x19513))),f10(x19511,f13(x19511,x19512,x19513))))
% 19.29/19.55 [1954]~P1(x19541)+P80(f51(f18(a1,f28(x19541,f13(x19541,x19542,x19543))),f15(a1,f28(x19541,x19542),f28(x19541,x19543))))
% 19.29/19.55 [1955]~P1(x19551)+P80(f51(f18(a1,f28(x19551,f15(x19551,x19552,x19553))),f15(a1,f28(x19551,x19552),f28(x19551,x19553))))
% 19.29/19.55 [1956]~P32(x19561)+P80(f51(f18(x19561,f10(x19561,f13(x19561,x19562,x19563))),f15(x19561,f10(x19561,x19562),f10(x19561,x19563))))
% 19.29/19.55 [1957]~P32(x19571)+P80(f51(f18(x19571,f10(x19571,f15(x19571,x19572,x19573))),f15(x19571,f10(x19571,x19572),f10(x19571,x19573))))
% 19.29/19.55 [1960]~P44(x19601)+P80(f51(f18(a1,f28(x19601,f51(f51(f14(x19601),x19602),x19603))),f51(f51(f14(a1),f28(x19601,x19603)),f87(x19602,x19601))))
% 19.29/19.55 [1961]~P44(x19611)+P80(f51(f18(a1,f28(x19611,f51(f51(f14(x19611),x19612),x19613))),f51(f51(f14(a1),f28(x19611,x19612)),f28(x19611,x19613))))
% 19.29/19.55 [1962]~P44(x19621)+P80(f51(f18(a1,f28(x19621,f51(f51(f14(x19621),x19622),x19623))),f51(f51(f14(a1),f28(x19621,x19622)),f54(x19623,x19621))))
% 19.29/19.55 [1963]~P50(x19631)+P80(f51(f18(a114,f22(x19631,f24(x19631,x19632,x19633))),f51(f51(f14(a114),f22(x19631,x19632)),f22(x19631,x19633))))
% 19.29/19.55 [1987]~P50(x19871)+P80(f51(f18(a114,f22(x19871,f51(f51(f14(f115(x19871)),x19872),x19873))),f15(a114,f22(x19871,x19872),f22(x19871,x19873))))
% 19.29/19.55 [2010]~P1(x20101)+P80(f51(f18(a1,f10(a1,f13(a1,f28(x20101,x20102),f28(x20101,x20103)))),f28(x20101,f13(x20101,x20102,x20103))))
% 19.29/19.55 [2011]~P32(x20111)+P80(f51(f18(x20111,f10(x20111,f13(x20111,f10(x20111,x20112),f10(x20111,x20113)))),f10(x20111,f13(x20111,x20112,x20113))))
% 19.29/19.55 [2021]~P44(x20211)+P80(f51(f18(a1,f28(x20211,f51(f51(f14(x20211),x20212),x20213))),f51(f51(f14(a1),f51(f51(f14(a1),f28(x20211,x20212)),f28(x20211,x20213))),f52(x20211))))
% 19.29/19.55 [1156]~P41(x11561)+E(f28(x11561,f51(f51(f20(x11561),x11562),x11563)),f51(f51(f20(a1),f28(x11561,x11562)),x11563))
% 19.29/19.55 [1169]~P48(x11691)+E(f51(f51(f20(x11691),f10(x11691,x11692)),x11693),f10(x11691,f51(f51(f20(x11691),x11692),x11693)))
% 19.29/19.55 [1201]~E(x12011,f6(a114))+E(f11(a114,f51(f51(f14(a114),x12011),x12012),f51(f51(f14(a114),x12011),x12013)),f6(a114))
% 19.29/19.55 [1211]~P74(x12111)+E(f51(f51(f20(x12111),f51(f5(x12111),x12112)),x12113),f51(f5(x12111),f51(f51(f20(a114),x12112),x12113)))
% 19.29/19.55 [1216]~P41(x12161)+E(f51(f51(f14(a1),f28(x12161,x12162)),f28(x12161,x12163)),f28(x12161,f51(f51(f14(x12161),x12162),x12163)))
% 19.29/19.55 [1224]~P48(x12241)+E(f51(f51(f14(x12241),f10(x12241,x12242)),f10(x12241,x12243)),f10(x12241,f51(f51(f14(x12241),x12242),x12243)))
% 19.29/19.55 [1280]~P74(x12801)+E(f51(f51(f14(x12801),f51(f5(x12801),x12802)),f51(f5(x12801),x12803)),f51(f5(x12801),f51(f51(f14(a114),x12802),x12803)))
% 19.29/19.55 [1285]E(x12851,f6(a114))+E(f11(a114,f51(f51(f14(a114),x12851),x12852),f51(f51(f14(a114),x12851),x12853)),f11(a114,x12852,x12853))
% 19.29/19.55 [1331]~P43(x13311)+E(f51(f51(f14(x13311),x13312),f51(f51(f20(x13311),x13312),x13313)),f51(f51(f20(x13311),x13312),f15(a114,x13313,f7(a114))))
% 19.29/19.55 [1332]~P54(x13321)+E(f51(f51(f14(x13321),x13322),f51(f51(f20(x13321),x13322),x13323)),f51(f51(f20(x13321),x13322),f15(a114,x13323,f7(a114))))
% 19.29/19.55 [1413]~P3(a114,f6(a114),x14131)+E(f11(a114,f51(f51(f14(a114),x14131),x14132),f51(f51(f14(a114),x14131),x14133)),f11(a114,x14132,x14133))
% 19.29/19.55 [1428]~P3(a112,f6(a112),x14283)+E(f11(a112,x14281,f51(f51(f14(a112),x14282),x14283)),f11(a112,f11(a112,x14281,x14282),x14283))
% 19.29/19.55 [1529]~P54(x15291)+E(f15(x15291,x15292,f51(f51(f14(x15291),x15293),x15292)),f51(f51(f14(x15291),f15(x15291,x15293,f7(x15291))),x15292))
% 19.29/19.55 [1530]~P54(x15301)+E(f15(x15301,f51(f51(f14(x15301),x15302),x15303),x15303),f51(f51(f14(x15301),f15(x15301,x15302,f7(x15301))),x15303))
% 19.29/19.55 [1535]~P16(x15351)+E(f29(x15351,f7(x15351),f51(f51(f20(x15351),x15352),x15353)),f51(f51(f20(x15351),f29(x15351,f7(x15351),x15352)),x15353))
% 19.29/19.55 [1597]~P48(x15971)+P80(f51(f18(x15971,f6(x15971)),f51(f51(f20(x15971),f10(x15971,x15972)),x15973)))
% 19.29/19.55 [1612]P3(a112,x16121,x16122)+~E(x16122,f15(a112,x16121,f51(f5(a112),f15(a114,x16123,f7(a114)))))
% 19.29/19.55 [1727]P3(a114,f6(a114),x17271)+P80(f51(f18(a114,f51(f51(f14(a114),x17272),x17271)),f51(f51(f14(a114),x17273),x17271)))
% 19.29/19.55 [1728]P3(a114,f6(a114),x17281)+P80(f51(f18(a114,f51(f51(f14(a114),x17281),x17282)),f51(f51(f14(a114),x17281),x17283)))
% 19.29/19.55 [1763]~P80(f51(f18(a114,x17632),x17633))+P80(f51(f18(a114,f51(f51(f14(a114),x17631),x17632)),f51(f51(f14(a114),x17631),x17633)))
% 19.29/19.55 [1765]~P80(f51(f18(a114,x17651),x17653))+P80(f51(f18(a114,f51(f51(f14(a114),x17651),x17652)),f51(f51(f14(a114),x17653),x17652)))
% 19.29/19.55 [1806]E(x18061,x18062)+~E(f51(f51(f14(a114),f15(a114,x18063,f7(a114))),x18061),f51(f51(f14(a114),f15(a114,x18063,f7(a114))),x18062))
% 19.29/19.55 [1846]~P58(x18461)+~P3(x18461,f15(x18461,f51(f51(f14(x18461),x18462),x18462),f51(f51(f14(x18461),x18463),x18463)),f6(x18461))
% 19.29/19.55 [1914]~P3(a114,x19142,x19143)+P3(a114,f51(f51(f14(a114),f15(a114,x19141,f7(a114))),x19142),f51(f51(f14(a114),f15(a114,x19141,f7(a114))),x19143))
% 19.29/19.55 [1948]~P42(x19481)+P80(f51(f18(a1,f28(x19481,f51(f51(f20(x19481),x19482),x19483))),f51(f51(f20(a1),f28(x19481,x19482)),x19483)))
% 19.29/19.55 [1984]~P54(x19841)+P80(f51(f18(a114,f22(x19841,f51(f51(f20(f115(x19841)),x19842),x19843))),f51(f51(f14(a114),f22(x19841,x19842)),x19843)))
% 19.29/19.55 [2000]~P52(x20001)+E(f13(x20001,f51(f51(f20(x20001),x20002),f15(a114,f15(a114,f6(a114),f7(a114)),f7(a114))),f51(f51(f20(x20001),x20003),f15(a114,f15(a114,f6(a114),f7(a114)),f7(a114)))),f51(f51(f14(x20001),f13(x20001,x20002,x20003)),f15(x20001,x20002,x20003)))
% 19.29/19.55 [1465]~P26(x14651)+E(f51(f51(f14(x14651),f51(f51(f20(x14651),x14652),x14653)),x14652),f51(f51(f14(x14651),x14652),f51(f51(f20(x14651),x14652),x14653)))
% 19.29/19.55 [1485]~P26(x14851)+E(f51(f51(f14(x14851),f51(f51(f20(x14851),x14852),x14853)),x14852),f51(f51(f20(x14851),x14852),f15(a114,x14853,f7(a114))))
% 19.29/19.55 [1486]~P54(x14861)+E(f51(f51(f14(x14861),f51(f51(f20(x14861),x14862),x14863)),x14862),f51(f51(f20(x14861),x14862),f15(a114,x14863,f7(a114))))
% 19.29/19.55 [1905]~P58(x19051)+P80(f51(f18(x19051,f6(x19051)),f15(x19051,f51(f51(f14(x19051),x19052),x19052),f51(f51(f14(x19051),x19053),x19053))))
% 19.29/19.55 [2042]~P3(a112,f6(a112),x20423)+P3(a112,x20421,f15(a112,x20422,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x20422,x20421)),f7(a112))),x20423)))
% 19.29/19.55 [2043]~P3(a112,f6(a112),x20433)+P3(a112,f13(a112,x20431,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x20431,x20432)),f7(a112))),x20433)),x20432)
% 19.29/19.55 [2044]P80(f51(f18(a114,x20441),x20442))+~P80(f51(f18(a114,f51(f51(f14(a114),f15(a114,x20443,f7(a114))),x20441)),f51(f51(f14(a114),f15(a114,x20443,f7(a114))),x20442)))
% 19.29/19.55 [1343]~P54(x13431)+E(f15(x13431,x13432,f15(x13431,x13433,x13434)),f15(x13431,x13433,f15(x13431,x13432,x13434)))
% 19.29/19.55 [1345]~P54(x13451)+E(f15(x13451,f15(x13451,x13452,x13453),x13454),f15(x13451,x13452,f15(x13451,x13453,x13454)))
% 19.29/19.55 [1346]~P20(x13461)+E(f15(x13461,f15(x13461,x13462,x13463),x13464),f15(x13461,x13462,f15(x13461,x13463,x13464)))
% 19.29/19.55 [1347]~P54(x13471)+E(f15(x13471,f15(x13471,x13472,x13473),x13474),f15(x13471,f15(x13471,x13472,x13474),x13473))
% 19.29/19.55 [1500]~P55(x15001)+E(f13(x15001,f29(x15001,x15002,x15003),f29(x15001,x15004,x15003)),f29(x15001,f13(x15001,x15002,x15004),x15003))
% 19.29/19.55 [1501]~P46(x15011)+E(f13(x15011,f29(x15011,x15012,x15013),f29(x15011,x15014,x15013)),f29(x15011,f13(x15011,x15012,x15014),x15013))
% 19.29/19.55 [1502]~P55(x15021)+E(f15(x15021,f29(x15021,x15022,x15023),f29(x15021,x15024,x15023)),f29(x15021,f15(x15021,x15022,x15024),x15023))
% 19.29/19.55 [1503]~P46(x15031)+E(f15(x15031,f29(x15031,x15032,x15033),f29(x15031,x15034,x15033)),f29(x15031,f15(x15031,x15032,x15034),x15033))
% 19.29/19.55 [1318]~P54(x13181)+E(f51(f51(f14(x13181),x13182),f51(f51(f14(x13181),x13183),x13184)),f51(f51(f14(x13181),x13183),f51(f51(f14(x13181),x13182),x13184)))
% 19.29/19.55 [1329]~P55(x13291)+E(f29(x13291,f51(f51(f14(x13291),x13292),x13293),x13294),f51(f51(f14(x13291),x13292),f29(x13291,x13293,x13294)))
% 19.29/19.55 [1481]~P44(x14811)+E(f13(x14811,f51(f51(f14(x14811),x14812),x14813),f51(f51(f14(x14811),x14812),x14814)),f51(f51(f14(x14811),x14812),f13(x14811,x14813,x14814)))
% 19.29/19.55 [1483]~P44(x14831)+E(f15(x14831,f51(f51(f14(x14831),x14832),x14833),f51(f51(f14(x14831),x14832),x14834)),f51(f51(f14(x14831),x14832),f15(x14831,x14833,x14834)))
% 19.29/19.55 [1484]~P54(x14841)+E(f15(x14841,f51(f51(f14(x14841),x14842),x14843),f51(f51(f14(x14841),x14842),x14844)),f51(f51(f14(x14841),x14842),f15(x14841,x14843,x14844)))
% 19.29/19.55 [1592]~P26(x15921)+E(f51(f51(f14(x15921),f51(f51(f20(x15921),x15922),x15923)),f51(f51(f20(x15921),x15922),x15924)),f51(f51(f20(x15921),x15922),f15(a114,x15923,x15924)))
% 19.29/19.55 [1593]~P54(x15931)+E(f51(f51(f14(x15931),f51(f51(f20(x15931),x15932),x15933)),f51(f51(f20(x15931),x15932),x15934)),f51(f51(f20(x15931),x15932),f15(a114,x15933,x15934)))
% 19.29/19.55 [1604]~P16(x16041)+E(f29(x16041,f51(f51(f20(x16041),x16042),x16043),f51(f51(f20(x16041),x16044),x16043)),f51(f51(f20(x16041),f29(x16041,x16042,x16044)),x16043))
% 19.29/19.55 [1606]~P44(x16061)+E(f13(x16061,f51(f51(f14(x16061),x16062),x16063),f51(f51(f14(x16061),x16064),x16063)),f51(f51(f14(x16061),f13(x16061,x16062,x16064)),x16063))
% 19.29/19.55 [1608]~P44(x16081)+E(f15(x16081,f51(f51(f14(x16081),x16082),x16083),f51(f51(f14(x16081),x16084),x16083)),f51(f51(f14(x16081),f15(x16081,x16082,x16084)),x16083))
% 19.29/19.55 [1610]~P51(x16101)+E(f15(x16101,f51(f51(f14(x16101),x16102),x16103),f51(f51(f14(x16101),x16104),x16103)),f51(f51(f14(x16101),f15(x16101,x16102,x16104)),x16103))
% 19.29/19.55 [1611]~P54(x16111)+E(f15(x16111,f51(f51(f14(x16111),x16112),x16113),f51(f51(f14(x16111),x16114),x16113)),f51(f51(f14(x16111),f15(x16111,x16112,x16114)),x16113))
% 19.29/19.55 [1436]~P15(x14361)+E(f11(f115(x14361),x14362,f51(f51(f14(f115(x14361)),x14363),x14364)),f11(f115(x14361),f11(f115(x14361),x14362,x14363),x14364))
% 19.29/19.55 [1453]~P54(x14531)+E(f51(f51(f20(x14531),f51(f51(f20(x14531),x14532),x14533)),x14534),f51(f51(f20(x14531),x14532),f51(f51(f14(a114),x14533),x14534)))
% 19.29/19.55 [1454]~P26(x14541)+E(f51(f51(f20(x14541),f51(f51(f20(x14541),x14542),x14543)),x14544),f51(f51(f20(x14541),x14542),f51(f51(f14(a114),x14543),x14544)))
% 19.29/19.55 [1466]~P19(x14661)+E(f51(f51(f14(x14661),f51(f51(f14(x14661),x14662),x14663)),x14664),f51(f51(f14(x14661),x14662),f51(f51(f14(x14661),x14663),x14664)))
% 19.29/19.55 [1467]~P54(x14671)+E(f51(f51(f14(x14671),f51(f51(f14(x14671),x14672),x14673)),x14674),f51(f51(f14(x14671),x14672),f51(f51(f14(x14671),x14673),x14674)))
% 19.29/19.55 [1590]~P54(x15901)+E(f51(f51(f14(x15901),f51(f51(f14(x15901),x15902),x15903)),x15904),f51(f51(f14(x15901),f51(f51(f14(x15901),x15902),x15904)),x15903))
% 19.29/19.55 [1691]~P21(x16911)+E(f51(f51(f14(x16911),f51(f51(f20(x16911),x16912),x16913)),f51(f51(f20(x16911),x16914),x16913)),f51(f51(f20(x16911),f51(f51(f14(x16911),x16912),x16914)),x16913))
% 19.29/19.55 [1692]~P54(x16921)+E(f51(f51(f14(x16921),f51(f51(f20(x16921),x16922),x16923)),f51(f51(f20(x16921),x16924),x16923)),f51(f51(f20(x16921),f51(f51(f14(x16921),x16922),x16924)),x16923))
% 19.29/19.55 [1742]~P50(x17421)+E(f15(f115(x17421),f51(f51(f14(f115(x17421)),x17422),x17423),f51(f51(f14(f115(x17421)),x17424),x17423)),f51(f51(f14(f115(x17421)),f15(f115(x17421),x17422,x17424)),x17423))
% 19.29/19.55 [1624]~P13(x16241)+E(f15(x16241,f13(x16241,x16242,x16243),f13(x16241,x16244,x16245)),f13(x16241,f15(x16241,x16242,x16244),f15(x16241,x16243,x16245)))
% 19.29/19.55 [1625]~P54(x16251)+E(f15(x16251,f15(x16251,x16252,x16253),f15(x16251,x16254,x16255)),f15(x16251,f15(x16251,x16252,x16254),f15(x16251,x16253,x16255)))
% 19.29/19.55 [1758]~P54(x17581)+E(f51(f51(f14(x17581),f51(f51(f14(x17581),x17582),x17583)),f51(f51(f14(x17581),x17584),x17585)),f51(f51(f14(x17581),f51(f51(f14(x17581),x17582),x17584)),f51(f51(f14(x17581),x17583),x17585)))
% 19.29/19.55 [1906]~P73(x19061)+E(f15(x19061,f51(f51(f14(x19061),x19062),f13(x19061,x19063,x19064)),f51(f51(f14(x19061),f13(x19061,x19062,x19065)),x19064)),f13(x19061,f51(f51(f14(x19061),x19062),x19063),f51(f51(f14(x19061),x19065),x19064)))
% 19.29/19.55 [2023]~P44(x20231)+E(f15(x20231,f15(x20231,f51(f51(f14(x20231),f13(x20231,x20232,x20233)),f13(x20231,x20234,x20235)),f51(f51(f14(x20231),f13(x20231,x20232,x20233)),x20235)),f51(f51(f14(x20231),x20233),f13(x20231,x20234,x20235))),f13(x20231,f51(f51(f14(x20231),x20232),x20234),f51(f51(f14(x20231),x20233),x20235)))
% 19.29/19.55 [2050]~P1(x20501)+P80(f51(f18(a1,f28(x20501,f13(x20501,f15(x20501,x20502,x20503),f15(x20501,x20504,x20505)))),f15(a1,f28(x20501,f13(x20501,x20502,x20504)),f28(x20501,f13(x20501,x20503,x20505)))))
% 19.29/19.55 [2051]~P32(x20511)+P80(f51(f18(x20511,f10(x20511,f13(x20511,f15(x20511,x20512,x20513),f15(x20511,x20514,x20515)))),f15(x20511,f10(x20511,f13(x20511,x20512,x20514)),f10(x20511,f13(x20511,x20513,x20515)))))
% 19.29/19.55 [1888]~P77(x18881)+E(f15(x18881,f51(f51(f14(x18881),x18882),x18883),f15(x18881,f51(f51(f14(x18881),x18884),x18883),x18885)),f15(x18881,f51(f51(f14(x18881),f15(x18881,x18882,x18884)),x18883),x18885))
% 19.29/19.55 [1989]~P80(f51(f18(a114,x19891),x19894))+E(f13(a114,f15(a114,f51(f51(f14(a114),x19891),x19892),x19893),f15(a114,f51(f51(f14(a114),x19894),x19892),x19895)),f13(a114,x19893,f15(a114,f51(f51(f14(a114),f13(a114,x19894,x19891)),x19892),x19895)))
% 19.29/19.55 [1990]~P80(f51(f18(a114,x19904),x19901))+E(f13(a114,f15(a114,f51(f51(f14(a114),x19901),x19902),x19903),f15(a114,f51(f51(f14(a114),x19904),x19902),x19905)),f13(a114,f15(a114,f51(f51(f14(a114),f13(a114,x19901,x19904)),x19902),x19903),x19905))
% 19.29/19.55 [2018]~P45(x20181)+E(f15(x20181,f51(f51(f14(x20181),x20182),f29(x20181,f13(x20181,x20183,x20184),x20185)),f51(f51(f14(x20181),f29(x20181,f13(x20181,x20182,x20186),x20185)),x20184)),f29(x20181,f13(x20181,f51(f51(f14(x20181),x20182),x20183),f51(f51(f14(x20181),x20186),x20184)),x20185))
% 19.29/19.55 [1743]E(x17431,f6(a114))+E(x17431,f15(a114,f6(a114),f7(a114)))+~P3(a114,x17431,f15(a114,f15(a114,f6(a114),f7(a114)),f7(a114)))
% 19.29/19.55 [801]~P40(x8011)+~P9(x8011,x8012)+P8(x8011,x8012)
% 19.29/19.55 [802]~P40(x8021)+~P11(x8021,x8022)+P8(x8021,x8022)
% 19.29/19.55 [947]E(x9471,x9472)+P3(a114,x9472,x9471)+P3(a114,x9471,x9472)
% 19.29/19.55 [948]E(x9481,x9482)+P3(a112,x9482,x9481)+P3(a112,x9481,x9482)
% 19.29/19.55 [785]~P1(x7851)+~E(x7852,f6(x7851))+E(f28(x7851,x7852),f6(a1))
% 19.29/19.55 [786]~P32(x7861)+~E(x7862,f6(x7861))+E(f10(x7861,x7862),f6(x7861))
% 19.29/19.55 [794]~P1(x7942)+E(x7941,f6(x7942))+~E(f28(x7942,x7941),f6(a1))
% 19.29/19.55 [795]~P32(x7952)+~E(f10(x7952,x7951),f6(x7952))+E(x7951,f6(x7952))
% 19.29/19.55 [830]~E(x8302,f6(a114))+~E(x8301,f6(a114))+E(f15(a114,x8301,x8302),f6(a114))
% 19.29/19.55 [849]~P14(x8492)+E(f11(x8492,x8491,x8491),f7(x8492))+E(x8491,f6(x8492))
% 19.29/19.55 [850]~P55(x8502)+E(f29(x8502,x8501,x8501),f7(x8502))+E(x8501,f6(x8502))
% 19.29/19.55 [851]~P56(x8512)+E(f29(x8512,x8511,x8511),f7(x8512))+E(x8511,f6(x8512))
% 19.29/19.55 [866]~P27(x8661)+~E(x8662,f6(x8661))+E(f15(x8661,x8662,x8662),f6(x8661))
% 19.29/19.55 [867]~P56(x8671)+~E(x8672,f6(x8671))+E(f29(x8671,x8672,x8672),f6(x8671))
% 19.29/19.55 [908]~P2(x9081)+P3(a1,f6(a1),f96(x9081,x9082))+P82(a500)
% 19.29/19.55 [918]~P1(x9182)+E(x9181,f6(x9182))+P3(a1,f6(a1),f28(x9182,x9181))
% 19.29/19.55 [931]~P32(x9312)+P3(x9312,f6(x9312),f10(x9312,x9311))+E(x9311,f6(x9312))
% 19.29/19.55 [937]~P27(x9372)+~E(f15(x9372,x9371,x9371),f6(x9372))+E(x9371,f6(x9372))
% 19.29/19.55 [951]~P1(x9512)+~P10(x9512,x9511)+P3(a1,f6(a1),f30(x9511,x9512))
% 19.29/19.55 [952]~P1(x9522)+~P10(x9522,x9521)+P3(a1,f6(a1),f33(x9521,x9522))
% 19.29/19.55 [961]~P32(x9611)+~P3(x9611,f6(x9611),x9612)+E(f10(x9611,x9612),x9612)
% 19.29/19.55 [969]~P6(x9692)+~P6(x9691)+P6(f15(a1,x9691,x9692))
% 19.29/19.55 [997]~P1(x9972)+~E(x9971,f6(x9972))+~P3(a1,f6(a1),f28(x9972,x9971))
% 19.29/19.55 [1016]~P32(x10162)+~P3(x10162,f6(x10162),f10(x10162,x10161))+~E(x10161,f6(x10162))
% 19.29/19.55 [1071]E(x10711,x10712)+~E(f13(a114,x10712,x10711),f6(a114))+~E(f13(a114,x10711,x10712),f6(a114))
% 19.29/19.55 [1237]~P3(a1,f6(a1),x12371)+~P3(a114,f6(a114),x12372)+P3(a1,f6(a1),f91(x12371,x12372))
% 19.29/19.55 [1256]~P27(x12561)+~P3(x12561,f6(x12561),x12562)+P3(x12561,f6(x12561),f15(x12561,x12562,x12562))
% 19.29/19.55 [1257]~P48(x12571)+~P3(x12571,x12572,f6(x12571))+P3(x12571,f15(x12571,x12572,x12572),f6(x12571))
% 19.29/19.55 [1258]~P27(x12581)+~P3(x12581,x12582,f6(x12581))+P3(x12581,f15(x12581,x12582,x12582),f6(x12581))
% 19.29/19.55 [1260]~P3(a112,x12601,x12602)+~P3(a112,f6(a112),x12602)+P3(a114,f51(a16,x12601),f51(a16,x12602))
% 19.29/19.55 [1351]~P48(x13511)+~P3(x13511,f15(x13511,x13512,x13512),f6(x13511))+P3(x13511,x13512,f6(x13511))
% 19.29/19.55 [1352]~P27(x13521)+~P3(x13521,f15(x13521,x13522,x13522),f6(x13521))+P3(x13521,x13522,f6(x13521))
% 19.29/19.55 [1353]~P27(x13531)+~P3(x13531,f6(x13531),f15(x13531,x13532,x13532))+P3(x13531,f6(x13531),x13532)
% 19.29/19.55 [1360]P3(a114,f13(a114,x13601,x13602),x13601)+~P3(a114,f6(a114),x13601)+~P3(a114,f6(a114),x13602)
% 19.29/19.55 [1361]P3(a114,f11(a114,x13611,x13612),x13611)+~P3(a114,f6(a114),x13611)+~P3(a114,f7(a114),x13612)
% 19.29/19.55 [1362]P3(a112,f11(a112,x13621,x13622),x13621)+~P3(a112,f6(a112),x13621)+~P3(a112,f7(a112),x13622)
% 19.29/19.55 [1366]~P3(a112,x13662,f6(a112))+~P3(a112,f6(a112),x13661)+P3(a112,f11(a112,x13661,x13662),f6(a112))
% 19.29/19.55 [1368]~P3(a112,x13681,f6(a112))+~P3(a112,f6(a112),x13682)+P3(a112,f11(a112,x13681,x13682),f6(a112))
% 19.29/19.55 [1405]P3(a114,f6(a114),x14051)+P3(a114,f6(a114),x14052)+~P3(a114,f6(a114),f15(a114,x14052,x14051))
% 19.29/19.55 [1434]P3(a112,x14341,f6(a112))+~P3(a112,f6(a112),x14342)+~P3(a112,f11(a112,x14341,x14342),f6(a112))
% 19.29/19.55 [1435]P3(a112,f6(a112),x14351)+~P3(a112,x14352,f6(a112))+~P3(a112,f11(a112,x14351,x14352),f6(a112))
% 19.29/19.55 [797]~P31(x7971)+E(f12(x7971,x7972),f6(a114))+~E(x7972,f6(f115(x7971)))
% 19.29/19.55 [803]~P31(x8032)+~E(f12(x8032,x8031),f6(a114))+E(x8031,f6(f115(x8032)))
% 19.29/19.55 [804]E(x8041,f51(a16,x8042))+~E(x8041,f6(a114))+~E(x8042,f51(f5(a112),x8041))
% 19.29/19.55 [805]E(f51(a16,x8051),x8052)+~E(x8052,f6(a114))+~E(x8051,f51(f5(a112),x8052))
% 19.29/19.55 [958]~P31(x9582)+E(x9581,f6(f115(x9582)))+E(f15(a114,f22(x9582,x9581),f7(a114)),f12(x9582,x9581))
% 19.29/19.55 [1040]~P80(f51(x10401,x10402))+P80(f51(x10401,f41(x10402,x10401)))+P80(f51(x10401,f6(a114)))
% 19.29/19.55 [1058]E(x10581,x10582)+P3(a1,x10581,x10582)+~P80(f51(f18(a1,x10581),x10582))
% 19.29/19.55 [1061]E(x10611,x10612)+P3(a114,x10611,x10612)+~P80(f51(f18(a114,x10611),x10612))
% 19.29/19.55 [1062]E(x10621,x10622)+P3(a112,x10621,x10622)+~P80(f51(f18(a112,x10621),x10622))
% 19.29/19.55 [1067]P3(a112,x10671,f6(a112))+E(f51(f5(a112),f82(x10671,x10672)),x10671)+P80(f51(x10672,f51(a16,x10671)))
% 19.29/19.55 [1072]E(f51(f5(a112),f82(x10721,x10722)),x10721)+P80(f51(x10722,f51(a16,x10721)))+~P80(f51(x10722,f6(a114)))
% 19.29/19.55 [1097]E(x10971,f6(a114))+E(x10972,f6(a114))+~E(f15(a114,x10972,x10971),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1098]E(x10981,f6(a114))+E(x10982,f6(a114))+~E(f15(a114,f6(a114),f7(a114)),f15(a114,x10982,x10981))
% 19.29/19.55 [1123]~P47(x11231)+P3(x11231,f6(x11231),f51(f5(x11231),x11232))+~P3(a114,f6(a114),x11232)
% 19.29/19.55 [1137]~P1(x11371)+~E(x11372,f6(x11371))+P80(f51(f18(a1,f28(x11371,x11372)),f6(a1)))
% 19.29/19.55 [1146]~E(x11462,f6(a114))+~E(x11461,f15(a114,f6(a114),f7(a114)))+E(f15(a114,x11461,x11462),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1147]~E(x11471,f6(a114))+~E(x11472,f15(a114,f6(a114),f7(a114)))+E(f15(a114,x11471,x11472),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1148]~E(x11482,f6(a114))+~E(x11481,f15(a114,f6(a114),f7(a114)))+E(f15(a114,f6(a114),f7(a114)),f15(a114,x11481,x11482))
% 19.29/19.55 [1149]~E(x11491,f6(a114))+~E(x11492,f15(a114,f6(a114),f7(a114)))+E(f15(a114,f6(a114),f7(a114)),f15(a114,x11491,x11492))
% 19.29/19.55 [1150]~P32(x11501)+~E(x11502,f6(x11501))+P80(f51(f18(x11501,f10(x11501,x11502)),f6(x11501)))
% 19.29/19.55 [1154]~P47(x11542)+~P3(x11542,f6(x11542),f51(f5(x11542),x11541))+P3(a114,f6(a114),x11541)
% 19.29/19.55 [1192]E(x11921,f6(a114))+E(x11921,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,x11922,x11921),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1193]E(x11931,f6(a114))+E(x11931,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,x11931,x11932),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1194]E(x11941,f6(a114))+E(x11941,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,f6(a114),f7(a114)),f15(a114,x11942,x11941))
% 19.29/19.55 [1195]E(x11951,f6(a114))+E(x11951,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,f6(a114),f7(a114)),f15(a114,x11951,x11952))
% 19.29/19.55 [1203]E(x12031,x12032)+~P80(f51(f18(a1,x12032),x12031))+~P80(f51(f18(a1,x12031),x12032))
% 19.29/19.55 [1204]E(x12041,x12042)+~P80(f51(f18(a114,x12042),x12041))+~P80(f51(f18(a114,x12041),x12042))
% 19.29/19.55 [1205]E(x12051,x12052)+~P80(f51(f18(a112,x12052),x12051))+~P80(f51(f18(a112,x12051),x12052))
% 19.29/19.55 [1210]~P3(a112,x12102,f6(a112))+~P80(f51(x12101,f51(a16,x12102)))+P80(f51(x12101,f6(a114)))
% 19.29/19.55 [1225]~P40(x12251)+P9(x12251,x12252)+P80(f51(f18(a114,f104(x12252,x12251)),f111(x12252,x12251)))
% 19.29/19.55 [1226]~P40(x12261)+P11(x12261,x12262)+P80(f51(f18(a114,f31(x12262,x12261)),f32(x12262,x12261)))
% 19.29/19.55 [1227]~P40(x12271)+P8(x12271,x12272)+P80(f51(f18(a114,f34(x12272,x12271)),f36(x12272,x12271)))
% 19.29/19.55 [1228]~P40(x12281)+P8(x12281,x12282)+P80(f51(f18(a114,f37(x12282,x12281)),f38(x12282,x12281)))
% 19.29/19.55 [1229]~P40(x12291)+P8(x12291,x12292)+P80(f51(f18(a114,f42(x12292,x12291)),f45(x12292,x12291)))
% 19.29/19.55 [1230]~P40(x12301)+P8(x12301,x12302)+P80(f51(f18(a114,f46(x12302,x12301)),f47(x12302,x12301)))
% 19.29/19.55 [1240]P3(a112,x12401,f6(a112))+~P80(f51(x12402,f82(x12401,x12402)))+P80(f51(x12402,f51(a16,x12401)))
% 19.29/19.55 [1242]~P80(f51(x12421,f82(x12422,x12421)))+P80(f51(x12421,f51(a16,x12422)))+~P80(f51(x12421,f6(a114)))
% 19.29/19.55 [1253]~P3(a112,x12532,x12531)+E(f11(a112,x12531,x12532),f6(a112))+~P80(f51(f18(a112,x12531),f6(a112)))
% 19.29/19.55 [1290]E(x12901,f15(a114,f6(a114),f7(a114)))+E(x12902,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,x12901,x12902),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1291]E(x12911,f15(a114,f6(a114),f7(a114)))+E(x12912,f15(a114,f6(a114),f7(a114)))+~E(f15(a114,f6(a114),f7(a114)),f15(a114,x12911,x12912))
% 19.29/19.55 [1300]~P3(a114,x13001,x13002)+P3(a114,f15(a114,x13001,f7(a114)),x13002)+E(f15(a114,x13001,f7(a114)),x13002)
% 19.29/19.55 [1301]~P1(x13012)+E(x13011,f6(x13012))+~P80(f51(f18(a1,f28(x13012,x13011)),f6(a1)))
% 19.29/19.55 [1311]E(x13111,x13112)+P3(a114,x13111,x13112)+~P3(a114,x13111,f15(a114,x13112,f7(a114)))
% 19.29/19.55 [1312]E(x13121,x13122)+P3(a112,x13121,x13122)+~P3(a112,x13121,f15(a112,x13122,f7(a112)))
% 19.29/19.55 [1335]~P32(x13352)+E(x13351,f6(x13352))+~P80(f51(f18(x13352,f10(x13352,x13351)),f6(x13352)))
% 19.29/19.55 [1370]P3(a114,f63(x13702,x13701),x13702)+E(x13701,f6(a114))+~P3(a114,x13701,f15(a114,x13702,f7(a114)))
% 19.29/19.55 [1375]E(x13751,f6(a114))+~P3(a114,x13751,f15(a114,x13752,f7(a114)))+E(f15(a114,f63(x13752,x13751),f7(a114)),x13751)
% 19.29/19.55 [1408]~P3(a112,f6(a112),x14082)+P3(a112,f6(a112),f11(a112,x14081,x14082))+~P80(f51(f18(a112,x14082),x14081))
% 19.29/19.55 [1415]E(x14151,x14152)+~P3(a114,x14151,f15(a114,x14152,f7(a114)))+~P80(f51(f18(a114,x14152),x14151))
% 19.29/19.55 [1462]~P3(a112,f6(a112),x14621)+~P3(a112,f6(a112),f11(a112,x14622,x14621))+P80(f51(f18(a112,x14621),x14622))
% 19.29/19.55 [1476]~P3(a112,f6(a112),x14761)+~P80(f51(f18(a112,x14761),x14762))+P80(f51(f18(a114,f51(a16,x14761)),f51(a16,x14762)))
% 19.29/19.55 [1581]~P3(a112,f6(a112),x15811)+P80(f51(f18(a112,x15811),x15812))+~P80(f51(f18(a114,f51(a16,x15811)),f51(a16,x15812)))
% 19.29/19.55 [1587]~P3(a112,x15872,f6(a112))+P80(f51(f18(a112,f6(a112)),f11(a112,x15871,x15872)))+~P80(f51(f18(a112,x15871),f6(a112)))
% 19.29/19.55 [1637]P80(f51(f18(a1,f6(a1)),f29(a1,x16371,x16372)))+~P80(f51(f18(a1,x16371),f6(a1)))+~P80(f51(f18(a1,x16372),f6(a1)))
% 19.29/19.55 [1639]P3(a114,x16391,x16392)+~P3(a114,f6(a114),x16392)+E(f15(a114,f11(a114,f13(a114,x16391,x16392),x16392),f7(a114)),f11(a114,x16391,x16392))
% 19.29/19.55 [1695]~P3(a114,f6(a114),x16952)+E(f15(a114,f11(a114,f13(a114,x16951,x16952),x16952),f7(a114)),f11(a114,x16951,x16952))+~P80(f51(f18(a114,x16952),x16951))
% 19.29/19.55 [1704]~P3(a112,x17042,f6(a112))+~P80(f51(f18(a112,f6(a112)),f11(a112,x17041,x17042)))+P80(f51(f18(a112,x17041),f6(a112)))
% 19.29/19.55 [1734]~P27(x17341)+~P80(f51(f18(x17341,x17342),f6(x17341)))+P80(f51(f18(x17341,f15(x17341,x17342,x17342)),f6(x17341)))
% 19.29/19.55 [1754]~P3(a112,f6(a112),x17542)+~P80(f51(f18(a112,x17541),f6(a112)))+P80(f51(f18(a112,f11(a112,x17541,x17542)),f6(a112)))
% 19.29/19.55 [1851]~P27(x18511)+~P80(f51(f18(x18511,f15(x18511,x18512,x18512)),f6(x18511)))+P80(f51(f18(x18511,x18512),f6(x18511)))
% 19.29/19.55 [819]~E(x8192,f7(a114))+~E(x8191,f7(a114))+E(f51(f51(f14(a114),x8191),x8192),f7(a114))
% 19.29/19.55 [885]E(x8851,f7(a114))+E(x8852,f6(a114))+~E(f51(f51(f14(a114),x8852),x8851),x8852)
% 19.29/19.55 [886]E(x8861,f6(a114))+E(x8862,f6(a114))+~E(f51(f51(f14(a114),x8862),x8861),f6(a114))
% 19.29/19.55 [943]E(x9431,f51(a16,x9432))+~E(x9431,f6(a114))+P80(f51(f18(a112,f6(a112)),x9432))
% 19.29/19.55 [944]E(f51(a16,x9441),x9442)+~E(x9442,f6(a114))+P80(f51(f18(a112,f6(a112)),x9441))
% 19.29/19.55 [945]~P6(x9452)+~P6(x9451)+P6(f51(f51(f14(a1),x9451),x9452))
% 19.29/19.55 [956]~E(x9561,f51(a16,x9562))+E(x9561,f6(a114))+P80(f51(f18(a112,f6(a112)),x9562))
% 19.29/19.55 [957]~E(f51(a16,x9572),x9571)+E(x9571,f6(a114))+P80(f51(f18(a112,f6(a112)),x9572))
% 19.29/19.55 [1045]E(x10451,f7(a112))+~P3(a112,f6(a112),x10452)+~E(f51(f51(f14(a112),x10452),x10451),f7(a112))
% 19.29/19.55 [1046]E(x10461,f7(a112))+~P3(a112,f6(a112),x10461)+~E(f51(f51(f14(a112),x10461),x10462),f7(a112))
% 19.29/19.55 [1075]~E(x10752,f51(a16,x10751))+E(x10751,f51(f5(a112),x10752))+~P80(f51(f18(a112,f6(a112)),x10751))
% 19.29/19.55 [1076]~E(f51(a16,x10761),x10762)+E(x10761,f51(f5(a112),x10762))+~P80(f51(f18(a112,f6(a112)),x10761))
% 19.29/19.55 [1077]~E(x10771,f51(a16,x10772))+E(f51(f5(a112),x10771),x10772)+~P80(f51(f18(a112,f6(a112)),x10772))
% 19.29/19.55 [1095]E(x10951,f51(a16,x10952))+~E(x10952,f51(f5(a112),x10951))+~P80(f51(f18(a112,f6(a112)),x10952))
% 19.29/19.55 [1096]E(f51(a16,x10961),x10962)+~E(x10961,f51(f5(a112),x10962))+~P80(f51(f18(a112,f6(a112)),x10961))
% 19.29/19.55 [1107]~P32(x11071)+E(f10(x11071,x11072),x11072)+~P80(f51(f18(x11071,f6(x11071)),x11072))
% 19.29/19.55 [1112]~P43(x11121)+~P75(x11121)+E(f51(f51(f20(x11121),f6(x11121)),f15(a114,x11122,f7(a114))),f6(x11121))
% 19.29/19.55 [1171]E(x11711,f6(a114))+E(x11712,f15(a114,f6(a114),f7(a114)))+~E(f51(f51(f20(a114),x11712),x11711),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1244]~P80(f51(x12441,x12442))+P80(f51(x12441,f6(a114)))+P80(f51(f18(a114,f41(x12442,x12441)),x12442))
% 19.29/19.55 [1264]~P3(a1,f6(a1),x12641)+~P3(a114,f6(a114),x12642)+E(f51(f51(f20(a1),f91(x12641,x12642)),x12642),x12641)
% 19.29/19.55 [1273]~P3(a112,x12731,x12732)+E(f11(a112,x12731,x12732),f6(a112))+~P80(f51(f18(a112,f6(a112)),x12731))
% 19.29/19.55 [1276]~P80(f51(x12761,f77(x12761)))+P80(f51(x12761,f51(a16,x12762)))+~P80(f51(f18(a112,f6(a112)),x12762))
% 19.29/19.55 [1287]E(x12871,f6(a114))+P3(a114,f6(a114),x12872)+~P3(a114,f6(a114),f51(f51(f20(a114),x12872),x12871))
% 19.29/19.55 [1288]~E(x12882,f15(a114,f6(a114),f7(a114)))+~E(x12881,f15(a114,f6(a114),f7(a114)))+E(f51(f51(f14(a114),x12881),x12882),f15(a114,f6(a114),f7(a114)))
% 19.29/19.55 [1298]P80(f51(x12981,f83(x12981)))+~P80(f51(x12981,f51(a16,x12982)))+~P80(f51(f18(a112,f6(a112)),x12982))
% 19.29/19.55 [1305]~P80(f51(x13051,x13052))+~P80(f51(f18(a112,f6(a112)),x13052))+P80(f51(x13051,f51(f5(a112),f68(x13051))))
% 19.29/19.55 [1328]~P3(a112,x13281,x13282)+P3(a114,f51(a16,x13281),f51(a16,x13282))+~P80(f51(f18(a112,f6(a112)),x13281))
% 19.29/19.55 [1333]~P3(a1,f6(a1),x13332)+~P3(a1,f6(a1),x13331)+P3(a1,f6(a1),f51(f51(f14(a1),x13331),x13332))
% 19.29/19.55 [1334]~P3(a114,f6(a114),x13342)+~P3(a114,f6(a114),x13341)+P3(a114,f6(a114),f51(f51(f14(a114),x13341),x13342))
% 19.29/19.55 [1357]P3(a114,f27(x13571),x13572)+~P3(a1,x13571,f51(f4(a114),x13572))+~P80(f51(f18(a1,f6(a1)),x13571))
% 19.29/19.55 [1376]~P3(a114,f51(a16,x13761),x13762)+P3(a112,x13761,f51(f5(a112),x13762))+~P80(f51(f18(a112,f6(a112)),x13761))
% 19.29/19.55 [1383]P3(a114,f51(a16,x13831),x13832)+~P3(a112,x13831,f51(f5(a112),x13832))+~P80(f51(f18(a112,f6(a112)),x13831))
% 19.29/19.55 [1389]P80(f51(x13891,x13892))+~P80(f51(f18(a112,f6(a112)),x13892))+~P80(f51(x13891,f51(f5(a112),f75(x13891))))
% 19.29/19.55 [1421]E(x14211,f6(a114))+~E(x14212,f6(a112))+~P3(a112,f6(a112),f51(f51(f20(a112),f10(a112,x14212)),x14211))
% 19.29/19.55 [1458]E(f13(a114,f51(a16,x14581),f51(a16,x14582)),f51(a16,f19(x14581,x14582)))+~P80(f51(f18(a112,f6(a112)),x14582))+~P80(f51(f18(a112,f6(a112)),x14581))
% 19.29/19.55 [1469]P80(f51(f18(a112,f6(a112)),f19(x14691,x14692)))+~P80(f51(f18(a112,f6(a112)),x14692))+~P80(f51(f18(a112,f6(a112)),x14691))
% 19.29/19.55 [1505]~P80(f51(f18(a1,f6(a1)),x15051))+~P80(f51(f18(a114,f17(x15051)),x15052))+P80(f51(f18(a1,x15051),f51(f4(a114),x15052)))
% 19.29/19.55 [1514]P3(a112,f6(a112),x15141)+~P3(a112,f6(a112),f11(a112,x15142,x15141))+~P80(f51(f18(a112,f6(a112)),x15142))
% 19.29/19.55 [1542]~P3(a112,f6(a112),f11(a112,x15422,x15421))+P80(f51(f18(a112,x15421),x15422))+~P80(f51(f18(a112,f6(a112)),x15422))
% 19.29/19.55 [1548]~P80(f51(f18(a112,x15481),x15482))+P80(f51(f18(a114,f51(a16,x15481)),f51(a16,x15482)))+~P80(f51(f18(a112,f6(a112)),x15482))
% 19.29/19.55 [1549]E(f13(a114,f51(a16,x15491),f51(a16,x15492)),f51(a16,f13(a112,x15491,x15492)))+~P80(f51(f18(a112,x15492),x15491))+~P80(f51(f18(a112,f6(a112)),x15492))
% 19.29/19.55 [1570]E(f15(a114,f51(a16,x15701),f51(a16,x15702)),f51(a16,f15(a112,x15701,x15702)))+~P80(f51(f18(a112,f6(a112)),x15702))+~P80(f51(f18(a112,f6(a112)),x15701))
% 19.29/19.55 [1574]~P27(x15741)+P80(f51(f18(x15741,f6(x15741)),f15(x15741,x15742,x15742)))+~P80(f51(f18(x15741,f6(x15741)),x15742))
% 19.29/19.55 [1594]~P3(a112,f6(a112),x15942)+P80(f51(f18(a112,f6(a112)),f11(a112,x15941,x15942)))+~P80(f51(f18(a112,f6(a112)),x15941))
% 19.29/19.55 [1630]P80(f51(f18(a112,x16301),x16302))+~P80(f51(f18(a114,f51(a16,x16301)),f51(a16,x16302)))+~P80(f51(f18(a112,f6(a112)),x16302))
% 19.29/19.55 [1642]P80(f51(f18(a1,f6(a1)),f29(a1,x16421,x16422)))+~P80(f51(f18(a1,x16422),f6(a1)))+~P80(f51(f18(a1,f6(a1)),x16422))
% 19.29/19.55 [1643]P80(f51(f18(a1,f6(a1)),f29(a1,x16431,x16432)))+~P80(f51(f18(a1,x16431),f6(a1)))+~P80(f51(f18(a1,f6(a1)),x16431))
% 19.29/19.55 [1656]P80(f51(f18(a1,f6(a1)),f29(a1,x16561,x16562)))+~P80(f51(f18(a1,f6(a1)),x16562))+~P80(f51(f18(a1,f6(a1)),x16561))
% 19.29/19.55 [1657]P80(f51(f18(a112,f6(a112)),f11(a112,x16571,x16572)))+~P80(f51(f18(a112,f6(a112)),x16572))+~P80(f51(f18(a112,f6(a112)),x16571))
% 19.29/19.55 [1658]P80(f51(f18(a112,f6(a112)),f15(a112,x16581,x16582)))+~P80(f51(f18(a112,f6(a112)),x16582))+~P80(f51(f18(a112,f6(a112)),x16581))
% 19.29/19.55 [1672]E(x16721,f15(a114,x16722,f7(a114)))+P80(f51(f18(a114,x16721),x16722))+~P80(f51(f18(a114,x16721),f15(a114,x16722,f7(a114))))
% 19.29/19.55 [1689]~P27(x16891)+~P80(f51(f18(x16891,f6(x16891)),f15(x16891,x16892,x16892)))+P80(f51(f18(x16891,f6(x16891)),x16892))
% 19.29/19.55 [1702]~P80(f51(f18(a1,f6(a1)),f29(a1,x17022,x17021)))+P80(f51(f18(a1,x17021),f6(a1)))+P80(f51(f18(a1,f6(a1)),x17022))
% 19.29/19.55 [1703]~P80(f51(f18(a1,f6(a1)),f29(a1,x17031,x17032)))+P80(f51(f18(a1,x17031),f6(a1)))+P80(f51(f18(a1,f6(a1)),x17032))
% 19.29/19.55 [1711]~P3(a112,f6(a112),x17112)+~P80(f51(f18(a112,f6(a112)),f11(a112,x17111,x17112)))+P80(f51(f18(a112,f6(a112)),x17111))
% 19.29/19.55 [1731]~P3(a114,f15(a114,f6(a114),f7(a114)),x17312)+~P3(a114,f15(a114,f6(a114),f7(a114)),x17311)+P3(a114,x17311,f51(f51(f14(a114),x17312),x17311))
% 19.29/19.55 [1732]~P3(a114,f15(a114,f6(a114),f7(a114)),x17322)+~P3(a114,f15(a114,f6(a114),f7(a114)),x17321)+P3(a114,x17321,f51(f51(f14(a114),x17321),x17322))
% 19.29/19.55 [1759]~P3(a112,x17592,f6(a112))+P80(f51(f18(a112,f11(a112,x17591,x17592)),f6(a112)))+~P80(f51(f18(a112,f6(a112)),x17591))
% 19.29/19.55 [1777]~P3(a114,f15(a114,f6(a114),f7(a114)),x17771)+~P3(a114,f15(a114,f6(a114),f7(a114)),x17772)+P3(a114,f15(a114,f6(a114),f7(a114)),f51(f51(f14(a114),x17771),x17772))
% 19.29/19.55 [1823]~P3(a1,f51(f4(a114),x18232),x18231)+E(f17(x18231),f15(a114,x18232,f7(a114)))+~P80(f51(f18(a1,x18231),f15(a1,f51(f4(a114),x18232),f7(a1))))
% 19.29/19.55 [1832]~P40(x18321)+P9(x18321,x18322)+~P80(f51(f18(x18321,f51(x18322,f111(x18322,x18321))),f51(x18322,f104(x18322,x18321))))
% 19.29/19.55 [1833]~P40(x18331)+P11(x18331,x18332)+~P80(f51(f18(x18331,f51(x18332,f31(x18332,x18331))),f51(x18332,f32(x18332,x18331))))
% 19.29/19.55 [1834]~P40(x18341)+P8(x18341,x18342)+~P80(f51(f18(x18341,f51(x18342,f34(x18342,x18341))),f51(x18342,f36(x18342,x18341))))
% 19.29/19.55 [1835]~P40(x18351)+P8(x18351,x18352)+~P80(f51(f18(x18351,f51(x18352,f38(x18352,x18351))),f51(x18352,f37(x18352,x18351))))
% 19.29/19.55 [1836]~P40(x18361)+P8(x18361,x18362)+~P80(f51(f18(x18361,f51(x18362,f45(x18362,x18361))),f51(x18362,f42(x18362,x18361))))
% 19.29/19.55 [1837]~P40(x18371)+P8(x18371,x18372)+~P80(f51(f18(x18371,f51(x18372,f46(x18372,x18371))),f51(x18372,f47(x18372,x18371))))
% 19.29/19.55 [2015]~P40(x20151)+P8(x20151,x20152)+~P80(f51(f18(x20151,f51(x20152,f15(a114,f72(x20152,x20151),f7(a114)))),f51(x20152,f72(x20152,x20151))))
% 19.29/19.55 [1217]~E(x12172,f6(a1))+~E(x12171,f6(a1))+E(f15(a1,f51(f51(f14(a1),x12171),x12171),f51(f51(f14(a1),x12172),x12172)),f6(a1))
% 19.29/19.55 [1534]~P3(a114,f6(a114),x15342)+E(f27(f29(a1,x15341,f51(f4(a114),x15342))),f11(a114,f27(x15341),x15342))+~P80(f51(f18(a1,f7(a1)),x15341))
% 19.29/19.55 [1553]~P80(f51(f18(a114,x15531),f27(x15532)))+~P80(f51(f18(a1,f6(a1)),x15532))+P80(f51(f18(a1,f51(f4(a114),x15531)),x15532))
% 19.29/19.55 [1626]~P80(f51(f18(a112,f6(a112)),x16262))+~P80(f51(f18(a112,f6(a112)),x16261))+P80(f51(f18(a112,f6(a112)),f51(f51(f14(a112),x16261),x16262)))
% 19.29/19.55 [1741]E(f27(x17411),x17412)+~P3(a1,x17411,f15(a1,f51(f4(a114),x17412),f7(a1)))+~P80(f51(f18(a1,f51(f4(a114),x17412)),x17411))
% 19.29/19.55 [1750]~P3(a114,f6(a114),x17502)+~P3(a112,f6(a112),x17501)+E(f11(a112,f51(f51(f20(a112),x17501),x17502),x17501),f51(f51(f20(a112),x17501),f13(a114,x17502,f15(a114,f6(a114),f7(a114)))))
% 19.29/19.55 [1761]~P3(a1,f6(a1),x17612)+P3(a1,f28(a2,f13(a2,f117(f51(a3,x17611)),a70)),x17612)+~P80(f51(f18(a114,f79(x17612)),x17611))
% 19.29/19.55 [1982]~P40(x19821)+P11(x19821,x19822)+~P80(f51(f18(x19821,f51(x19822,f80(x19822,x19821))),f51(x19822,f15(a114,f80(x19822,x19821),f7(a114)))))
% 19.29/19.55 [1983]~P40(x19831)+P8(x19831,x19832)+~P80(f51(f18(x19831,f51(x19832,f71(x19832,x19831))),f51(x19832,f15(a114,f71(x19832,x19831),f7(a114)))))
% 19.29/19.55 [2012]~P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),x20121))+~P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),x20122))+P80(f51(f18(a114,f15(a114,f6(a114),f7(a114))),f51(f51(f14(a114),x20121),x20122)))
% 19.29/19.55 [1921]~P80(f51(f18(a1,f6(a1)),x19212))+~P80(f51(f18(a1,f6(a1)),x19211))+P80(f51(f18(a114,f51(f51(f14(a114),f27(x19211)),f27(x19212))),f27(f51(f51(f14(a1),x19211),x19212))))
% 19.29/19.55 [1985]~P3(a1,f6(a1),x19852)+P3(a1,x19851,f51(f51(f14(a1),f51(f4(a114),f15(a114,f85(x19851,x19852),f7(a114)))),x19852))+~P80(f51(f18(a1,f6(a1)),x19851))
% 19.29/19.55 [2001]~P3(a1,f6(a1),x20012)+~P80(f51(f18(a1,f6(a1)),x20011))+P80(f51(f18(a1,f51(f51(f14(a1),f51(f4(a114),f85(x20011,x20012))),x20012)),x20011))
% 19.29/19.55 [2005]E(x20051,f6(a114))+E(x20052,f6(a2))+P3(a1,f28(a2,f15(a2,f7(a2),f51(f51(f14(a2),x20052),f51(f51(f20(a2),f103(x20051,x20052)),x20051)))),f7(a1))
% 19.29/19.55 [924]~P3(x9243,x9241,x9242)+~E(x9241,x9242)+~P37(x9243)
% 19.29/19.55 [925]~P3(x9253,x9251,x9252)+~E(x9251,x9252)+~P40(x9253)
% 19.29/19.55 [1082]~P3(x10821,x10823,x10822)+~P30(x10821)+~P3(x10821,x10822,x10823)
% 19.29/19.55 [1083]~P3(x10831,x10833,x10832)+~P37(x10831)+~P3(x10831,x10832,x10833)
% 19.29/19.55 [1084]~P3(x10841,x10843,x10842)+~P40(x10841)+~P3(x10841,x10842,x10843)
% 19.29/19.55 [840]~E(x8402,x8403)+~P13(x8401)+E(f13(x8401,x8402,x8403),f6(x8401))
% 19.29/19.55 [841]~E(x8412,x8413)+~P18(x8411)+E(f13(x8411,x8412,x8413),f6(x8411))
% 19.29/19.55 [852]~P79(x8521)+~E(x8523,f6(x8521))+E(f15(x8521,x8522,x8523),x8522)
% 19.29/19.55 [932]~P79(x9322)+~E(f15(x9322,x9323,x9321),x9323)+E(x9321,f6(x9322))
% 19.29/19.55 [934]~P13(x9343)+E(x9341,x9342)+~E(f13(x9343,x9341,x9342),f6(x9343))
% 19.29/19.55 [935]~P18(x9353)+E(x9351,x9352)+~E(f13(x9353,x9351,x9352),f6(x9353))
% 19.29/19.55 [1128]~P2(x11281)+~P3(a114,x11282,x11283)+P3(a114,f51(x11281,x11282),f51(x11281,x11283))
% 19.29/19.55 [1238]~P12(x12381)+~P3(x12381,x12382,x12383)+P3(x12381,f13(x12381,x12382,x12383),f6(x12381))
% 19.29/19.55 [1337]~P12(x13371)+P3(x13371,x13372,x13373)+~P3(x13371,f13(x13371,x13372,x13373),f6(x13371))
% 19.29/19.55 [1348]~P3(a1,x13483,x13482)+~P3(a1,x13482,x13481)+P3(a1,f6(a1),f57(x13481,x13482,x13483))
% 19.29/19.55 [1349]~P3(a1,x13493,x13492)+~P3(a1,x13492,x13491)+P3(a1,f6(a1),f78(x13491,x13492,x13493))
% 19.29/19.55 [1490]~P3(a114,x14903,x14901)+~P3(a114,x14903,x14902)+P3(a114,f13(a114,x14901,x14902),f13(a114,x14901,x14903))
% 19.29/19.55 [863]~P38(x8633)+E(x8631,x8632)+~E(f51(f5(x8633),x8631),f51(f5(x8633),x8632))
% 19.29/19.55 [913]~E(x9132,x9133)+~P30(x9131)+P80(f51(f18(x9131,x9132),x9133))
% 19.29/19.55 [915]~E(x9152,x9153)+~P40(x9151)+P80(f51(f18(x9151,x9152),x9153))
% 19.29/19.55 [930]~P50(x9301)+~E(f22(x9301,x9302),f6(a114))+E(f23(x9301,x9302,x9303),f6(f115(x9301)))
% 19.29/19.55 [972]~P50(x9721)+E(f22(x9721,x9722),f6(a114))+~E(f23(x9721,x9722,x9723),f6(f115(x9721)))
% 19.29/19.55 [976]~P81(x9761,x9762,x9763)+~E(x9762,f6(a112))+P80(f51(x9761,f6(a112)))
% 19.29/19.55 [994]~P37(x9941)+P3(x9941,x9942,x9943)+P80(f51(f18(x9941,x9943),x9942))
% 19.29/19.55 [1053]~P37(x10531)+P80(f51(f18(x10531,x10533),x10532))+P80(f51(f18(x10531,x10532),x10533))
% 19.29/19.55 [1064]~P30(x10641)+~P3(x10641,x10642,x10643)+P80(f51(f18(x10641,x10642),x10643))
% 19.29/19.55 [1066]~P40(x10661)+~P3(x10661,x10662,x10663)+P80(f51(f18(x10661,x10662),x10663))
% 19.29/19.55 [1078]P80(f51(x10781,x10782))+~E(x10783,f51(f5(a112),x10782))+~P80(f51(x10781,f51(a16,x10783)))
% 19.29/19.55 [1158]~P47(x11581)+~P3(a114,x11582,x11583)+P3(x11581,f51(f5(x11581),x11582),f51(f5(x11581),x11583))
% 19.29/19.55 [1159]~P30(x11591)+~P3(x11591,x11592,x11593)+~P80(f51(f18(x11591,x11593),x11592))
% 19.29/19.55 [1162]~P37(x11621)+~P3(x11621,x11622,x11623)+~P80(f51(f18(x11621,x11623),x11622))
% 19.29/19.55 [1189]~P46(x11892)+E(x11891,f6(x11892))+E(f29(a1,f28(x11892,x11893),f28(x11892,x11891)),f28(x11892,f29(x11892,x11893,x11891)))
% 19.29/19.55 [1191]~P46(x11911)+~P16(x11911)+E(f29(a1,f28(x11911,x11912),f28(x11911,x11913)),f28(x11911,f29(x11911,x11912,x11913)))
% 19.29/19.55 [1206]~P15(x12061)+~P3(a114,f22(x12061,x12062),f22(x12061,x12063))+E(f11(f115(x12061),x12062,x12063),f6(f115(x12061)))
% 19.29/19.55 [1235]~E(f13(a114,x12351,x12353),x12352)+E(x12351,f15(a114,x12352,x12353))+~P80(f51(f18(a114,x12353),x12351))
% 19.29/19.55 [1236]~E(x12361,f15(a114,x12363,x12362))+E(f13(a114,x12361,x12362),x12363)+~P80(f51(f18(a114,x12362),x12361))
% 19.29/19.55 [1247]~P47(x12473)+P3(a114,x12471,x12472)+~P3(x12473,f51(f5(x12473),x12471),f51(f5(x12473),x12472))
% 19.29/19.55 [1292]~P2(x12922)+P82(a500)+P80(f51(f18(a114,x12921),f106(x12922,x12923,x12921)))
% 19.29/19.55 [1297]~E(x12973,f6(a114))+P80(f51(x12971,f11(a114,x12972,x12973)))+~P80(f51(x12971,f6(a114)))
% 19.29/19.55 [1315]~P80(f51(f18(a1,x13151),x13153))+P80(f51(f18(a1,x13151),x13152))+~P80(f51(f18(a1,x13153),x13152))
% 19.29/19.55 [1316]~P80(f51(f18(a114,x13161),x13163))+P80(f51(f18(a114,x13161),x13162))+~P80(f51(f18(a114,x13163),x13162))
% 19.29/19.55 [1317]~P80(f51(f18(a112,x13171),x13173))+P80(f51(f18(a112,x13171),x13172))+~P80(f51(f18(a112,x13173),x13172))
% 19.29/19.55 [1350]~P3(a114,x13501,x13503)+~P3(a114,x13503,x13502)+P3(a114,f15(a114,x13501,f7(a114)),x13502)
% 19.29/19.55 [1365]~P3(a114,x13653,x13652)+P3(a114,x13651,f15(a114,x13652,f7(a114)))+~E(x13651,f15(a114,x13653,f7(a114)))
% 19.29/19.55 [1373]~P14(x13732)+E(x13731,f6(x13732))+E(f11(x13732,f15(x13732,x13733,x13731),x13731),f15(x13732,f11(x13732,x13733,x13731),f7(x13732)))
% 19.29/19.55 [1374]~P14(x13742)+E(x13741,f6(x13742))+E(f11(x13742,f15(x13742,x13741,x13743),x13741),f15(x13742,f11(x13742,x13743,x13741),f7(x13742)))
% 19.29/19.55 [1437]P3(a114,f98(x14371,x14372,x14373),x14371)+E(x14371,f6(a114))+P80(f51(x14373,f11(a114,x14372,x14371)))
% 19.29/19.55 [1461]~E(x14612,f6(a114))+~P80(f51(x14611,f11(a114,x14613,x14612)))+P80(f51(x14611,f6(a114)))
% 19.29/19.55 [1527]P3(a114,x15272,x15271)+E(f15(a114,x15271,f99(x15271,x15272,x15273)),x15272)+P80(f51(x15273,f13(a114,x15272,x15271)))
% 19.29/19.55 [1528]P3(a114,x15282,x15281)+E(f15(a114,x15281,f100(x15281,x15282,x15283)),x15282)+P80(f51(x15283,f13(a114,x15282,x15281)))
% 19.29/19.55 [1531]P3(a114,f98(x15311,x15312,x15313),x15311)+P80(f51(x15313,f11(a114,x15312,x15311)))+~P80(f51(x15313,f6(a114)))
% 19.29/19.55 [1532]E(f15(a114,x15321,f99(x15321,x15322,x15323)),x15322)+P80(f51(x15323,f13(a114,x15322,x15321)))+~P80(f51(x15323,f6(a114)))
% 19.29/19.55 [1533]E(f15(a114,x15331,f100(x15331,x15332,x15333)),x15332)+P80(f51(x15333,f13(a114,x15332,x15331)))+~P80(f51(x15333,f6(a114)))
% 19.29/19.55 [1539]~P3(a114,x15391,x15393)+P3(a114,f13(a114,x15391,x15392),f13(a114,x15393,x15392))+~P80(f51(f18(a114,x15392),x15391))
% 19.29/19.55 [1544]~P1(x15441)+~P10(x15441,x15442)+P80(f51(f18(a1,f28(x15441,f51(x15442,x15443))),f30(x15442,x15441)))
% 19.29/19.55 [1545]~P1(x15451)+~P10(x15451,x15452)+P80(f51(f18(a1,f28(x15451,f51(x15452,x15453))),f33(x15452,x15451)))
% 19.29/19.55 [1573]~P3(a114,x15732,x15733)+~P80(f51(x15731,f13(a114,x15732,x15733)))+P80(f51(x15731,f6(a114)))
% 19.29/19.55 [1635]E(f13(a114,f13(a114,x16351,x16352),f13(a114,x16353,x16352)),f13(a114,x16351,x16353))+~P80(f51(f18(a114,x16352),x16351))+~P80(f51(f18(a114,x16352),x16353))
% 19.29/19.55 [1655]~P49(x16552)+E(x16551,f6(f115(x16552)))+P80(f51(f18(a114,f25(x16552,x16553,x16551)),f22(x16552,x16551)))
% 19.29/19.55 [1690]E(x16901,f6(a114))+P80(f51(x16902,f84(x16901,x16903,x16902)))+~P80(f51(x16902,f11(a114,x16903,x16901)))
% 19.29/19.55 [1694]E(x16941,f6(a114))+~P80(f51(x16942,f101(x16941,x16943,x16942)))+P80(f51(x16942,f11(a114,x16943,x16941)))
% 19.29/19.55 [1719]P80(f51(x17191,f84(x17192,x17193,x17191)))+~P80(f51(x17191,f11(a114,x17193,x17192)))+P80(f51(x17191,f6(a114)))
% 19.29/19.55 [1723]~P12(x17231)+~P80(f51(f18(x17231,x17232),x17233))+P80(f51(f18(x17231,f13(x17231,x17232,x17233)),f6(x17231)))
% 19.29/19.55 [1729]P3(a114,x17291,x17292)+~P80(f51(x17293,f99(x17292,x17291,x17293)))+P80(f51(x17293,f13(a114,x17291,x17292)))
% 19.29/19.55 [1730]P3(a114,x17301,x17302)+~P80(f51(x17303,f100(x17302,x17301,x17303)))+P80(f51(x17303,f13(a114,x17301,x17302)))
% 19.29/19.55 [1736]~P80(f51(x17361,f99(x17363,x17362,x17361)))+P80(f51(x17361,f13(a114,x17362,x17363)))+~P80(f51(x17361,f6(a114)))
% 19.29/19.55 [1737]~P80(f51(x17371,f100(x17373,x17372,x17371)))+P80(f51(x17371,f13(a114,x17372,x17373)))+~P80(f51(x17371,f6(a114)))
% 19.29/19.55 [1738]~P80(f51(x17381,f101(x17383,x17382,x17381)))+P80(f51(x17381,f11(a114,x17382,x17383)))+~P80(f51(x17381,f6(a114)))
% 19.29/19.55 [1753]E(x17531,f6(a114))+E(f15(a114,f51(f51(f14(a114),x17531),f101(x17531,x17532,x17533)),f98(x17531,x17532,x17533)),x17532)+P80(f51(x17533,f11(a114,x17532,x17531)))
% 19.29/19.55 [1774]E(f15(a114,f51(f51(f14(a114),x17741),f101(x17741,x17742,x17743)),f98(x17741,x17742,x17743)),x17742)+P80(f51(x17743,f11(a114,x17742,x17741)))+~P80(f51(x17743,f6(a114)))
% 19.29/19.55 [1841]~P3(a112,x18412,f6(a112))+~P80(f51(f18(a112,x18413),x18411))+P80(f51(f18(a112,f11(a112,x18411,x18412)),f11(a112,x18413,x18412)))
% 19.29/19.55 [1842]~P3(a114,f6(a114),x18423)+~P80(f51(f18(a114,x18423),x18422))+P80(f51(f18(a114,f11(a114,x18421,x18422)),f11(a114,x18421,x18423)))
% 19.29/19.55 [1843]~P3(a112,f6(a112),x18432)+~P80(f51(f18(a112,x18431),x18433))+P80(f51(f18(a112,f11(a112,x18431,x18432)),f11(a112,x18433,x18432)))
% 19.29/19.55 [1844]~P12(x18441)+~P80(f51(f18(x18441,f13(x18441,x18442,x18443)),f6(x18441)))+P80(f51(f18(x18441,x18442),x18443))
% 19.29/19.55 [2026]~P59(x20262)+E(x20261,f6(x20262))+~P80(f51(f18(x20262,f15(x20262,f51(f51(f14(x20262),x20263),x20263),f51(f51(f14(x20262),x20261),x20261))),f6(x20262)))
% 19.29/19.55 [2027]~P59(x20272)+E(x20271,f6(x20272))+~P80(f51(f18(x20272,f15(x20272,f51(f51(f14(x20272),x20271),x20271),f51(f51(f14(x20272),x20273),x20273))),f6(x20272)))
% 19.29/19.55 [842]~P43(x8421)+~E(x8423,f6(a114))+E(f51(f51(f20(x8421),x8422),x8423),f7(x8421))
% 19.29/19.55 [858]~P76(x8581)+~E(x8583,f6(x8581))+E(f51(f51(f14(x8581),x8582),x8583),f6(x8581))
% 19.29/19.55 [859]~P76(x8591)+~E(x8592,f6(x8591))+E(f51(f51(f14(x8591),x8592),x8593),f6(x8591))
% 19.29/19.55 [933]~P60(x9332)+E(x9331,f6(x9332))+~E(f51(f51(f20(x9332),x9331),x9333),f6(x9332))
% 19.29/19.55 [1005]E(x10051,x10052)+E(x10053,f6(a1))+~E(f51(f51(f14(a1),x10053),x10051),f51(f51(f14(a1),x10053),x10052))
% 19.29/19.55 [1007]E(x10071,x10072)+E(x10073,f6(a114))+~E(f51(f51(f14(a114),x10073),x10071),f51(f51(f14(a114),x10073),x10072))
% 19.29/19.55 [1008]E(x10081,x10082)+E(x10083,f6(a1))+~E(f51(f51(f14(a1),x10081),x10083),f51(f51(f14(a1),x10082),x10083))
% 19.29/19.55 [1009]E(x10091,x10092)+E(x10093,f6(a114))+~E(f51(f51(f14(a114),x10091),x10093),f51(f51(f14(a114),x10092),x10093))
% 19.29/19.55 [1182]E(x11821,x11822)+~P3(a114,f6(a114),x11823)+~E(f51(f51(f14(a114),x11823),x11821),f51(f51(f14(a114),x11823),x11822))
% 19.29/19.55 [1245]~P47(x12451)+~P3(x12451,f6(x12451),x12452)+P3(x12451,f6(x12451),f51(f51(f20(x12451),x12452),x12453))
% 19.29/19.55 [1320]~P22(x13201)+~P3(a114,f22(x13201,x13203),f22(x13201,x13202))+E(f22(x13201,f15(f115(x13201),x13202,x13203)),f22(x13201,x13202))
% 19.29/19.55 [1321]~P22(x13211)+~P3(a114,f22(x13211,x13212),f22(x13211,x13213))+E(f22(x13211,f15(f115(x13211),x13212,x13213)),f22(x13211,x13213))
% 19.29/19.55 [1419]~P67(x14191)+E(f13(x14191,f51(f5(x14191),x14192),f51(f5(x14191),x14193)),f51(f5(x14191),f13(a114,x14192,x14193)))+~P80(f51(f18(a114,x14193),x14192))
% 19.29/19.55 [1420]~P32(x14201)+P80(f51(f18(x14201,x14202),x14203))+~P80(f51(f18(x14201,f10(x14201,x14202)),x14203))
% 19.29/19.55 [1445]~P3(a1,x14451,x14453)+~P3(a1,f6(a1),x14452)+P3(a1,f51(f51(f14(a1),x14451),x14452),f51(f51(f14(a1),x14453),x14452))
% 19.29/19.55 [1446]~P3(a1,x14462,x14463)+~P3(a1,f6(a1),x14461)+P3(a1,f51(f51(f14(a1),x14461),x14462),f51(f51(f14(a1),x14461),x14463))
% 19.29/19.55 [1450]~P3(a114,x14501,x14503)+~P3(a114,f6(a114),x14502)+P3(a114,f51(f51(f14(a114),x14501),x14502),f51(f51(f14(a114),x14503),x14502))
% 19.29/19.55 [1451]~P3(a114,x14512,x14513)+~P3(a114,f6(a114),x14511)+P3(a114,f51(f51(f14(a114),x14511),x14512),f51(f51(f14(a114),x14511),x14513))
% 19.29/19.55 [1452]~P3(a112,x14522,x14523)+~P3(a112,f6(a112),x14521)+P3(a112,f51(f51(f14(a112),x14521),x14522),f51(f51(f14(a112),x14521),x14523))
% 19.29/19.55 [1506]~P47(x15061)+~P80(f51(f18(a114,x15062),x15063))+P80(f51(f18(x15061,f51(f5(x15061),x15062)),f51(f5(x15061),x15063)))
% 19.29/19.55 [1559]~P47(x15591)+~P3(x15591,f7(x15591),x15592)+P3(x15591,f7(x15591),f51(f51(f20(x15591),x15592),f15(a114,x15593,f7(a114))))
% 19.29/19.55 [1583]P3(a1,x15831,x15832)+~P3(a1,f6(a1),x15833)+~P3(a1,f51(f51(f14(a1),x15831),x15833),f51(f51(f14(a1),x15832),x15833))
% 19.29/19.55 [1584]P3(a114,x15841,x15842)+~P3(a114,f6(a114),x15843)+~P3(a114,f51(f51(f20(a114),x15843),x15841),f51(f51(f20(a114),x15843),x15842))
% 19.29/19.55 [1588]~P1(x15881)+~P10(x15881,x15882)+P3(a1,f28(x15881,f51(x15882,x15883)),f51(f4(a114),f15(a114,f64(x15882,x15881),f7(a114))))
% 19.29/19.55 [1616]~E(x16163,f11(a114,x16161,x16162))+~P3(a114,f6(a114),x16162)+P3(a114,x16161,f51(f51(f14(a114),x16162),f15(a114,x16163,f7(a114))))
% 19.29/19.55 [1650]~P47(x16503)+P80(f51(f18(a114,x16501),x16502))+~P80(f51(f18(x16503,f51(f5(x16503),x16501)),f51(f5(x16503),x16502)))
% 19.29/19.55 [1710]P3(a114,x17101,x17102)+P80(f51(f18(a114,x17102),x17101))+P80(f51(x17103,f51(f5(a112),f13(a114,x17101,x17102))))
% 19.29/19.55 [1712]P80(f51(f18(a114,x17121),x17122))+~P80(f51(x17123,f6(a112)))+P80(f51(x17123,f51(f5(a112),f13(a114,x17122,x17121))))
% 19.29/19.55 [1788]E(x17881,f6(a1))+~P80(f51(f18(a1,x17882),f6(a1)))+~P80(f51(f18(a1,f10(a1,x17881)),f51(f51(f14(a1),x17882),f10(a1,x17883))))
% 19.29/19.55 [1850]~P3(a114,x18502,x18503)+P80(f51(x18501,f6(a112)))+~P80(f51(x18501,f51(f5(a112),f13(a114,x18502,x18503))))
% 19.29/19.55 [1886]~P80(f51(f18(a114,x18862),x18863))+~P80(f51(f18(a114,x18861),f13(a114,x18863,x18862)))+P80(f51(f18(a114,f15(a114,x18861,x18862)),x18863))
% 19.29/19.55 [1907]E(x19071,f6(a114))+P3(a114,x19072,f51(f51(f14(a114),x19071),f15(a114,f84(x19071,x19072,x19073),f7(a114))))+~P80(f51(x19073,f11(a114,x19072,x19071)))
% 19.29/19.55 [1911]~P80(f51(f18(a114,x19113),x19112))+P80(f51(f18(a114,x19111),f13(a114,x19112,x19113)))+~P80(f51(f18(a114,f15(a114,x19111,x19113)),x19112))
% 19.29/19.55 [1915]P3(a114,x19152,f51(f51(f14(a114),x19153),f15(a114,f84(x19153,x19152,x19151),f7(a114))))+~P80(f51(x19151,f11(a114,x19152,x19153)))+P80(f51(x19151,f6(a114)))
% 19.29/19.55 [1938]~P1(x19381)+P10(x19381,x19382)+~P3(a1,f28(x19381,f51(x19382,f65(x19382,x19381,x19383))),f51(f4(a114),f15(a114,x19383,f7(a114))))
% 19.29/19.55 [1944]~P1(x19442)+P3(a1,f6(a1),f58(x19441,x19442))+~P3(a1,f28(x19442,f51(x19441,f48(x19441,x19442,x19443))),f51(f4(a114),f15(a114,x19443,f7(a114))))
% 19.29/19.55 [1049]~P14(x10492)+E(x10491,f6(x10492))+E(f11(x10492,f51(f51(f14(x10492),x10493),x10491),x10491),x10493)
% 19.29/19.55 [1050]~P14(x10502)+E(x10501,f6(x10502))+E(f11(x10502,f51(f51(f14(x10502),x10501),x10503),x10501),x10503)
% 19.29/19.55 [1433]~P48(x14331)+E(f51(f51(f14(x14331),f10(x14331,x14332)),x14333),f10(x14331,f51(f51(f14(x14331),x14332),x14333)))+~P80(f51(f18(x14331,f6(x14331)),x14333))
% 19.29/19.55 [1487]~P59(x14872)+E(x14871,f6(x14872))+~E(f15(x14872,f51(f51(f14(x14872),x14873),x14873),f51(f51(f14(x14872),x14871),x14871)),f6(x14872))
% 19.29/19.55 [1488]~P59(x14882)+E(x14881,f6(x14882))+~E(f15(x14882,f51(f51(f14(x14882),x14881),x14881),f51(f51(f14(x14882),x14883),x14883)),f6(x14882))
% 19.29/19.55 [1504]~P43(x15042)+E(x15041,f6(a114))+E(f51(f51(f14(x15042),x15043),f51(f51(f20(x15042),x15043),f13(a114,x15041,f7(a114)))),f51(f51(f20(x15042),x15043),x15041))
% 19.29/19.55 [1546]~P47(x15461)+~P3(x15461,f7(x15461),x15462)+P3(x15461,f7(x15461),f51(f51(f14(x15461),x15462),f51(f51(f20(x15461),x15462),x15463)))
% 19.29/19.55 [1560]~P47(x15601)+~P80(f51(f18(x15601,f6(x15601)),x15602))+P80(f51(f18(x15601,f6(x15601)),f51(f51(f20(x15601),x15602),x15603)))
% 19.29/19.55 [1561]~P47(x15611)+~P80(f51(f18(x15611,f7(x15611)),x15612))+P80(f51(f18(x15611,f7(x15611)),f51(f51(f20(x15611),x15612),x15613)))
% 19.29/19.55 [1647]~P47(x16471)+~P3(x16471,f7(x16471),x16472)+P3(x16471,f51(f51(f20(x16471),x16472),x16473),f51(f51(f14(x16471),x16472),f51(f51(f20(x16471),x16472),x16473)))
% 19.29/19.55 [1665]~P59(x16652)+E(x16651,f6(x16652))+P3(x16652,f6(x16652),f15(x16652,f51(f51(f14(x16652),x16653),x16653),f51(f51(f14(x16652),x16651),x16651)))
% 19.29/19.55 [1666]~P59(x16662)+E(x16661,f6(x16662))+P3(x16662,f6(x16662),f15(x16662,f51(f51(f14(x16662),x16661),x16661),f51(f51(f14(x16662),x16663),x16663)))
% 19.29/19.55 [1724]~P3(a112,x17242,x17243)+~P3(a114,f6(a114),x17241)+P3(a112,f51(f51(f14(a112),f51(f5(a112),x17241)),x17242),f51(f51(f14(a112),f51(f5(a112),x17241)),x17243))
% 19.29/19.55 [1789]~P3(a1,f6(a1),x17891)+~P80(f51(f18(a1,x17892),x17893))+P80(f51(f18(a1,f51(f51(f14(a1),x17891),x17892)),f51(f51(f14(a1),x17891),x17893)))
% 19.29/19.55 [1790]~P3(a1,f6(a1),x17902)+~P80(f51(f18(a1,x17901),x17903))+P80(f51(f18(a1,f51(f51(f14(a1),x17901),x17902)),f51(f51(f14(a1),x17903),x17902)))
% 19.29/19.55 [1896]~P1(x18961)+~P10(x18961,x18962)+P80(f51(f18(a1,f28(x18961,f51(x18962,x18963))),f51(f4(a114),f15(a114,f73(x18962,x18961),f7(a114)))))
% 19.29/19.55 [1899]~P3(a1,f6(a1),x18993)+P80(f51(f18(a1,x18991),x18992))+~P80(f51(f18(a1,f51(f51(f14(a1),x18993),x18991)),f51(f51(f14(a1),x18993),x18992)))
% 19.29/19.55 [1900]~P3(a1,f6(a1),x19003)+P80(f51(f18(a1,x19001),x19002))+~P80(f51(f18(a1,f51(f51(f14(a1),x19001),x19003)),f51(f51(f14(a1),x19002),x19003)))
% 19.29/19.55 [1902]~P3(a114,f6(a114),x19023)+P80(f51(f18(a114,x19021),x19022))+~P80(f51(f18(a114,f51(f51(f14(a114),x19023),x19021)),f51(f51(f14(a114),x19023),x19022)))
% 19.29/19.55 [1903]~P3(a114,f6(a114),x19033)+P80(f51(f18(a114,x19031),x19032))+~P80(f51(f18(a114,f51(f51(f14(a114),x19031),x19033)),f51(f51(f14(a114),x19032),x19033)))
% 19.29/19.55 [1942]P3(a114,x19421,x19422)+P80(f51(x19423,f51(f5(a112),f13(a114,x19421,x19422))))+~P80(f51(x19423,f13(a112,f51(f5(a112),x19421),f51(f5(a112),x19422))))
% 19.29/19.55 [1943]~P80(f51(x19431,f6(a112)))+P80(f51(x19431,f51(f5(a112),f13(a114,x19432,x19433))))+~P80(f51(x19431,f13(a112,f51(f5(a112),x19432),f51(f5(a112),x19433))))
% 19.29/19.55 [1953]~P80(f51(f18(a114,x19533),x19532))+~P80(f51(x19531,f51(f5(a112),f13(a114,x19532,x19533))))+P80(f51(x19531,f13(a112,f51(f5(a112),x19532),f51(f5(a112),x19533))))
% 19.29/19.55 [1971]E(x19711,f6(a114))+~P80(f51(x19713,f11(a114,x19712,x19711)))+P80(f51(f18(a114,f51(f51(f14(a114),x19711),f84(x19711,x19712,x19713))),x19712))
% 19.29/19.55 [1976]~P80(f51(x19761,f11(a114,x19763,x19762)))+P80(f51(x19761,f6(a114)))+P80(f51(f18(a114,f51(f51(f14(a114),x19762),f84(x19762,x19763,x19761))),x19763))
% 19.29/19.55 [2038]~P1(x20381)+P10(x20381,x20382)+~P80(f51(f18(a1,f28(x20381,f51(x20382,f74(x20382,x20381,x20383)))),f51(f4(a114),f15(a114,x20383,f7(a114)))))
% 19.29/19.55 [2039]~P1(x20392)+P3(a1,f6(a1),f59(x20391,x20392))+~P80(f51(f18(a1,f28(x20392,f51(x20391,f60(x20391,x20392,x20393)))),f51(f4(a114),f15(a114,x20393,f7(a114)))))
% 19.29/19.55 [1683]~E(x16832,f11(a114,x16833,x16831))+~P3(a114,f6(a114),x16831)+P80(f51(f18(a114,f51(f51(f14(a114),x16831),x16832)),x16833))
% 19.29/19.55 [1807]~P26(x18071)+~P3(a114,f6(a114),x18073)+E(f51(f51(f14(x18071),f51(f51(f20(x18071),x18072),f13(a114,x18073,f7(a114)))),x18072),f51(f51(f20(x18071),x18072),x18073))
% 19.29/19.55 [2024]~P1(x20241)+P10(x20241,x20242)+~P80(f51(f18(a1,f28(x20241,f51(x20242,f44(x20243,x20242,x20241)))),x20243))
% 19.29/19.55 [2032]~P2(x20321)+P82(a500)+~P3(a1,f28(a2,f13(a2,f117(f51(x20321,f106(x20321,x20322,x20323))),x20322)),f96(x20321,x20322))
% 19.29/19.55 [1089]~P23(x10893)+E(x10891,x10892)+~E(f15(x10893,x10894,x10891),f15(x10893,x10894,x10892))
% 19.29/19.55 [1090]~P24(x10903)+E(x10901,x10902)+~E(f15(x10903,x10904,x10901),f15(x10903,x10904,x10902))
% 19.29/19.55 [1092]~P23(x10923)+E(x10921,x10922)+~E(f15(x10923,x10921,x10924),f15(x10923,x10922,x10924))
% 19.29/19.55 [1299]~P3(a114,x12993,x12994)+P3(a114,x12991,x12992)+~E(f15(a114,x12993,x12992),f15(a114,x12991,x12994))
% 19.29/19.55 [1395]~P33(x13951)+~P3(x13951,x13953,x13954)+P3(x13951,f15(x13951,x13952,x13953),f15(x13951,x13952,x13954))
% 19.29/19.55 [1396]~P35(x13961)+~P3(x13961,x13963,x13964)+P3(x13961,f15(x13961,x13962,x13963),f15(x13961,x13962,x13964))
% 19.29/19.55 [1397]~P33(x13971)+~P3(x13971,x13972,x13974)+P3(x13971,f15(x13971,x13972,x13973),f15(x13971,x13974,x13973))
% 19.29/19.55 [1398]~P35(x13981)+~P3(x13981,x13982,x13984)+P3(x13981,f15(x13981,x13982,x13983),f15(x13981,x13984,x13983))
% 19.29/19.55 [1491]~P3(a114,x14912,x14914)+~P3(a114,x14911,x14913)+P3(a114,f15(a114,x14911,x14912),f15(a114,x14913,x14914))
% 19.29/19.55 [1556]~P33(x15561)+P3(x15561,x15562,x15563)+~P3(x15561,f15(x15561,x15564,x15562),f15(x15561,x15564,x15563))
% 19.29/19.55 [1558]~P33(x15581)+P3(x15581,x15582,x15583)+~P3(x15581,f15(x15581,x15582,x15584),f15(x15581,x15583,x15584))
% 19.29/19.55 [1540]~P3(a112,x15401,x15403)+P3(a112,f15(a112,x15401,x15402),f15(a112,x15403,x15404))+~P80(f51(f18(a112,x15402),x15404))
% 19.29/19.55 [1565]~E(x15653,f15(a114,x15654,x15652))+P80(f51(x15651,x15652))+~P80(f51(x15651,f13(a114,x15653,x15654)))
% 19.29/19.55 [1697]~P48(x16971)+P3(x16971,x16972,f15(x16971,x16973,x16974))+~P3(x16971,f10(x16971,f13(x16971,x16972,x16973)),x16974)
% 19.29/19.55 [1698]~P48(x16981)+P3(x16981,f13(x16981,x16982,x16983),x16984)+~P3(x16981,f10(x16981,f13(x16981,x16984,x16982)),x16983)
% 19.29/19.55 [1819]~P33(x18191)+~P80(f51(f18(x18191,x18193),x18194))+P80(f51(f18(x18191,f15(x18191,x18192,x18193)),f15(x18191,x18192,x18194)))
% 19.29/19.55 [1820]~P34(x18201)+~P80(f51(f18(x18201,x18203),x18204))+P80(f51(f18(x18201,f15(x18201,x18202,x18203)),f15(x18201,x18202,x18204)))
% 19.29/19.55 [1821]~P33(x18211)+~P80(f51(f18(x18211,x18212),x18214))+P80(f51(f18(x18211,f15(x18211,x18212,x18213)),f15(x18211,x18214,x18213)))
% 19.29/19.55 [1822]~P34(x18221)+~P80(f51(f18(x18221,x18222),x18224))+P80(f51(f18(x18221,f15(x18221,x18222,x18223)),f15(x18221,x18224,x18223)))
% 19.29/19.55 [1859]~P80(f51(f18(a114,x18592),x18594))+~P80(f51(f18(a114,x18591),x18593))+P80(f51(f18(a114,f15(a114,x18591,x18592)),f15(a114,x18593,x18594)))
% 19.29/19.55 [1890]~P1(x18901)+P10(x18901,x18902)+P80(f51(f18(a114,x18903),f43(x18904,x18902,x18903,x18901)))
% 19.29/19.55 [1917]~P33(x19171)+~P80(f51(f18(x19171,f15(x19171,x19174,x19172)),f15(x19171,x19174,x19173)))+P80(f51(f18(x19171,x19172),x19173))
% 19.29/19.55 [1919]~P33(x19191)+~P80(f51(f18(x19191,f15(x19191,x19192,x19194)),f15(x19191,x19193,x19194)))+P80(f51(f18(x19191,x19192),x19193))
% 19.29/19.55 [1994]E(x19941,x19942)+~P15(x19943)+~P7(x19943,x19942,f6(f115(x19943)),x19944,x19941)
% 19.29/19.55 [1995]~P15(x19952)+~P7(x19952,x19953,f6(f115(x19952)),x19951,x19954)+E(x19951,f6(f115(x19952)))
% 19.29/19.55 [1996]~P15(x19962)+~P7(x19962,f6(f115(x19962)),x19963,x19964,x19961)+E(x19961,f6(f115(x19962)))
% 19.29/19.55 [1997]~P15(x19972)+~P7(x19972,f6(f115(x19972)),x19973,x19971,x19974)+E(x19971,f6(f115(x19972)))
% 19.29/19.55 [1326]~P39(x13262)+~P3(f118(x13261,x13262),x13263,x13264)+P80(f51(f18(f118(x13261,x13262),x13263),x13264))
% 19.29/19.55 [1489]~P39(x14891)+~P3(f118(x14892,x14891),x14893,x14894)+~P80(f51(f18(f118(x14892,x14891),x14894),x14893))
% 19.29/19.55 [1979]~P1(x19791)+~P3(a1,f28(x19791,f51(x19792,f48(x19792,x19791,x19794))),f51(f4(a114),f15(a114,x19794,f7(a114))))+P80(f51(f18(a1,f28(x19791,f51(x19792,x19793))),f58(x19792,x19791)))
% 19.29/19.55 [2057]~P39(x20572)+~P80(f51(f18(x20572,f51(x20573,f108(x20574,x20573,x20571,x20572))),f51(x20574,f108(x20574,x20573,x20571,x20572))))+P80(f51(f18(f118(x20571,x20572),x20573),x20574))
% 19.29/19.55 [1274]~P14(x12741)+~E(x12742,f6(x12741))+E(f11(x12741,f51(f51(f14(x12741),x12742),x12743),f51(f51(f14(x12741),x12742),x12744)),f6(x12741))
% 19.29/19.55 [1338]~P14(x13382)+E(x13381,f6(x13382))+E(f11(x13382,f51(f51(f14(x13382),x13383),x13381),f51(f51(f14(x13382),x13384),x13381)),f11(x13382,x13383,x13384))
% 19.29/19.55 [1340]~P14(x13402)+E(x13401,f6(x13402))+E(f11(x13402,f51(f51(f14(x13402),x13401),x13403),f51(f51(f14(x13402),x13401),x13404)),f11(x13402,x13403,x13404))
% 19.29/19.55 [1617]~P15(x16172)+E(x16171,f6(x16172))+E(f29(x16172,f51(f51(f20(x16172),x16173),x16174),f51(f51(f20(x16172),x16171),x16174)),f51(f51(f20(x16172),f29(x16172,x16173,x16171)),x16174))
% 19.29/19.55 [1815]~P80(f51(f18(a114,x18152),x18154))+~P80(f51(f18(a114,x18151),x18153))+P80(f51(f18(a114,f51(f51(f14(a114),x18151),x18152)),f51(f51(f14(a114),x18153),x18154)))
% 19.29/19.55 [1910]~P26(x19101)+E(f51(f51(f14(x19101),f51(f51(f20(x19101),x19102),f13(a114,x19103,x19104))),x19102),f51(f51(f20(x19101),x19102),f13(a114,f15(a114,x19103,f7(a114)),x19104)))+~P80(f51(f18(a114,x19104),x19103))
% 19.29/19.55 [1958]~P31(x19582)+E(f26(x19581,x19582,x19583,x19584,f6(f115(x19582))),x19583)+~E(f51(f51(f51(x19584,f6(x19582)),f6(f115(x19582))),x19583),x19583)
% 19.29/19.55 [2041]~P1(x20411)+P80(f51(f18(a1,f28(x20411,f51(x20412,x20413))),f59(x20412,x20411)))+~P80(f51(f18(a1,f28(x20411,f51(x20412,f60(x20412,x20411,x20414)))),f51(f4(a114),f15(a114,x20414,f7(a114)))))
% 19.29/19.55 [1621]~P14(x16212)+E(x16211,f6(x16212))+E(f11(x16212,f15(x16212,x16213,f51(f51(f14(x16212),x16214),x16211)),x16211),f15(x16212,x16214,f11(x16212,x16213,x16211)))
% 19.29/19.55 [1622]~P14(x16222)+E(x16221,f6(x16222))+E(f11(x16222,f15(x16222,x16223,f51(f51(f14(x16222),x16221),x16224)),x16221),f15(x16222,x16224,f11(x16222,x16223,x16221)))
% 19.29/19.55 [2058]~P1(x20581)+P10(x20581,x20582)+~P80(f51(f18(a1,f28(x20581,f51(x20582,f43(x20583,x20582,x20584,x20581)))),x20583))
% 19.29/19.55 [1998]~P15(x19981)+~P7(x19981,x19982,x19983,x19984,x19985)+E(f11(f115(x19981),x19982,x19983),x19984)
% 19.29/19.55 [1620]~P39(x16201)+P80(f51(f18(x16201,f51(x16202,x16203)),f51(x16204,x16203)))+~P80(f51(f18(f118(x16205,x16201),x16202),x16204))
% 19.29/19.55 [1599]~E(x15992,x15994)+~P79(x15991)+E(f15(x15991,f51(f51(f14(x15991),x15992),x15993),f51(f51(f14(x15991),x15994),x15995)),f15(x15991,f51(f51(f14(x15991),x15992),x15995),f51(f51(f14(x15991),x15994),x15993)))
% 19.29/19.55 [1897]~P80(f51(f18(a114,x18973),x18972))+E(x18971,f15(a114,f51(f51(f14(a114),f13(a114,x18972,x18973)),x18974),x18975))+~E(f15(a114,f51(f51(f14(a114),x18973),x18974),x18971),f15(a114,f51(f51(f14(a114),x18972),x18974),x18975))
% 19.29/19.55 [1898]~P80(f51(f18(a114,x18982),x18981))+E(f15(a114,f51(f51(f14(a114),f13(a114,x18981,x18982)),x18983),x18984),x18985)+~E(f15(a114,f51(f51(f14(a114),x18981),x18983),x18984),f15(a114,f51(f51(f14(a114),x18982),x18983),x18985))
% 19.29/19.55 [1934]~P80(f51(f18(a114,x19344),x19341))+~E(x19345,f15(a114,f51(f51(f14(a114),f13(a114,x19341,x19344)),x19342),x19343))+E(f15(a114,f51(f51(f14(a114),x19341),x19342),x19343),f15(a114,f51(f51(f14(a114),x19344),x19342),x19345))
% 19.29/19.55 [1935]~P80(f51(f18(a114,x19354),x19351))+~E(f15(a114,f51(f51(f14(a114),f13(a114,x19351,x19354)),x19352),x19353),x19355)+E(f15(a114,f51(f51(f14(a114),x19351),x19352),x19353),f15(a114,f51(f51(f14(a114),x19354),x19352),x19355))
% 19.29/19.55 [2006]P3(a114,x20061,f15(a114,f51(f51(f14(a114),f13(a114,x20062,x20063)),x20064),x20065))+~P3(a114,f15(a114,f51(f51(f14(a114),x20063),x20064),x20061),f15(a114,f51(f51(f14(a114),x20062),x20064),x20065))+~P80(f51(f18(a114,x20063),x20062))
% 19.29/19.55 [2007]P3(a114,f15(a114,f51(f51(f14(a114),f13(a114,x20071,x20072)),x20073),x20074),x20075)+~P3(a114,f15(a114,f51(f51(f14(a114),x20071),x20073),x20074),f15(a114,f51(f51(f14(a114),x20072),x20073),x20075))+~P80(f51(f18(a114,x20072),x20071))
% 19.29/19.55 [2013]~P3(a114,x20133,f15(a114,f51(f51(f14(a114),f13(a114,x20134,x20131)),x20132),x20135))+P3(a114,f15(a114,f51(f51(f14(a114),x20131),x20132),x20133),f15(a114,f51(f51(f14(a114),x20134),x20132),x20135))+~P80(f51(f18(a114,x20131),x20134))
% 19.29/19.55 [2014]~P3(a114,f15(a114,f51(f51(f14(a114),f13(a114,x20141,x20144)),x20142),x20143),x20145)+P3(a114,f15(a114,f51(f51(f14(a114),x20141),x20142),x20143),f15(a114,f51(f51(f14(a114),x20144),x20142),x20145))+~P80(f51(f18(a114,x20144),x20141))
% 19.29/19.55 [2003]~P15(x20032)+~P7(x20032,x20031,x20034,x20033,x20035)+E(x20031,f15(f115(x20032),f51(f51(f14(f115(x20032)),x20033),x20034),x20035))
% 19.29/19.55 [2045]~P80(f51(f18(a114,x20453),x20452))+P80(f51(f18(a114,x20451),f15(a114,f51(f51(f14(a114),f13(a114,x20452,x20453)),x20454),x20455)))+~P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),x20453),x20454),x20451)),f15(a114,f51(f51(f14(a114),x20452),x20454),x20455)))
% 19.29/19.55 [2047]~P80(f51(f18(a114,x20471),x20474))+~P80(f51(f18(a114,x20473),f15(a114,f51(f51(f14(a114),f13(a114,x20474,x20471)),x20472),x20475)))+P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),x20471),x20472),x20473)),f15(a114,f51(f51(f14(a114),x20474),x20472),x20475)))
% 19.29/19.55 [2052]~P80(f51(f18(a114,x20522),x20521))+~P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),x20521),x20523),x20524)),f15(a114,f51(f51(f14(a114),x20522),x20523),x20525)))+P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),f13(a114,x20521,x20522)),x20523),x20524)),x20525))
% 19.29/19.55 [2055]~P80(f51(f18(a114,x20554),x20551))+P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),x20551),x20552),x20553)),f15(a114,f51(f51(f14(a114),x20554),x20552),x20555)))+~P80(f51(f18(a114,f15(a114,f51(f51(f14(a114),f13(a114,x20551,x20554)),x20552),x20553)),x20555))
% 19.29/19.55 [1891]~P73(x18912)+~E(f15(x18912,f51(f51(f14(x18912),x18914),x18915),x18911),f15(x18912,f51(f51(f14(x18912),x18913),x18915),x18916))+E(x18911,f15(x18912,f51(f51(f14(x18912),f13(x18912,x18913,x18914)),x18915),x18916))
% 19.29/19.55 [1892]~P73(x18921)+~E(f15(x18921,f51(f51(f14(x18921),x18922),x18924),x18925),f15(x18921,f51(f51(f14(x18921),x18923),x18924),x18926))+E(f15(x18921,f51(f51(f14(x18921),f13(x18921,x18922,x18923)),x18924),x18925),x18926)
% 19.29/19.55 [1922]~P73(x19221)+~E(x19226,f15(x19221,f51(f51(f14(x19221),f13(x19221,x19222,x19225)),x19223),x19224))+E(f15(x19221,f51(f51(f14(x19221),x19222),x19223),x19224),f15(x19221,f51(f51(f14(x19221),x19225),x19223),x19226))
% 19.29/19.55 [1923]~P73(x19231)+~E(f15(x19231,f51(f51(f14(x19231),f13(x19231,x19232,x19235)),x19233),x19234),x19236)+E(f15(x19231,f51(f51(f14(x19231),x19232),x19233),x19234),f15(x19231,f51(f51(f14(x19231),x19235),x19233),x19236))
% 19.29/19.55 [2008]~P69(x20081)+~P3(x20081,f15(x20081,f51(f51(f14(x20081),x20084),x20085),x20082),f15(x20081,f51(f51(f14(x20081),x20083),x20085),x20086))+P3(x20081,x20082,f15(x20081,f51(f51(f14(x20081),f13(x20081,x20083,x20084)),x20085),x20086))
% 19.29/19.55 [2009]~P69(x20091)+~P3(x20091,f15(x20091,f51(f51(f14(x20091),x20092),x20094),x20095),f15(x20091,f51(f51(f14(x20091),x20093),x20094),x20096))+P3(x20091,f15(x20091,f51(f51(f14(x20091),f13(x20091,x20092,x20093)),x20094),x20095),x20096)
% 19.29/19.55 [2016]~P69(x20161)+~P3(x20161,x20164,f15(x20161,f51(f51(f14(x20161),f13(x20161,x20165,x20162)),x20163),x20166))+P3(x20161,f15(x20161,f51(f51(f14(x20161),x20162),x20163),x20164),f15(x20161,f51(f51(f14(x20161),x20165),x20163),x20166))
% 19.29/19.55 [2017]~P69(x20171)+~P3(x20171,f15(x20171,f51(f51(f14(x20171),f13(x20171,x20172,x20175)),x20173),x20174),x20176)+P3(x20171,f15(x20171,f51(f51(f14(x20171),x20172),x20173),x20174),f15(x20171,f51(f51(f14(x20171),x20175),x20173),x20176))
% 19.29/19.55 [2046]~P69(x20461)+~P80(f51(f18(x20461,f15(x20461,f51(f51(f14(x20461),x20464),x20465),x20462)),f15(x20461,f51(f51(f14(x20461),x20463),x20465),x20466)))+P80(f51(f18(x20461,x20462),f15(x20461,f51(f51(f14(x20461),f13(x20461,x20463,x20464)),x20465),x20466)))
% 19.29/19.55 [2049]~P69(x20491)+~P80(f51(f18(x20491,x20494),f15(x20491,f51(f51(f14(x20491),f13(x20491,x20495,x20492)),x20493),x20496)))+P80(f51(f18(x20491,f15(x20491,f51(f51(f14(x20491),x20492),x20493),x20494)),f15(x20491,f51(f51(f14(x20491),x20495),x20493),x20496)))
% 19.29/19.55 [2054]~P69(x20541)+~P80(f51(f18(x20541,f15(x20541,f51(f51(f14(x20541),x20542),x20544),x20545)),f15(x20541,f51(f51(f14(x20541),x20543),x20544),x20546)))+P80(f51(f18(x20541,f15(x20541,f51(f51(f14(x20541),f13(x20541,x20542,x20543)),x20544),x20545)),x20546))
% 19.29/19.55 [2056]~P69(x20561)+P80(f51(f18(x20561,f15(x20561,f51(f51(f14(x20561),x20562),x20563),x20564)),f15(x20561,f51(f51(f14(x20561),x20565),x20563),x20566)))+~P80(f51(f18(x20561,f15(x20561,f51(f51(f14(x20561),f13(x20561,x20562,x20565)),x20563),x20564)),x20566))
% 19.29/19.55 [1129]P3(a112,x11291,x11292)+P3(a112,x11292,x11291)+E(x11291,f6(a112))+~E(f11(a112,x11292,x11291),f6(a112))
% 19.29/19.55 [1168]P3(a112,x11682,x11681)+E(x11681,f6(a112))+~E(f11(a112,x11682,x11681),f6(a112))+P80(f51(f18(a112,x11682),f6(a112)))
% 19.29/19.55 [888]~P43(x8882)+~P75(x8882)+E(x8881,f6(a114))+E(f51(f51(f20(x8882),f6(x8882)),x8881),f6(x8882))
% 19.29/19.55 [1003]~E(x10032,f7(a112))+~E(x10031,f7(a112))+~P3(a112,f6(a112),x10031)+E(f51(f51(f14(a112),x10031),x10032),f7(a112))
% 19.29/19.55 [1176]P3(a112,x11761,x11762)+E(x11761,f6(a112))+~E(f11(a112,x11762,x11761),f6(a112))+P80(f51(f18(a112,f6(a112)),x11762))
% 19.29/19.55 [1325]E(x13251,x13252)+~E(f51(a16,x13251),f51(a16,x13252))+~P80(f51(f18(a112,f6(a112)),x13252))+~P80(f51(f18(a112,f6(a112)),x13251))
% 19.29/19.55 [967]P3(x9673,x9671,x9672)+~P48(x9673)+E(x9671,x9672)+P3(x9673,x9672,x9671)
% 19.29/19.55 [968]P3(x9683,x9681,x9682)+~P37(x9683)+E(x9681,x9682)+P3(x9683,x9682,x9681)
% 19.29/19.55 [868]~E(x8683,x8681)+~P55(x8682)+E(f29(x8682,x8683,x8681),f7(x8682))+E(x8681,f6(x8682))
% 19.29/19.55 [942]~P55(x9423)+E(x9421,x9422)+~E(f29(x9423,x9421,x9422),f7(x9423))+E(x9422,f6(x9423))
% 19.29/19.55 [1262]P81(x12622,x12621,x12623)+P3(a112,f105(x12623,x12621,x12622),x12621)+E(x12621,f6(a112))+P3(a112,x12621,f6(a112))
% 19.29/19.55 [1263]P81(x12632,x12631,x12633)+P3(a112,x12631,f109(x12633,x12631,x12632))+E(x12631,f6(a112))+P3(a112,f6(a112),x12631)
% 19.29/19.55 [1406]~P36(x14061)+~P3(x14061,f6(x14061),x14063)+~P3(x14061,f6(x14061),x14062)+P3(x14061,f6(x14061),f15(x14061,x14062,x14063))
% 19.29/19.55 [1407]~P36(x14071)+~P3(x14071,x14073,f6(x14071))+~P3(x14071,x14072,f6(x14071))+P3(x14071,f15(x14071,x14072,x14073),f6(x14071))
% 19.29/19.55 [1416]P81(x14162,x14161,x14163)+P3(a112,x14161,f109(x14163,x14161,x14162))+P3(a112,f105(x14163,x14161,x14162),x14161)+E(x14161,f6(a112))
% 19.29/19.55 [1000]~E(x10002,x10003)+~P37(x10001)+P3(x10001,x10002,x10003)+P80(f51(f18(x10001,x10002),x10003))
% 19.29/19.55 [1113]~P40(x11133)+E(x11131,x11132)+P3(x11133,x11132,x11131)+~P80(f51(f18(x11133,x11132),x11131))
% 19.29/19.55 [1115]~P37(x11153)+E(x11151,x11152)+P3(x11153,x11151,x11152)+~P80(f51(f18(x11153,x11151),x11152))
% 19.29/19.55 [1121]~P40(x11213)+E(x11211,x11212)+P3(x11213,x11211,x11212)+~P80(f51(f18(x11213,x11211),x11212))
% 19.29/19.55 [1164]P81(x11641,x11642,x11643)+P3(a112,x11642,f6(a112))+P3(a112,f6(a112),x11642)+~P80(f51(x11641,f6(a112)))
% 19.29/19.55 [1233]~P3(a114,x12333,f41(x12332,x12331))+~P80(f51(x12331,x12332))+~P80(f51(x12331,x12333))+P80(f51(x12331,f6(a114)))
% 19.29/19.55 [1251]E(x12511,x12512)+~P40(x12513)+~P80(f51(f18(x12513,x12512),x12511))+~P80(f51(f18(x12513,x12511),x12512))
% 19.29/19.55 [1261]~P30(x12611)+P3(x12611,x12612,x12613)+P80(f51(f18(x12611,x12613),x12612))+~P80(f51(f18(x12611,x12612),x12613))
% 19.29/19.55 [1341]P81(x13411,x13412,x13413)+P3(a112,f105(x13413,x13412,x13411),x13412)+P3(a112,x13412,f6(a112))+~P80(f51(x13411,f6(a112)))
% 19.29/19.55 [1342]P81(x13421,x13422,x13423)+P3(a112,x13422,f109(x13423,x13422,x13421))+P3(a112,f6(a112),x13422)+~P80(f51(x13421,f6(a112)))
% 19.29/19.55 [1456]E(x14561,x14562)+~E(f13(a114,x14561,x14563),f13(a114,x14562,x14563))+~P80(f51(f18(a114,x14563),x14561))+~P80(f51(f18(a114,x14563),x14562))
% 19.29/19.55 [1463]P81(x14632,x14631,x14633)+E(x14631,f6(a112))+P3(a112,x14631,f6(a112))+P80(f51(f18(a112,f6(a112)),f105(x14633,x14631,x14632)))
% 19.29/19.55 [1470]~P36(x14701)+~P3(x14701,x14703,f6(x14701))+P3(x14701,f15(x14701,x14702,x14703),f6(x14701))+~P80(f51(f18(x14701,x14702),f6(x14701)))
% 19.29/19.55 [1471]~P36(x14711)+~P3(x14711,x14712,f6(x14711))+P3(x14711,f15(x14711,x14712,x14713),f6(x14711))+~P80(f51(f18(x14711,x14713),f6(x14711)))
% 19.29/19.55 [1493]P81(x14931,x14932,x14933)+P3(a112,x14932,f109(x14933,x14932,x14931))+P3(a112,f105(x14933,x14932,x14931),x14932)+~P80(f51(x14931,f6(a112)))
% 19.29/19.55 [1547]P81(x15471,x15472,x15473)+P3(a112,x15472,f6(a112))+P80(f51(f18(a112,f6(a112)),f105(x15473,x15472,x15471)))+~P80(f51(x15471,f6(a112)))
% 19.29/19.55 [1579]P81(x15792,x15791,x15793)+E(x15791,f6(a112))+P3(a112,x15791,f6(a112))+~P80(f51(x15792,f107(x15793,x15791,x15792)))
% 19.29/19.55 [1580]P81(x15802,x15801,x15803)+E(x15801,f6(a112))+P3(a112,f6(a112),x15801)+~P80(f51(x15802,f110(x15803,x15801,x15802)))
% 19.29/19.55 [1591]P81(x15912,x15911,x15913)+P3(a112,x15911,f109(x15913,x15911,x15912))+E(x15911,f6(a112))+P80(f51(f18(a112,f6(a112)),f105(x15913,x15911,x15912)))
% 19.29/19.55 [1633]P81(x16331,x16332,x16333)+P3(a112,x16332,f6(a112))+~P80(f51(x16331,f107(x16333,x16332,x16331)))+~P80(f51(x16331,f6(a112)))
% 19.29/19.55 [1634]P81(x16341,x16342,x16343)+P3(a112,f6(a112),x16342)+~P80(f51(x16341,f110(x16343,x16342,x16341)))+~P80(f51(x16341,f6(a112)))
% 19.29/19.55 [1659]P81(x16591,x16592,x16593)+P3(a112,x16592,f109(x16593,x16592,x16591))+P80(f51(f18(a112,f6(a112)),f105(x16593,x16592,x16591)))+~P80(f51(x16591,f6(a112)))
% 19.29/19.55 [1661]P81(x16613,x16611,x16612)+E(x16611,f6(a112))+P3(a112,x16611,f6(a112))+E(f15(a112,f51(f51(f14(a112),x16611),f107(x16612,x16611,x16613)),f105(x16612,x16611,x16613)),x16612)
% 19.29/19.55 [1662]P81(x16623,x16621,x16622)+E(x16621,f6(a112))+P3(a112,f6(a112),x16621)+E(f15(a112,f51(f51(f14(a112),x16621),f110(x16622,x16621,x16623)),f109(x16622,x16621,x16623)),x16622)
% 19.29/19.55 [1680]P81(x16802,x16801,x16803)+P3(a112,x16801,f109(x16803,x16801,x16802))+E(x16801,f6(a112))+~P80(f51(x16802,f107(x16803,x16801,x16802)))
% 19.29/19.55 [1681]P81(x16812,x16811,x16813)+P3(a112,f105(x16813,x16811,x16812),x16811)+E(x16811,f6(a112))+~P80(f51(x16812,f110(x16813,x16811,x16812)))
% 19.29/19.55 [1693]P81(x16932,x16931,x16933)+E(x16931,f6(a112))+P3(a112,f6(a112),x16931)+P80(f51(f18(a112,f109(x16933,x16931,x16932)),f6(a112)))
% 19.29/19.55 [1700]P81(x17003,x17001,x17002)+P3(a112,x17001,f6(a112))+E(f15(a112,f51(f51(f14(a112),x17001),f107(x17002,x17001,x17003)),f105(x17002,x17001,x17003)),x17002)+~P80(f51(x17003,f6(a112)))
% 19.29/19.55 [1701]P81(x17013,x17011,x17012)+P3(a112,f6(a112),x17011)+E(f15(a112,f51(f51(f14(a112),x17011),f110(x17012,x17011,x17013)),f109(x17012,x17011,x17013)),x17012)+~P80(f51(x17013,f6(a112)))
% 19.29/19.55 [1721]P81(x17211,x17212,x17213)+P3(a112,x17212,f109(x17213,x17212,x17211))+~P80(f51(x17211,f107(x17213,x17212,x17211)))+~P80(f51(x17211,f6(a112)))
% 19.29/19.55 [1722]P81(x17221,x17222,x17223)+P3(a112,f105(x17223,x17222,x17221),x17222)+~P80(f51(x17221,f110(x17223,x17222,x17221)))+~P80(f51(x17221,f6(a112)))
% 19.29/19.55 [1735]P81(x17351,x17352,x17353)+P3(a112,f6(a112),x17352)+~P80(f51(x17351,f6(a112)))+P80(f51(f18(a112,f109(x17353,x17352,x17351)),f6(a112)))
% 19.29/19.55 [1739]P81(x17393,x17391,x17392)+P3(a112,x17391,f109(x17392,x17391,x17393))+E(x17391,f6(a112))+E(f15(a112,f51(f51(f14(a112),x17391),f107(x17392,x17391,x17393)),f105(x17392,x17391,x17393)),x17392)
% 19.29/19.55 [1740]P81(x17403,x17401,x17402)+P3(a112,f105(x17402,x17401,x17403),x17401)+E(x17401,f6(a112))+E(f15(a112,f51(f51(f14(a112),x17401),f110(x17402,x17401,x17403)),f109(x17402,x17401,x17403)),x17402)
% 19.29/19.55 [1752]P3(a114,x17521,x17522)+~P3(a114,f13(a114,x17521,x17523),f13(a114,x17522,x17523))+~P80(f51(f18(a114,x17523),x17521))+~P80(f51(f18(a114,x17523),x17522))
% 19.29/19.55 [1760]P81(x17602,x17601,x17603)+P3(a112,f105(x17603,x17601,x17602),x17601)+E(x17601,f6(a112))+P80(f51(f18(a112,f109(x17603,x17601,x17602)),f6(a112)))
% 19.29/19.55 [1766]P81(x17663,x17661,x17662)+P3(a112,x17661,f109(x17662,x17661,x17663))+E(f15(a112,f51(f51(f14(a112),x17661),f107(x17662,x17661,x17663)),f105(x17662,x17661,x17663)),x17662)+~P80(f51(x17663,f6(a112)))
% 19.29/19.55 [1767]P81(x17673,x17671,x17672)+P3(a112,f105(x17672,x17671,x17673),x17671)+E(f15(a112,f51(f51(f14(a112),x17671),f110(x17672,x17671,x17673)),f109(x17672,x17671,x17673)),x17672)+~P80(f51(x17673,f6(a112)))
% 19.29/19.55 [1768]P81(x17682,x17681,x17683)+E(x17681,f6(a112))+P80(f51(f18(a112,f6(a112)),f105(x17683,x17681,x17682)))+~P80(f51(x17682,f110(x17683,x17681,x17682)))
% 19.29/19.55 [1776]P81(x17761,x17762,x17763)+P3(a112,f105(x17763,x17762,x17761),x17762)+~P80(f51(x17761,f6(a112)))+P80(f51(f18(a112,f109(x17763,x17762,x17761)),f6(a112)))
% 19.29/19.55 [1778]P81(x17781,x17782,x17783)+P80(f51(f18(a112,f6(a112)),f105(x17783,x17782,x17781)))+~P80(f51(x17781,f110(x17783,x17782,x17781)))+~P80(f51(x17781,f6(a112)))
% 19.29/19.55 [1792]P81(x17923,x17921,x17922)+E(x17921,f6(a112))+E(f15(a112,f51(f51(f14(a112),x17921),f110(x17922,x17921,x17923)),f109(x17922,x17921,x17923)),x17922)+P80(f51(f18(a112,f6(a112)),f105(x17922,x17921,x17923)))
% 19.29/19.55 [1795]P81(x17952,x17951,x17953)+E(x17951,f6(a112))+~P80(f51(x17952,f107(x17953,x17951,x17952)))+~P80(f51(x17952,f110(x17953,x17951,x17952)))
% 19.29/19.55 [1796]~P36(x17961)+~P80(f51(f18(x17961,x17963),f6(x17961)))+~P80(f51(f18(x17961,x17962),f6(x17961)))+P80(f51(f18(x17961,f15(x17961,x17962,x17963)),f6(x17961)))
% 19.29/19.55 [1828]P81(x18282,x18281,x18283)+E(x18281,f6(a112))+P80(f51(f18(a112,f6(a112)),f105(x18283,x18281,x18282)))+P80(f51(f18(a112,f109(x18283,x18281,x18282)),f6(a112)))
% 19.29/19.55 [1830]P81(x18303,x18301,x18302)+E(f15(a112,f51(f51(f14(a112),x18301),f110(x18302,x18301,x18303)),f109(x18302,x18301,x18303)),x18302)+P80(f51(f18(a112,f6(a112)),f105(x18302,x18301,x18303)))+~P80(f51(x18303,f6(a112)))
% 19.29/19.55 [1831]P81(x18311,x18312,x18313)+~P80(f51(x18311,f107(x18313,x18312,x18311)))+~P80(f51(x18311,f110(x18313,x18312,x18311)))+~P80(f51(x18311,f6(a112)))
% 19.29/19.55 [1839]P81(x18393,x18391,x18392)+E(x18391,f6(a112))+E(f15(a112,f51(f51(f14(a112),x18391),f107(x18392,x18391,x18393)),f105(x18392,x18391,x18393)),x18392)+~P80(f51(x18393,f110(x18392,x18391,x18393)))
% 19.29/19.55 [1840]P81(x18403,x18401,x18402)+E(x18401,f6(a112))+E(f15(a112,f51(f51(f14(a112),x18401),f110(x18402,x18401,x18403)),f109(x18402,x18401,x18403)),x18402)+~P80(f51(x18403,f107(x18402,x18401,x18403)))
% 19.29/19.55 [1852]P81(x18521,x18522,x18523)+P80(f51(f18(a112,f6(a112)),f105(x18523,x18522,x18521)))+~P80(f51(x18521,f6(a112)))+P80(f51(f18(a112,f109(x18523,x18522,x18521)),f6(a112)))
% 19.29/19.55 [1860]P81(x18602,x18601,x18603)+E(x18601,f6(a112))+~P80(f51(x18602,f107(x18603,x18601,x18602)))+P80(f51(f18(a112,f109(x18603,x18601,x18602)),f6(a112)))
% 19.29/19.55 [1861]P81(x18613,x18611,x18612)+E(f15(a112,f51(f51(f14(a112),x18611),f107(x18612,x18611,x18613)),f105(x18612,x18611,x18613)),x18612)+~P80(f51(x18613,f110(x18612,x18611,x18613)))+~P80(f51(x18613,f6(a112)))
% 19.29/19.55 [1862]P81(x18623,x18621,x18622)+E(f15(a112,f51(f51(f14(a112),x18621),f110(x18622,x18621,x18623)),f109(x18622,x18621,x18623)),x18622)+~P80(f51(x18623,f107(x18622,x18621,x18623)))+~P80(f51(x18623,f6(a112)))
% 19.29/19.55 [1869]~P59(x18691)+~P80(f51(f18(x18691,f51(f51(f14(x18691),x18693),x18692)),f6(x18691)))+P80(f51(f18(x18691,x18692),f6(x18691)))+P80(f51(f18(x18691,x18693),f6(x18691)))
% 19.29/19.55 [1870]P81(x18703,x18701,x18702)+E(x18701,f6(a112))+E(f15(a112,f51(f51(f14(a112),x18701),f110(x18702,x18701,x18703)),f109(x18702,x18701,x18703)),x18702)+E(f15(a112,f51(f51(f14(a112),x18701),f107(x18702,x18701,x18703)),f105(x18702,x18701,x18703)),x18702)
% 19.29/19.55 [1873]~P3(a112,x18731,f6(a112))+~P3(a112,f6(a112),x18732)+~P80(f51(f18(a112,x18732),x18733))+P80(f51(f18(a112,f11(a112,x18731,x18732)),f11(a112,x18731,x18733)))
% 19.29/19.55 [1880]P81(x18801,x18802,x18803)+~P80(f51(x18801,f107(x18803,x18802,x18801)))+~P80(f51(x18801,f6(a112)))+P80(f51(f18(a112,f109(x18803,x18802,x18801)),f6(a112)))
% 19.29/19.55 [1882]P81(x18823,x18821,x18822)+E(x18821,f6(a112))+E(f15(a112,f51(f51(f14(a112),x18821),f107(x18822,x18821,x18823)),f105(x18822,x18821,x18823)),x18822)+P80(f51(f18(a112,f109(x18822,x18821,x18823)),f6(a112)))
% 19.29/19.55 [1883]P81(x18833,x18831,x18832)+E(f15(a112,f51(f51(f14(a112),x18831),f110(x18832,x18831,x18833)),f109(x18832,x18831,x18833)),x18832)+E(f15(a112,f51(f51(f14(a112),x18831),f107(x18832,x18831,x18833)),f105(x18832,x18831,x18833)),x18832)+~P80(f51(x18833,f6(a112)))
% 19.29/19.55 [1893]P81(x18933,x18931,x18932)+E(f15(a112,f51(f51(f14(a112),x18931),f107(x18932,x18931,x18933)),f105(x18932,x18931,x18933)),x18932)+~P80(f51(x18933,f6(a112)))+P80(f51(f18(a112,f109(x18932,x18931,x18933)),f6(a112)))
% 19.29/19.55 [1952]~P80(f51(f18(a114,x19523),x19521))+P80(f51(f18(a114,x19521),x19522))+~P80(f51(f18(a114,x19523),x19522))+~P80(f51(f18(a114,f13(a114,x19521,x19523)),f13(a114,x19522,x19523)))
% 19.29/19.55 [2004]~P59(x20041)+~E(x20043,f6(x20041))+~E(x20042,f6(x20041))+P80(f51(f18(x20041,f15(x20041,f51(f51(f14(x20041),x20042),x20042),f51(f51(f14(x20041),x20043),x20043))),f6(x20041)))
% 19.29/19.55 [940]~P66(x9402)+E(x9401,f6(x9402))+E(x9403,f6(x9402))+~E(f51(f51(f14(x9402),x9403),x9401),f6(x9402))
% 19.29/19.55 [941]~P76(x9412)+E(x9411,f6(x9412))+E(x9413,f6(x9412))+~E(f51(f51(f14(x9412),x9413),x9411),f6(x9412))
% 19.29/19.55 [1386]~P47(x13861)+~P3(x13861,f7(x13861),x13862)+~P3(a114,f6(a114),x13863)+P3(x13861,f7(x13861),f51(f51(f20(x13861),x13862),x13863))
% 19.29/19.55 [1399]~P59(x13991)+~P3(x13991,x13993,f6(x13991))+~P3(x13991,x13992,f6(x13991))+P3(x13991,f6(x13991),f51(f51(f14(x13991),x13992),x13993))
% 19.29/19.55 [1400]~P62(x14001)+~P3(x14001,f6(x14001),x14003)+~P3(x14001,f6(x14001),x14002)+P3(x14001,f6(x14001),f51(f51(f14(x14001),x14002),x14003))
% 19.29/19.55 [1401]~P47(x14011)+~P3(x14011,f7(x14011),x14013)+~P3(x14011,f7(x14011),x14012)+P3(x14011,f7(x14011),f51(f51(f14(x14011),x14012),x14013))
% 19.29/19.55 [1403]~P62(x14031)+~P3(x14031,x14033,f6(x14031))+~P3(x14031,f6(x14031),x14032)+P3(x14031,f51(f51(f14(x14031),x14032),x14033),f6(x14031))
% 19.29/19.55 [1404]~P62(x14041)+~P3(x14041,x14042,f6(x14041))+~P3(x14041,f6(x14041),x14043)+P3(x14041,f51(f51(f14(x14041),x14042),x14043),f6(x14041))
% 19.29/19.55 [1474]~P62(x14741)+P3(x14741,f6(x14741),x14742)+~P3(x14741,f6(x14741),x14743)+~P3(x14741,f6(x14741),f51(f51(f14(x14741),x14743),x14742))
% 19.29/19.55 [1475]~P62(x14751)+P3(x14751,f6(x14751),x14752)+~P3(x14751,f6(x14751),x14753)+~P3(x14751,f6(x14751),f51(f51(f14(x14751),x14752),x14753))
% 19.29/19.55 [1663]~P47(x16631)+~P3(x16631,x16632,f7(x16631))+~P3(x16631,f6(x16631),x16632)+P3(x16631,f51(f51(f20(x16631),x16632),f15(a114,x16633,f7(a114))),f7(x16631))
% 19.29/19.55 [1798]~P59(x17981)+~P80(f51(f18(x17981,x17983),f6(x17981)))+P80(f51(f18(x17981,f51(f51(f14(x17981),x17982),x17983)),f6(x17981)))+~P80(f51(f18(x17981,f6(x17981)),x17982))
% 19.29/19.55 [1799]~P59(x17991)+~P80(f51(f18(x17991,x17992),f6(x17991)))+P80(f51(f18(x17991,f51(f51(f14(x17991),x17992),x17993)),f6(x17991)))+~P80(f51(f18(x17991,f6(x17991)),x17993))
% 19.29/19.55 [1801]~P68(x18011)+~P80(f51(f18(x18011,x18013),f6(x18011)))+P80(f51(f18(x18011,f51(f51(f14(x18011),x18012),x18013)),f6(x18011)))+~P80(f51(f18(x18011,f6(x18011)),x18012))
% 19.29/19.55 [1803]~P68(x18031)+~P80(f51(f18(x18031,x18032),f6(x18031)))+P80(f51(f18(x18031,f51(f51(f14(x18031),x18032),x18033)),f6(x18031)))+~P80(f51(f18(x18031,f6(x18031)),x18033))
% 19.29/19.55 [1874]~P59(x18741)+~P80(f51(f18(x18741,f51(f51(f14(x18741),x18743),x18742)),f6(x18741)))+P80(f51(f18(x18741,x18742),f6(x18741)))+P80(f51(f18(x18741,f6(x18741)),x18742))
% 19.29/19.55 [1875]~P59(x18751)+~P80(f51(f18(x18751,f51(f51(f14(x18751),x18752),x18753)),f6(x18751)))+P80(f51(f18(x18751,x18752),f6(x18751)))+P80(f51(f18(x18751,f6(x18751)),x18752))
% 19.29/19.55 [1881]~P59(x18811)+~P80(f51(f18(x18811,f51(f51(f14(x18811),x18812),x18813)),f6(x18811)))+P80(f51(f18(x18811,f6(x18811)),x18812))+P80(f51(f18(x18811,f6(x18811)),x18813))
% 19.29/19.55 [1884]~P3(a112,f6(a112),x18843)+~P80(f51(f18(a112,x18843),x18842))+P80(f51(f18(a112,f11(a112,x18841,x18842)),f11(a112,x18841,x18843)))+~P80(f51(f18(a112,f6(a112)),x18841))
% 19.29/19.55 [1284]~P59(x12841)+~E(x12843,f6(x12841))+~E(x12842,f6(x12841))+E(f15(x12841,f51(f51(f14(x12841),x12842),x12842),f51(f51(f14(x12841),x12843),x12843)),f6(x12841))
% 19.29/19.55 [1563]~P3(a112,x15632,x15633)+~P3(a112,f6(a112),x15633)+~E(f15(a112,x15632,f51(f51(f14(a112),x15633),x15631)),x15633)+P80(f51(f18(a112,f7(a112)),x15631))
% 19.29/19.55 [1613]~P3(a112,f6(a112),x16133)+~E(f15(a112,x16132,f51(f51(f14(a112),x16133),x16131)),x16133)+P80(f51(f18(a112,x16131),f7(a112)))+~P80(f51(f18(a112,f6(a112)),x16132))
% 19.29/19.55 [1629]~P72(x16291)+~P80(f51(f18(x16291,x16292),f6(x16291)))+~P80(f51(f18(x16291,x16293),f6(x16291)))+E(f51(f51(f14(x16291),f10(x16291,x16292)),f10(x16291,x16293)),f10(x16291,f51(f51(f14(x16291),x16292),x16293)))
% 19.29/19.55 [1648]~P72(x16481)+~P80(f51(f18(x16481,x16482),f6(x16481)))+E(f51(f51(f14(x16481),f10(x16481,x16482)),f10(x16481,x16483)),f10(x16481,f51(f51(f14(x16481),x16482),x16483)))+~P80(f51(f18(x16481,f6(x16481)),x16483))
% 19.29/19.55 [1649]~P72(x16491)+~P80(f51(f18(x16491,x16493),f6(x16491)))+E(f51(f51(f14(x16491),f10(x16491,x16492)),f10(x16491,x16493)),f10(x16491,f51(f51(f14(x16491),x16492),x16493)))+~P80(f51(f18(x16491,f6(x16491)),x16492))
% 19.29/19.55 [1667]~P72(x16671)+E(f51(f51(f14(x16671),f10(x16671,x16672)),f10(x16671,x16673)),f10(x16671,f51(f51(f14(x16671),x16672),x16673)))+~P80(f51(f18(x16671,f6(x16671)),x16672))+~P80(f51(f18(x16671,f6(x16671)),x16673))
% 19.29/19.55 [1685]~P59(x16851)+~P80(f51(f18(x16851,x16853),f6(x16851)))+~P80(f51(f18(x16851,x16852),f6(x16851)))+P80(f51(f18(x16851,f6(x16851)),f51(f51(f14(x16851),x16852),x16853)))
% 19.29/19.55 [1687]~P69(x16871)+~P80(f51(f18(x16871,x16873),f6(x16871)))+~P80(f51(f18(x16871,x16872),f6(x16871)))+P80(f51(f18(x16871,f6(x16871)),f51(f51(f14(x16871),x16872),x16873)))
% 19.29/19.55 [1716]~P59(x17161)+~P80(f51(f18(x17161,f6(x17161)),x17163))+~P80(f51(f18(x17161,f6(x17161)),x17162))+P80(f51(f18(x17161,f6(x17161)),f51(f51(f14(x17161),x17162),x17163)))
% 19.29/19.55 [1717]~P68(x17171)+~P80(f51(f18(x17171,f6(x17171)),x17173))+~P80(f51(f18(x17171,f6(x17171)),x17172))+P80(f51(f18(x17171,f6(x17171)),f51(f51(f14(x17171),x17172),x17173)))
% 19.29/19.55 [1718]~P69(x17181)+~P80(f51(f18(x17181,f6(x17181)),x17183))+~P80(f51(f18(x17181,f6(x17181)),x17182))+P80(f51(f18(x17181,f6(x17181)),f51(f51(f14(x17181),x17182),x17183)))
% 19.29/19.55 [1725]~P47(x17251)+~P3(x17251,x17252,f7(x17251))+~P3(x17251,f6(x17251),x17252)+P3(x17251,f51(f51(f14(x17251),x17252),f51(f51(f20(x17251),x17252),x17253)),f51(f51(f20(x17251),x17252),x17253))
% 19.29/19.55 [1746]~P59(x17461)+P80(f51(f18(x17461,x17462),f6(x17461)))+P80(f51(f18(x17461,f6(x17461)),x17463))+~P80(f51(f18(x17461,f6(x17461)),f51(f51(f14(x17461),x17463),x17462)))
% 19.29/19.55 [1747]~P59(x17471)+P80(f51(f18(x17471,x17472),f6(x17471)))+P80(f51(f18(x17471,f6(x17471)),x17473))+~P80(f51(f18(x17471,f6(x17471)),f51(f51(f14(x17471),x17472),x17473)))
% 19.29/19.55 [1748]~P59(x17481)+P80(f51(f18(x17481,x17482),f6(x17481)))+P80(f51(f18(x17481,f6(x17481)),x17482))+~P80(f51(f18(x17481,f6(x17481)),f51(f51(f14(x17481),x17483),x17482)))
% 19.29/19.55 [1749]~P59(x17491)+P80(f51(f18(x17491,x17492),f6(x17491)))+P80(f51(f18(x17491,f6(x17491)),x17492))+~P80(f51(f18(x17491,f6(x17491)),f51(f51(f14(x17491),x17492),x17493)))
% 19.29/19.55 [1808]~P3(a112,f6(a112),x18082)+~P3(a112,f15(a112,f51(f51(f14(a112),x18082),x18081),x18083),f6(a112))+P80(f51(f18(a112,x18081),f6(a112)))+~P80(f51(f18(a112,f6(a112)),x18083))
% 19.29/19.55 [1857]~P59(x18572)+~E(x18571,f6(x18572))+~E(x18573,f6(x18572))+~P3(x18572,f6(x18572),f15(x18572,f51(f51(f14(x18572),x18573),x18573),f51(f51(f14(x18572),x18571),x18571)))
% 19.29/19.55 [1294]~P49(x12942)+E(x12941,f6(f115(x12942)))+E(x12943,f6(f115(x12942)))+E(f22(x12942,f51(f51(f14(f115(x12942)),x12943),x12941)),f15(a114,f22(x12942,x12943),f22(x12942,x12941)))
% 19.29/19.55 [1937]~P3(a112,x19372,x19373)+~P3(a112,f6(a112),x19373)+P80(f51(f18(a112,f6(a112)),x19371))+~P80(f51(f18(a112,f6(a112)),f15(a112,f51(f51(f14(a112),x19373),x19371),x19372)))
% 19.29/19.55 [1949]E(x19491,f11(a114,x19492,x19493))+~P3(a114,f6(a114),x19493)+~P3(a114,x19492,f51(f51(f14(a114),x19493),f15(a114,x19491,f7(a114))))+~P80(f51(f18(a114,f51(f51(f14(a114),x19493),x19491)),x19492))
% 19.29/19.55 [1975]~P47(x19751)+~P80(f51(f18(x19751,x19752),f7(x19751)))+~P80(f51(f18(x19751,f6(x19751)),x19752))+P80(f51(f18(x19751,f51(f51(f20(x19751),x19752),f15(a114,x19753,f7(a114)))),x19752))
% 19.29/19.55 [2028]~P1(x20281)+P10(x20281,x20282)+~P3(a1,f6(a1),x20283)+~P80(f51(f18(a1,f28(x20281,f51(x20282,f35(x20282,x20281,x20283)))),x20283))
% 19.29/19.55 [2029]~P1(x20291)+P10(x20291,x20292)+~P3(a1,f6(a1),x20293)+~P80(f51(f18(a1,f28(x20291,f51(x20292,f40(x20292,x20293,x20291)))),x20293))
% 19.29/19.55 [1177]~P40(x11771)+~P3(x11771,x11774,x11773)+P3(x11771,x11772,x11773)+~P3(x11771,x11772,x11774)
% 19.29/19.55 [1178]~P30(x11781)+~P3(x11781,x11782,x11784)+P3(x11781,x11782,x11783)+~P3(x11781,x11784,x11783)
% 19.29/19.55 [1384]~P47(x13841)+~P3(x13841,x13842,x13844)+~P3(x13841,f6(x13841),x13843)+P3(x13841,x13842,f15(x13841,x13843,x13844))
% 19.29/19.55 [1268]~P40(x12681)+P3(x12681,x12682,x12683)+~P3(x12681,x12682,x12684)+~P80(f51(f18(x12681,x12684),x12683))
% 19.29/19.55 [1269]~P40(x12691)+P3(x12691,x12692,x12693)+~P3(x12691,x12694,x12693)+~P80(f51(f18(x12691,x12692),x12694))
% 19.29/19.55 [1270]~P30(x12701)+P3(x12701,x12702,x12703)+~P3(x12701,x12704,x12703)+~P80(f51(f18(x12701,x12702),x12704))
% 19.29/19.55 [1271]~P30(x12711)+P3(x12711,x12712,x12713)+~P3(x12711,x12712,x12714)+~P80(f51(f18(x12711,x12714),x12713))
% 19.29/19.55 [1381]~P40(x13811)+~P80(f51(f18(x13811,x13814),x13813))+P80(f51(f18(x13811,x13812),x13813))+~P80(f51(f18(x13811,x13812),x13814))
% 19.29/19.55 [1382]~P30(x13821)+~P80(f51(f18(x13821,x13822),x13824))+P80(f51(f18(x13821,x13822),x13823))+~P80(f51(f18(x13821,x13824),x13823))
% 19.29/19.55 [1423]~P40(x14231)+~P9(x14231,x14232)+P80(f51(f18(x14231,f51(x14232,x14233)),f51(x14232,x14234)))+~P80(f51(f18(a114,x14234),x14233))
% 19.29/19.55 [1424]~P40(x14241)+~P11(x14241,x14242)+P80(f51(f18(x14241,f51(x14242,x14243)),f51(x14242,x14244)))+~P80(f51(f18(a114,x14243),x14244))
% 19.29/19.55 [1432]~P36(x14321)+~P3(x14321,f6(x14321),x14323)+P3(x14321,x14322,f15(x14321,x14323,x14324))+~P80(f51(f18(x14321,x14322),x14324))
% 19.29/19.55 [1779]~P48(x17791)+~P3(x17791,x17792,f15(x17791,x17793,x17794))+~P3(x17791,f13(x17791,x17793,x17794),x17792)+P3(x17791,f10(x17791,f13(x17791,x17792,x17793)),x17794)
% 19.29/19.55 [1804]~P3(a1,x18044,x18042)+P3(a1,x18041,x18042)+~P3(a1,x18043,x18044)+~P3(a1,f10(a1,f13(a1,x18044,x18041)),f78(x18042,x18044,x18043))
% 19.29/19.55 [1805]~P3(a1,x18051,x18053)+P3(a1,x18051,x18052)+~P3(a1,x18053,x18054)+~P3(a1,f10(a1,f13(a1,x18053,x18052)),f78(x18054,x18053,x18051))
% 19.29/19.55 [1817]~P3(a1,x18174,x18172)+~P3(a1,x18173,x18174)+~P3(a1,f10(a1,f13(a1,x18174,x18171)),f57(x18172,x18174,x18173))+P80(f51(f18(a1,x18171),x18172))
% 19.29/19.55 [1818]~P3(a1,x18181,x18183)+~P3(a1,x18183,x18184)+~P3(a1,f10(a1,f13(a1,x18183,x18182)),f57(x18184,x18183,x18181))+P80(f51(f18(a1,x18181),x18182))
% 19.29/19.55 [1925]~E(x19254,x19252)+~P15(x19251)+P7(x19251,x19252,f6(f115(x19251)),x19253,x19254)+~E(x19253,f6(f115(x19251)))
% 19.29/19.55 [1926]~P15(x19261)+P7(x19261,f6(f115(x19261)),x19262,x19263,x19264)+~E(x19264,f6(f115(x19261)))+~E(x19263,f6(f115(x19261)))
% 19.29/19.55 [1013]~P55(x10132)+E(x10131,f6(x10132))+E(x10133,f29(x10132,x10134,x10131))+~E(f51(f51(f14(x10132),x10133),x10131),x10134)
% 19.29/19.55 [1015]~P55(x10152)+E(x10151,f6(x10152))+E(f29(x10152,x10153,x10151),x10154)+~E(x10153,f51(f51(f14(x10152),x10154),x10151))
% 19.29/19.55 [1022]~P55(x10222)+~E(f29(x10222,x10223,x10221),x10224)+E(x10221,f6(x10222))+E(x10223,f51(f51(f14(x10222),x10224),x10221))
% 19.29/19.55 [1023]~P55(x10232)+~E(x10233,f29(x10232,x10234,x10231))+E(x10231,f6(x10232))+E(f51(f51(f14(x10232),x10233),x10231),x10234)
% 19.29/19.55 [1254]~P47(x12543)+E(x12541,x12542)+~P3(x12543,f7(x12543),x12544)+~E(f51(f51(f20(x12543),x12544),x12541),f51(f51(f20(x12543),x12544),x12542))
% 19.29/19.55 [1477]~P36(x14771)+~P3(x14771,x14772,x14774)+P3(x14771,x14772,f15(x14771,x14773,x14774))+~P80(f51(f18(x14771,f6(x14771)),x14773))
% 19.29/19.55 [1513]~P47(x15131)+~P3(a114,x15133,x15134)+~P3(x15131,f7(x15131),x15132)+P3(x15131,f51(f51(f20(x15131),x15132),x15133),f51(f51(f20(x15131),x15132),x15134))
% 19.29/19.55 [1519]~P59(x15191)+~P3(x15191,x15194,x15192)+~P3(x15191,x15193,f6(x15191))+P3(x15191,f51(f51(f14(x15191),x15192),x15193),f51(f51(f14(x15191),x15194),x15193))
% 19.29/19.55 [1520]~P59(x15201)+~P3(x15201,x15204,x15203)+~P3(x15201,x15202,f6(x15201))+P3(x15201,f51(f51(f14(x15201),x15202),x15203),f51(f51(f14(x15201),x15202),x15204))
% 19.29/19.55 [1522]~P62(x15221)+~P3(x15221,x15223,x15224)+~P3(x15221,f6(x15221),x15222)+P3(x15221,f51(f51(f14(x15221),x15222),x15223),f51(f51(f14(x15221),x15222),x15224))
% 19.29/19.55 [1523]~P57(x15231)+~P3(x15231,x15233,x15234)+~P3(x15231,f6(x15231),x15232)+P3(x15231,f51(f51(f14(x15231),x15232),x15233),f51(f51(f14(x15231),x15232),x15234))
% 19.29/19.55 [1524]~P59(x15241)+~P3(x15241,x15242,x15244)+~P3(x15241,f6(x15241),x15243)+P3(x15241,f51(f51(f14(x15241),x15242),x15243),f51(f51(f14(x15241),x15244),x15243))
% 19.29/19.55 [1525]~P62(x15251)+~P3(x15251,x15252,x15254)+~P3(x15251,f6(x15251),x15253)+P3(x15251,f51(f51(f14(x15251),x15252),x15253),f51(f51(f14(x15251),x15254),x15253))
% 19.29/19.55 [1526]~P59(x15261)+~P3(x15261,x15263,x15264)+~P3(x15261,f6(x15261),x15262)+P3(x15261,f51(f51(f14(x15261),x15262),x15263),f51(f51(f14(x15261),x15262),x15264))
% 19.29/19.55 [1595]P3(x15951,x15953,x15952)+~P59(x15951)+P3(x15951,x15952,x15953)+~P3(x15951,f51(f51(f14(x15951),x15954),x15952),f51(f51(f14(x15951),x15954),x15953))
% 19.29/19.55 [1596]P3(x15961,x15963,x15962)+~P59(x15961)+P3(x15961,x15962,x15963)+~P3(x15961,f51(f51(f14(x15961),x15962),x15964),f51(f51(f14(x15961),x15963),x15964))
% 19.29/19.55 [1600]~P59(x16001)+P3(x16001,x16002,x16003)+P3(x16001,x16004,f6(x16001))+~P3(x16001,f51(f51(f14(x16001),x16002),x16004),f51(f51(f14(x16001),x16003),x16004))
% 19.29/19.55 [1601]~P59(x16011)+P3(x16011,x16012,x16013)+P3(x16011,x16014,f6(x16011))+~P3(x16011,f51(f51(f14(x16011),x16014),x16012),f51(f51(f14(x16011),x16014),x16013))
% 19.29/19.55 [1602]~P59(x16021)+P3(x16021,x16022,x16023)+P3(x16021,f6(x16021),x16024)+~P3(x16021,f51(f51(f14(x16021),x16024),x16023),f51(f51(f14(x16021),x16024),x16022))
% 19.29/19.55 [1603]~P59(x16031)+P3(x16031,x16032,x16033)+P3(x16031,f6(x16031),x16034)+~P3(x16031,f51(f51(f14(x16031),x16033),x16034),f51(f51(f14(x16031),x16032),x16034))
% 19.29/19.55 [1614]~P59(x16141)+P3(x16141,f6(x16141),x16142)+P3(x16141,x16142,f6(x16141))+~P3(x16141,f51(f51(f14(x16141),x16143),x16142),f51(f51(f14(x16141),x16144),x16142))
% 19.29/19.55 [1615]~P59(x16151)+P3(x16151,f6(x16151),x16152)+P3(x16151,x16152,f6(x16151))+~P3(x16151,f51(f51(f14(x16151),x16152),x16153),f51(f51(f14(x16151),x16152),x16154))
% 19.29/19.55 [1641]~P47(x16413)+P3(a114,x16411,x16412)+~P3(x16413,f7(x16413),x16414)+~P3(x16413,f51(f51(f20(x16413),x16414),x16411),f51(f51(f20(x16413),x16414),x16412))
% 19.29/19.55 [1644]~P59(x16441)+P3(x16441,x16442,x16443)+~P3(x16441,x16444,f6(x16441))+~P3(x16441,f51(f51(f14(x16441),x16444),x16443),f51(f51(f14(x16441),x16444),x16442))
% 19.29/19.55 [1645]~P59(x16451)+P3(x16451,x16452,x16453)+~P3(x16451,f6(x16451),x16454)+~P3(x16451,f51(f51(f14(x16451),x16454),x16452),f51(f51(f14(x16451),x16454),x16453))
% 19.29/19.55 [1646]~P39(x16462)+P3(f118(x16461,x16462),x16463,x16464)+P80(f51(f18(f118(x16461,x16462),x16464),x16463))+~P80(f51(f18(f118(x16461,x16462),x16463),x16464))
% 19.29/19.55 [1653]~P13(x16531)+~P3(a114,f22(x16531,x16533),x16534)+~P3(a114,f22(x16531,x16532),x16534)+P3(a114,f22(x16531,f13(f115(x16531),x16532,x16533)),x16534)
% 19.29/19.55 [1654]~P22(x16541)+~P3(a114,f22(x16541,x16543),x16544)+~P3(a114,f22(x16541,x16542),x16544)+P3(a114,f22(x16541,f15(f115(x16541),x16542,x16543)),x16544)
% 19.29/19.55 [1678]~P36(x16781)+~P80(f51(f18(x16781,x16782),x16783))+P80(f51(f18(x16781,x16782),f15(x16781,x16783,x16784)))+~P80(f51(f18(x16781,f6(x16781)),x16784))
% 19.29/19.55 [1679]~P36(x16791)+~P80(f51(f18(x16791,x16792),x16794))+P80(f51(f18(x16791,x16792),f15(x16791,x16793,x16794)))+~P80(f51(f18(x16791,f6(x16791)),x16793))
% 19.29/19.55 [1705]~P62(x17051)+P3(x17051,x17052,x17053)+~P3(x17051,f51(f51(f14(x17051),x17054),x17052),f51(f51(f14(x17051),x17054),x17053))+~P80(f51(f18(x17051,f6(x17051)),x17054))
% 19.29/19.55 [1706]~P63(x17061)+P3(x17061,x17062,x17063)+~P3(x17061,f51(f51(f14(x17061),x17064),x17062),f51(f51(f14(x17061),x17064),x17063))+~P80(f51(f18(x17061,f6(x17061)),x17064))
% 19.29/19.55 [1707]~P47(x17071)+P3(x17071,x17072,x17073)+~P3(x17071,f51(f51(f20(x17071),x17072),x17074),f51(f51(f20(x17071),x17073),x17074))+~P80(f51(f18(x17071,f6(x17071)),x17073))
% 19.29/19.55 [1708]~P62(x17081)+P3(x17081,x17082,x17083)+~P3(x17081,f51(f51(f14(x17081),x17082),x17084),f51(f51(f14(x17081),x17083),x17084))+~P80(f51(f18(x17081,f6(x17081)),x17084))
% 19.29/19.55 [1709]~P63(x17091)+P3(x17091,x17092,x17093)+~P3(x17091,f51(f51(f14(x17091),x17092),x17094),f51(f51(f14(x17091),x17093),x17094))+~P80(f51(f18(x17091,f6(x17091)),x17094))
% 19.29/19.55 [1829]~P1(x18292)+E(x18291,f6(x18292))+~P80(f51(f18(a1,x18293),f6(a1)))+~P80(f51(f18(a1,f28(x18292,x18291)),f51(f51(f14(a1),x18293),f28(x18292,x18294))))
% 19.29/19.55 [1627]~P15(x16272)+E(x16271,f6(x16272))+E(f29(x16272,f51(f51(f20(x16272),x16271),x16273),f51(f51(f20(x16272),x16271),x16274)),f51(f51(f20(x16272),x16271),f13(a114,x16273,x16274)))+~P80(f51(f18(a114,x16274),x16273))
% 19.29/19.55 [1848]~P47(x18481)+~P3(x18481,f7(x18481),x18482)+~P80(f51(f18(a114,x18483),x18484))+P80(f51(f18(x18481,f51(f51(f20(x18481),x18482),x18483)),f51(f51(f20(x18481),x18482),x18484)))
% 19.29/19.55 [1853]~P59(x18531)+~P3(x18531,x18532,f6(x18531))+~P80(f51(f18(x18531,x18534),x18533))+P80(f51(f18(x18531,f51(f51(f14(x18531),x18532),x18533)),f51(f51(f14(x18531),x18532),x18534)))
% 19.29/19.55 [1854]~P59(x18541)+~P3(x18541,f6(x18541),x18542)+~P80(f51(f18(x18541,x18543),x18544))+P80(f51(f18(x18541,f51(f51(f14(x18541),x18542),x18543)),f51(f51(f14(x18541),x18542),x18544)))
% 19.29/19.55 [1865]~P69(x18651)+~P80(f51(f18(x18651,x18654),x18653))+~P80(f51(f18(x18651,x18652),f6(x18651)))+P80(f51(f18(x18651,f51(f51(f14(x18651),x18652),x18653)),f51(f51(f14(x18651),x18652),x18654)))
% 19.29/19.55 [1866]~P69(x18661)+~P80(f51(f18(x18661,x18664),x18662))+~P80(f51(f18(x18661,x18663),f6(x18661)))+P80(f51(f18(x18661,f51(f51(f14(x18661),x18662),x18663)),f51(f51(f14(x18661),x18664),x18663)))
% 19.29/19.55 [1872]~P47(x18721)+~P80(f51(f18(a114,x18723),x18724))+~P80(f51(f18(x18721,f7(x18721)),x18722))+P80(f51(f18(x18721,f51(f51(f20(x18721),x18722),x18723)),f51(f51(f20(x18721),x18722),x18724)))
% 19.29/19.55 [1876]~P47(x18761)+~P80(f51(f18(x18761,x18762),x18764))+~P80(f51(f18(x18761,f6(x18761)),x18762))+P80(f51(f18(x18761,f51(f51(f20(x18761),x18762),x18763)),f51(f51(f20(x18761),x18764),x18763)))
% 19.29/19.55 [1877]~P71(x18771)+~P80(f51(f18(x18771,x18773),x18774))+~P80(f51(f18(x18771,f6(x18771)),x18772))+P80(f51(f18(x18771,f51(f51(f14(x18771),x18772),x18773)),f51(f51(f14(x18771),x18772),x18774)))
% 19.29/19.55 [1878]~P70(x18781)+~P80(f51(f18(x18781,x18783),x18784))+~P80(f51(f18(x18781,f6(x18781)),x18782))+P80(f51(f18(x18781,f51(f51(f14(x18781),x18782),x18783)),f51(f51(f14(x18781),x18782),x18784)))
% 19.29/19.55 [1879]~P71(x18791)+~P80(f51(f18(x18791,x18792),x18794))+~P80(f51(f18(x18791,f6(x18791)),x18793))+P80(f51(f18(x18791,f51(f51(f14(x18791),x18792),x18793)),f51(f51(f14(x18791),x18794),x18793)))
% 19.29/19.55 [1929]~P47(x19293)+~P3(x19293,f7(x19293),x19294)+P80(f51(f18(a114,x19291),x19292))+~P80(f51(f18(x19293,f51(f51(f20(x19293),x19294),x19291)),f51(f51(f20(x19293),x19294),x19292)))
% 19.29/19.55 [1930]~P59(x19301)+~P3(x19301,x19304,f6(x19301))+P80(f51(f18(x19301,x19302),x19303))+~P80(f51(f18(x19301,f51(f51(f14(x19301),x19304),x19303)),f51(f51(f14(x19301),x19304),x19302)))
% 19.29/19.55 [1931]~P59(x19311)+~P3(x19311,f6(x19311),x19314)+P80(f51(f18(x19311,x19312),x19313))+~P80(f51(f18(x19311,f51(f51(f14(x19311),x19314),x19312)),f51(f51(f14(x19311),x19314),x19313)))
% 19.29/19.55 [1932]~P62(x19321)+~P3(x19321,f6(x19321),x19324)+P80(f51(f18(x19321,x19322),x19323))+~P80(f51(f18(x19321,f51(f51(f14(x19321),x19324),x19322)),f51(f51(f14(x19321),x19324),x19323)))
% 19.29/19.55 [1933]~P62(x19331)+~P3(x19331,f6(x19331),x19334)+P80(f51(f18(x19331,x19332),x19333))+~P80(f51(f18(x19331,f51(f51(f14(x19331),x19332),x19334)),f51(f51(f14(x19331),x19333),x19334)))
% 19.29/19.55 [1988]~P40(x19881)+~P8(x19881,x19882)+P80(f51(f18(x19881,f51(x19882,f15(a114,x19884,f7(a114)))),f51(x19882,x19884)))+P80(f51(f18(x19881,f51(x19882,x19883)),f51(x19882,f15(a114,x19883,f7(a114)))))
% 19.29/19.55 [2030]~P47(x20301)+P80(f51(f18(x20301,x20302),x20303))+~P80(f51(f18(x20301,f6(x20301)),x20303))+~P80(f51(f18(x20301,f51(f51(f20(x20301),x20302),f15(a114,x20304,f7(a114)))),f51(f51(f20(x20301),x20303),f15(a114,x20304,f7(a114)))))
% 19.29/19.55 [1889]~P17(x18891)+~P3(x18891,f6(x18891),x18893)+~P80(f51(f18(x18891,x18892),f29(x18891,x18894,x18893)))+P80(f51(f18(x18891,f51(f51(f14(x18891),x18892),x18893)),x18894))
% 19.29/19.55 [1908]~P17(x19081)+~P3(x19081,f6(x19081),x19084)+P80(f51(f18(x19081,x19082),f29(x19081,x19083,x19084)))+~P80(f51(f18(x19081,f51(f51(f14(x19081),x19082),x19084)),x19083))
% 19.29/19.55 [1964]~P80(f51(x19641,x19644))+~P3(a114,x19642,f51(f51(f14(a114),x19643),f15(a114,x19644,f7(a114))))+P80(f51(x19641,f11(a114,x19642,x19643)))+~P80(f51(f18(a114,f51(f51(f14(a114),x19643),x19644)),x19642))
% 19.29/19.55 [1977]~P13(x19771)+~P80(f51(f18(a114,f22(x19771,x19773)),x19774))+~P80(f51(f18(a114,f22(x19771,x19772)),x19774))+P80(f51(f18(a114,f22(x19771,f13(f115(x19771),x19772,x19773))),x19774))
% 19.29/19.55 [1978]~P22(x19781)+~P80(f51(f18(a114,f22(x19781,x19783)),x19784))+~P80(f51(f18(a114,f22(x19781,x19782)),x19784))+P80(f51(f18(a114,f22(x19781,f15(f115(x19781),x19782,x19783))),x19784))
% 19.29/19.55 [2037]~P1(x20371)+~P3(a1,f6(a1),x20374)+P3(a1,f28(x20371,f51(x20372,x20373)),f51(f4(a114),f15(a114,f49(x20372,x20371),f7(a114))))+~P80(f51(f18(a1,f28(x20371,f51(x20372,f50(x20372,x20371,x20374)))),x20374))
% 19.29/19.55 [2040]~P1(x20401)+~P3(a1,f6(a1),x20404)+P80(f51(f18(a1,f28(x20401,f51(x20402,x20403))),f51(f4(a114),f15(a114,f61(x20402,x20401),f7(a114)))))+~P80(f51(f18(a1,f28(x20401,f51(x20402,f62(x20402,x20401,x20404)))),x20404))
% 19.29/19.55 [1100]~P13(x11005)+E(x11001,x11002)+~E(x11003,x11004)+~E(f13(x11005,x11003,x11004),f13(x11005,x11001,x11002))
% 19.29/19.55 [1323]~P12(x13231)+~P3(x13231,x13234,x13235)+P3(x13231,x13232,x13233)+~E(f13(x13231,x13234,x13235),f13(x13231,x13232,x13233))
% 19.29/19.55 [1515]~P35(x15151)+~P3(x15151,x15153,x15155)+~P3(x15151,x15152,x15154)+P3(x15151,f15(x15151,x15152,x15153),f15(x15151,x15154,x15155))
% 19.29/19.55 [1430]~P12(x14301)+~E(f13(x14301,x14304,x14305),f13(x14301,x14302,x14303))+~P80(f51(f18(x14301,x14304),x14305))+P80(f51(f18(x14301,x14302),x14303))
% 19.29/19.55 [1566]~P35(x15661)+~P3(x15661,x15663,x15665)+P3(x15661,f15(x15661,x15662,x15663),f15(x15661,x15664,x15665))+~P80(f51(f18(x15661,x15662),x15664))
% 19.29/19.55 [1567]~P35(x15671)+~P3(x15671,x15672,x15674)+P3(x15671,f15(x15671,x15672,x15673),f15(x15671,x15674,x15675))+~P80(f51(f18(x15671,x15673),x15675))
% 19.29/19.55 [1714]~P1(x17141)+~P3(a1,f28(x17141,x17143),x17145)+~P3(a1,f28(x17141,x17142),x17144)+P3(a1,f28(x17141,f15(x17141,x17142,x17143)),f15(a1,x17144,x17145))
% 19.29/19.55 [1871]~P34(x18711)+~P80(f51(f18(x18711,x18713),x18715))+~P80(f51(f18(x18711,x18712),x18714))+P80(f51(f18(x18711,f15(x18711,x18712,x18713)),f15(x18711,x18714,x18715)))
% 19.29/19.55 [1993]~P15(x19932)+~P7(x19932,x19934,x19933,x19931,x19935)+E(x19931,f6(f115(x19932)))+~E(x19933,f6(f115(x19932)))
% 19.29/19.55 [1733]~P48(x17331)+~P3(x17331,f10(x17331,x17332),x17334)+~P3(x17331,f10(x17331,x17333),x17335)+P3(x17331,f51(f51(f14(x17331),f10(x17331,x17332)),f10(x17331,x17333)),f51(f51(f14(x17331),x17334),x17335))
% 19.29/19.55 [1696]~P44(x16961)+~P3(a1,f28(x16961,x16963),x16965)+~P3(a1,f28(x16961,x16962),x16964)+P3(a1,f28(x16961,f51(f51(f14(x16961),x16962),x16963)),f51(f51(f14(a1),x16964),x16965))
% 19.29/19.55 [1794]~P79(x17945)+E(x17941,x17942)+E(x17943,x17944)+~E(f15(x17945,f51(f51(f14(x17945),x17943),x17941),f51(f51(f14(x17945),x17944),x17942)),f15(x17945,f51(f51(f14(x17945),x17943),x17942),f51(f51(f14(x17945),x17944),x17941)))
% 19.29/19.55 [2035]E(x20351,x20352)+~P7(x20353,x20354,x20355,x20356,x20351)+~P7(x20353,x20354,x20355,x20357,x20352)+~P15(x20353)
% 19.29/19.55 [2036]E(x20361,x20362)+~P7(x20363,x20364,x20365,x20362,x20366)+~P7(x20363,x20364,x20365,x20361,x20367)+~P15(x20363)
% 19.29/19.55 [2048]~P15(x20481)+~P7(x20481,x20482,x20483,x20488,x20487)+~P7(x20481,x20488,x20484,x20485,x20486)+P7(x20481,x20482,f51(f51(f14(f115(x20481)),x20483),x20484),x20485,f15(f115(x20481),f51(f51(f14(f115(x20481)),x20483),x20486),x20487))
% 19.29/19.55 [1913]~E(f28(a2,x19131),f7(a1))+P3(a1,f28(a2,f15(a2,x19131,a9)),f7(a1))+P3(a1,f28(a2,f13(a2,x19131,a9)),f7(a1))+P3(a1,f28(a2,f13(a2,x19131,f7(a2))),f7(a1))+P3(a1,f28(a2,f15(a2,x19131,f7(a2))),f7(a1))
% 19.29/19.55 [1387]E(x13871,f91(x13872,x13873))+~P3(a1,f6(a1),x13872)+~P3(a1,f6(a1),x13871)+~P3(a114,f6(a114),x13873)+~E(f51(f51(f20(a1),x13871),x13873),x13872)
% 19.29/19.55 [1509]~P36(x15092)+~E(f15(x15092,x15093,x15091),f6(x15092))+E(x15091,f6(x15092))+~P80(f51(f18(x15092,f6(x15092)),x15093))+~P80(f51(f18(x15092,f6(x15092)),x15091))
% 19.29/19.55 [1510]~P36(x15102)+~E(f15(x15102,x15101,x15103),f6(x15102))+E(x15101,f6(x15102))+~P80(f51(f18(x15102,f6(x15102)),x15103))+~P80(f51(f18(x15102,f6(x15102)),x15101))
% 19.29/19.55 [1867]~P48(x18671)+~P80(f51(f18(x18671,x18672),f7(x18671)))+~P80(f51(f18(x18671,f6(x18671)),x18672))+~P80(f51(f18(x18671,f6(x18671)),x18673))+P80(f51(f18(x18671,f51(f51(f14(x18671),x18672),x18673)),x18673))
% 19.29/19.55 [1868]~P48(x18681)+~P80(f51(f18(x18681,x18683),f7(x18681)))+~P80(f51(f18(x18681,f6(x18681)),x18683))+~P80(f51(f18(x18681,f6(x18681)),x18682))+P80(f51(f18(x18681,f51(f51(f14(x18681),x18682),x18683)),x18682))
% 19.29/19.55 [1652]~P17(x16521)+P3(x16521,f6(x16521),x16522)+P3(x16521,x16522,f6(x16521))+P80(f51(f18(x16521,x16523),f29(x16521,x16524,x16522)))+~P80(f51(f18(x16521,x16523),f6(x16521)))
% 19.29/19.55 [1744]~P17(x17441)+P3(x17441,f6(x17441),x17442)+P3(x17441,x17442,f6(x17441))+~P80(f51(f18(x17441,x17443),f29(x17441,x17444,x17442)))+P80(f51(f18(x17441,x17443),f6(x17441)))
% 19.29/19.55 [1623]~P47(x16231)+~P3(a114,x16234,x16233)+~P3(x16231,x16232,f7(x16231))+~P3(x16231,f6(x16231),x16232)+P3(x16231,f51(f51(f20(x16231),x16232),x16233),f51(f51(f20(x16231),x16232),x16234))
% 19.29/19.55 [1682]~P47(x16821)+~P3(x16821,x16822,x16824)+~P3(a114,f6(a114),x16823)+P3(x16821,f51(f51(f20(x16821),x16822),x16823),f51(f51(f20(x16821),x16824),x16823))+~P80(f51(f18(x16821,f6(x16821)),x16822))
% 19.29/19.55 [1813]~P47(x18133)+E(x18131,x18132)+~E(f51(f51(f20(x18133),x18131),f15(a114,x18134,f7(a114))),f51(f51(f20(x18133),x18132),f15(a114,x18134,f7(a114))))+~P80(f51(f18(x18133,f6(x18133)),x18132))+~P80(f51(f18(x18133,f6(x18133)),x18131))
% 19.29/19.55 [1845]~P17(x18451)+~P3(x18451,x18452,f6(x18451))+P3(x18451,f6(x18451),x18452)+P80(f51(f18(x18451,x18453),f29(x18451,x18454,x18452)))+~P80(f51(f18(x18451,x18454),f51(f51(f14(x18451),x18453),x18452)))
% 19.29/19.55 [1847]~P17(x18471)+~P3(x18471,x18472,f6(x18471))+P3(x18471,f6(x18471),x18472)+~P80(f51(f18(x18471,x18474),f29(x18471,x18473,x18472)))+P80(f51(f18(x18471,x18473),f51(f51(f14(x18471),x18474),x18472)))
% 19.29/19.55 [1863]~P17(x18631)+P3(x18631,f6(x18631),x18632)+P80(f51(f18(x18631,x18633),f29(x18631,x18634,x18632)))+~P80(f51(f18(x18631,x18633),f6(x18631)))+~P80(f51(f18(x18631,x18634),f51(f51(f14(x18631),x18633),x18632)))
% 19.29/19.55 [1904]~P47(x19041)+~P80(f51(f18(x19041,x19042),f7(x19041)))+~P80(f51(f18(a114,x19044),x19043))+~P80(f51(f18(x19041,f6(x19041)),x19042))+P80(f51(f18(x19041,f51(f51(f20(x19041),x19042),x19043)),f51(f51(f20(x19041),x19042),x19044)))
% 19.29/19.55 [1894]~P3(a112,f6(a112),x18943)+~P80(f51(x18941,x18944))+P80(f51(x18941,f90(x18942,x18941,x18943)))+~P80(f51(f18(a112,f6(a112)),x18942))+P80(f51(x18941,f13(a112,x18944,f51(f51(f14(a112),x18942),x18943))))
% 19.29/19.55 [1895]~P3(a112,f6(a112),x18953)+~P80(f51(x18951,x18954))+P80(f51(x18951,f93(x18952,x18951,x18953)))+~P80(f51(f18(a112,f6(a112)),x18952))+P80(f51(x18951,f15(a112,x18954,f51(f51(f14(a112),x18952),x18953))))
% 19.29/19.55 [1936]~P17(x19361)+P3(x19361,x19362,f6(x19361))+P80(f51(f18(x19361,x19363),f29(x19361,x19364,x19362)))+~P80(f51(f18(x19361,x19363),f6(x19361)))+~P80(f51(f18(x19361,f51(f51(f14(x19361),x19363),x19362)),x19364))
% 19.29/19.55 [1970]~P17(x19701)+~P3(x19701,x19704,f6(x19701))+P80(f51(f18(x19701,x19702),f29(x19701,x19703,x19704)))+~P80(f51(f18(x19701,x19703),f51(f51(f14(x19701),x19702),x19704)))+~P80(f51(f18(x19701,f51(f51(f14(x19701),x19702),x19704)),x19703))
% 19.29/19.55 [1974]~P17(x19741)+~P80(f51(f18(x19741,x19742),f6(x19741)))+P80(f51(f18(x19741,x19742),f29(x19741,x19743,x19744)))+~P80(f51(f18(x19741,x19743),f51(f51(f14(x19741),x19742),x19744)))+~P80(f51(f18(x19741,f51(f51(f14(x19741),x19742),x19744)),x19743))
% 19.29/19.55 [1991]~P3(a112,f6(a112),x19914)+~P80(f51(x19911,x19912))+~P80(f51(f18(a112,f6(a112)),x19913))+~P80(f51(x19911,f13(a112,f90(x19913,x19911,x19914),x19914)))+P80(f51(x19911,f13(a112,x19912,f51(f51(f14(a112),x19913),x19914))))
% 19.29/19.55 [1992]~P3(a112,f6(a112),x19924)+~P80(f51(x19921,x19922))+~P80(f51(f18(a112,f6(a112)),x19923))+~P80(f51(x19921,f15(a112,f93(x19923,x19921,x19924),x19924)))+P80(f51(x19921,f15(a112,x19922,f51(f51(f14(a112),x19923),x19924))))
% 19.29/19.55 [2002]~P15(x20022)+~P7(x20022,x20024,x20023,x20025,x20021)+P3(a114,f22(x20022,x20021),f22(x20022,x20023))+E(x20021,f6(f115(x20022)))+E(x20023,f6(f115(x20022)))
% 19.29/19.55 [1969]~P1(x19694)+~P39(x19691)+P3(a1,f28(x19694,f51(x19693,x19695)),f15(a1,f7(a1),f28(x19694,f51(x19693,x19692))))+P80(f51(f18(x19691,x19692),f102(x19693,x19692,x19691,x19694)))+~P80(f51(f18(x19691,x19692),x19695))
% 19.29/19.55 [1755]~P3(a114,x17555,x17551)+E(x17551,f6(a114))+P80(f51(x17552,x17553))+~P80(f51(x17552,f11(a114,x17554,x17551)))+~E(x17554,f15(a114,f51(f51(f14(a114),x17551),x17553),x17555))
% 19.29/19.55 [2053]~P1(x20531)+~P39(x20535)+P3(a1,f28(x20531,f51(x20532,x20533)),f15(a1,f7(a1),f28(x20531,f51(x20532,x20534))))+~P3(a1,f28(x20531,f13(x20531,f51(x20532,x20534),f51(x20532,f102(x20532,x20534,x20535,x20531)))),f7(a1))+~P80(f51(f18(x20535,x20534),x20533))
% 19.29/19.55 [1966]~P15(x19662)+P7(x19662,x19663,x19661,x19664,x19665)+E(x19661,f6(f115(x19662)))+~E(x19665,f6(f115(x19662)))+~E(x19663,f15(f115(x19662),f51(f51(f14(f115(x19662)),x19664),x19661),x19665))
% 19.29/19.55 [1967]~P15(x19671)+P7(x19671,x19672,x19673,x19674,x19675)+~E(x19674,f6(f115(x19671)))+~E(x19675,f6(f115(x19671)))+~E(x19672,f15(f115(x19671),f51(f51(f14(f115(x19671)),x19674),x19673),x19675))
% 19.29/19.55 [1968]~P15(x19681)+P7(x19681,x19682,x19683,x19684,x19685)+~E(x19684,f6(f115(x19681)))+~E(x19683,f6(f115(x19681)))+~E(x19682,f15(f115(x19681),f51(f51(f14(f115(x19681)),x19684),x19683),x19685))
% 19.29/19.55 [1980]~P15(x19802)+P7(x19802,x19803,x19801,x19804,x19805)+~P3(a114,f22(x19802,x19805),f22(x19802,x19801))+E(x19801,f6(f115(x19802)))+~E(x19803,f15(f115(x19802),f51(f51(f14(f115(x19802)),x19804),x19801),x19805))
% 19.29/19.55 [1981]~P15(x19811)+P7(x19811,x19812,x19813,x19814,x19815)+~P3(a114,f22(x19811,x19815),f22(x19811,x19813))+~E(x19814,f6(f115(x19811)))+~E(x19812,f15(f115(x19811),f51(f51(f14(f115(x19811)),x19814),x19813),x19815))
% 19.29/19.55 [2020]~P3(a112,x20203,x20204)+~P3(a112,x20203,x20205)+P80(f51(f18(a112,x20201),x20202))+~P80(f51(f18(a112,x20204),f6(a112)))+~P80(f51(f18(a112,f15(a112,f51(f51(f14(a112),x20203),x20202),x20205)),f15(a112,f51(f51(f14(a112),x20203),x20201),x20204)))
% 19.29/19.55 [2022]~P3(a112,x20223,x20224)+~P3(a112,x20225,x20224)+P80(f51(f18(a112,x20221),x20222))+~P80(f51(f18(a112,f6(a112)),x20225))+~P80(f51(f18(a112,f15(a112,f51(f51(f14(a112),x20224),x20221),x20225)),f15(a112,f51(f51(f14(a112),x20224),x20222),x20223)))
% 19.29/19.55 [1586]~P79(x15864)+E(x15861,x15862)+~E(x15865,x15866)+E(x15863,f6(x15864))+~E(f15(x15864,x15865,f51(f51(f14(x15864),x15863),x15861)),f15(x15864,x15866,f51(f51(f14(x15864),x15863),x15862)))
% 19.29/19.55 [970]~P43(x9702)+~P61(x9702)+~P66(x9702)+~P78(x9702)+E(x9701,f6(x9702))+~E(f51(f51(f20(x9702),x9701),x9703),f6(x9702))
% 19.29/19.55 [971]~P43(x9712)+~P61(x9712)+~P66(x9712)+~P78(x9712)+~E(x9711,f6(a114))+~E(f51(f51(f20(x9712),x9713),x9711),f6(x9712))
% 19.29/19.55 [1468]~P36(x14681)+~E(x14683,f6(x14681))+~E(x14682,f6(x14681))+E(f15(x14681,x14682,x14683),f6(x14681))+~P80(f51(f18(x14681,f6(x14681)),x14683))+~P80(f51(f18(x14681,f6(x14681)),x14682))
% 19.29/19.55 [1670]~P47(x16703)+E(x16701,x16702)+~P3(a114,f6(a114),x16704)+~E(f51(f51(f20(x16703),x16701),x16704),f51(f51(f20(x16703),x16702),x16704))+~P80(f51(f18(x16703,f6(x16703)),x16702))+~P80(f51(f18(x16703,f6(x16703)),x16701))
% 19.29/19.55 [1636]~P3(a112,x16361,x16364)+E(f11(a112,x16362,x16361),x16363)+E(x16361,f6(a112))+P3(a112,f6(a112),x16361)+~E(x16362,f15(a112,f51(f51(f14(a112),x16361),x16363),x16364))+~P80(f51(f18(a112,x16364),f6(a112)))
% 19.29/19.55 [1669]~P3(a112,x16694,x16691)+E(f11(a112,x16692,x16691),x16693)+E(x16691,f6(a112))+~P3(a112,f6(a112),x16691)+~E(x16692,f15(a112,f51(f51(f14(a112),x16691),x16693),x16694))+~P80(f51(f18(a112,f6(a112)),x16694))
% 19.29/19.55 [1751]~P62(x17511)+~P3(x17511,x17513,x17515)+~P3(x17511,x17512,x17514)+~P3(x17511,f6(x17511),x17514)+P3(x17511,f51(f51(f14(x17511),x17512),x17513),f51(f51(f14(x17511),x17514),x17515))+~P80(f51(f18(x17511,f6(x17511)),x17513))
% 19.29/19.55 [1770]~P62(x17701)+~P3(x17701,x17703,x17705)+~P3(x17701,f6(x17701),x17702)+P3(x17701,f51(f51(f14(x17701),x17702),x17703),f51(f51(f14(x17701),x17704),x17705))+~P80(f51(f18(x17701,x17702),x17704))+~P80(f51(f18(x17701,f6(x17701)),x17703))
% 19.29/19.55 [1771]~P62(x17711)+~P3(x17711,x17712,x17714)+~P3(x17711,f6(x17711),x17713)+P3(x17711,f51(f51(f14(x17711),x17712),x17713),f51(f51(f14(x17711),x17714),x17715))+~P80(f51(f18(x17711,x17713),x17715))+~P80(f51(f18(x17711,f6(x17711)),x17712))
% 19.29/19.55 [1775]~P62(x17751)+~P3(x17751,x17753,x17755)+~P3(x17751,x17752,x17754)+P3(x17751,f51(f51(f14(x17751),x17752),x17753),f51(f51(f14(x17751),x17754),x17755))+~P80(f51(f18(x17751,f6(x17751)),x17753))+~P80(f51(f18(x17751,f6(x17751)),x17752))
% 19.29/19.55 [1713]~P81(x17131,x17134,x17133)+~P3(a112,x17134,x17135)+~P3(a112,x17134,f6(a112))+P80(f51(x17131,x17132))+~E(x17133,f15(a112,f51(f51(f14(a112),x17134),x17132),x17135))+~P80(f51(f18(a112,x17135),f6(a112)))
% 19.29/19.55 [1720]~P81(x17201,x17204,x17203)+~P3(a112,x17205,x17204)+~P3(a112,f6(a112),x17204)+P80(f51(x17201,x17202))+~E(x17203,f15(a112,f51(f51(f14(a112),x17204),x17202),x17205))+~P80(f51(f18(a112,f6(a112)),x17205))
% 19.29/19.55 [1939]~P71(x19391)+~P80(f51(f18(x19391,x19393),x19395))+~P80(f51(f18(x19391,x19392),x19394))+~P80(f51(f18(x19391,f6(x19391)),x19393))+~P80(f51(f18(x19391,f6(x19391)),x19394))+P80(f51(f18(x19391,f51(f51(f14(x19391),x19392),x19393)),f51(f51(f14(x19391),x19394),x19395)))
% 19.29/19.55 [1940]~P71(x19401)+~P80(f51(f18(x19401,x19403),x19405))+~P80(f51(f18(x19401,x19402),x19404))+~P80(f51(f18(x19401,f6(x19401)),x19403))+~P80(f51(f18(x19401,f6(x19401)),x19402))+P80(f51(f18(x19401,f51(f51(f14(x19401),x19402),x19403)),f51(f51(f14(x19401),x19404),x19405)))
% 19.29/19.55 [1769]~P40(x17691)+~P8(x17691,x17692)+P80(f51(f18(x17691,f51(x17692,x17693)),f51(x17692,x17694)))+P80(f51(f18(x17691,f51(x17692,x17695)),f51(x17692,x17696)))+~P80(f51(f18(a114,x17694),x17693))+~P80(f51(f18(a114,x17695),x17696))
% 19.29/19.55 [926]~P43(x9262)+~P61(x9262)+~P66(x9262)+~P78(x9262)+~E(x9263,f6(x9262))+E(x9261,f6(a114))+E(f51(f51(f20(x9262),x9263),x9261),f6(x9262))
% 19.29/19.55 [1756]~P3(a112,x17564,x17561)+~P3(a112,x17561,x17564)+E(f11(a112,x17562,x17561),x17563)+E(x17561,f6(a112))+~E(x17562,f15(a112,f51(f51(f14(a112),x17561),x17563),x17564))+~P80(f51(f18(a112,x17564),f6(a112)))+~P80(f51(f18(a112,f6(a112)),x17564))
% 19.29/19.55 [1912]~P65(x19121)+~P3(x19121,x19125,x19126)+~P3(x19121,x19123,x19126)+~E(f15(x19121,x19122,x19124),f7(x19121))+P3(x19121,f15(x19121,f51(f51(f14(x19121),x19122),x19123),f51(f51(f14(x19121),x19124),x19125)),x19126)+~P80(f51(f18(x19121,f6(x19121)),x19124))+~P80(f51(f18(x19121,f6(x19121)),x19122))
% 19.29/19.55 [1959]~P3(a112,x19594,x19593)+~P3(a112,f6(a112),x19595)+~P3(a112,f15(a112,f51(f51(f14(a112),x19595),x19591),x19596),f6(a112))+~P80(f51(f18(a112,x19595),x19593))+P80(f51(f18(a112,x19591),x19592))+~E(f15(a112,f51(f51(f14(a112),x19593),x19592),x19594),f15(a112,f51(f51(f14(a112),x19595),x19591),x19596))+~P80(f51(f18(a112,f6(a112)),x19596))
% 19.29/19.55 [1999]~P3(a112,x19996,x19995)+~P3(a112,f6(a112),x19995)+~P80(f51(f18(a112,x19995),x19993))+P80(f51(f18(a112,x19991),x19992))+~E(f15(a112,f51(f51(f14(a112),x19993),x19991),x19994),f15(a112,f51(f51(f14(a112),x19995),x19992),x19996))+~P80(f51(f18(a112,f6(a112)),x19994))+~P80(f51(f18(a112,f6(a112)),f15(a112,f51(f51(f14(a112),x19995),x19992),x19996)))
% 19.29/19.55 [2019]~P64(x20191)+~E(f15(x20191,x20192,x20194),f7(x20191))+~P80(f51(f18(x20191,x20195),x20196))+~P80(f51(f18(x20191,x20193),x20196))+~P80(f51(f18(x20191,f6(x20191)),x20194))+~P80(f51(f18(x20191,f6(x20191)),x20192))+P80(f51(f18(x20191,f15(x20191,f51(f51(f14(x20191),x20192),x20193),f51(f51(f14(x20191),x20194),x20195))),x20196))
% 19.29/19.55 %EqnAxiom
% 19.29/19.55 [1]E(x11,x11)
% 19.29/19.55 [2]E(x22,x21)+~E(x21,x22)
% 19.29/19.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 19.29/19.55 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 19.29/19.55 [5]~E(x51,x52)+E(f5(x51),f5(x52))
% 19.29/19.55 [6]~E(x61,x62)+E(f51(x61,x63),f51(x62,x63))
% 19.29/19.55 [7]~E(x71,x72)+E(f51(x73,x71),f51(x73,x72))
% 19.29/19.55 [8]~E(x81,x82)+E(f14(x81),f14(x82))
% 19.29/19.55 [9]~E(x91,x92)+E(f6(x91),f6(x92))
% 19.29/19.55 [10]~E(x101,x102)+E(f17(x101),f17(x102))
% 19.29/19.55 [11]~E(x111,x112)+E(f18(x111,x113),f18(x112,x113))
% 19.29/19.55 [12]~E(x121,x122)+E(f18(x123,x121),f18(x123,x122))
% 19.29/19.55 [13]~E(x131,x132)+E(f7(x131),f7(x132))
% 19.29/19.55 [14]~E(x141,x142)+E(f13(x141,x143,x144),f13(x142,x143,x144))
% 19.29/19.55 [15]~E(x151,x152)+E(f13(x153,x151,x154),f13(x153,x152,x154))
% 19.29/19.55 [16]~E(x161,x162)+E(f13(x163,x164,x161),f13(x163,x164,x162))
% 19.29/19.55 [17]~E(x171,x172)+E(f41(x171,x173),f41(x172,x173))
% 19.29/19.55 [18]~E(x181,x182)+E(f41(x183,x181),f41(x183,x182))
% 19.29/19.55 [19]~E(x191,x192)+E(f15(x191,x193,x194),f15(x192,x193,x194))
% 19.29/19.55 [20]~E(x201,x202)+E(f15(x203,x201,x204),f15(x203,x202,x204))
% 19.29/19.55 [21]~E(x211,x212)+E(f15(x213,x214,x211),f15(x213,x214,x212))
% 19.29/19.55 [22]~E(x221,x222)+E(f27(x221),f27(x222))
% 19.29/19.55 [23]~E(x231,x232)+E(f11(x231,x233,x234),f11(x232,x233,x234))
% 19.29/19.55 [24]~E(x241,x242)+E(f11(x243,x241,x244),f11(x243,x242,x244))
% 19.29/19.55 [25]~E(x251,x252)+E(f11(x253,x254,x251),f11(x253,x254,x252))
% 19.29/19.55 [26]~E(x261,x262)+E(f20(x261),f20(x262))
% 19.29/19.55 [27]~E(x271,x272)+E(f22(x271,x273),f22(x272,x273))
% 19.29/19.55 [28]~E(x281,x282)+E(f22(x283,x281),f22(x283,x282))
% 19.29/19.55 [29]~E(x291,x292)+E(f10(x291,x293),f10(x292,x293))
% 19.29/19.55 [30]~E(x301,x302)+E(f10(x303,x301),f10(x303,x302))
% 19.29/19.55 [31]~E(x311,x312)+E(f115(x311),f115(x312))
% 19.29/19.55 [32]~E(x321,x322)+E(f95(x321,x323),f95(x322,x323))
% 19.29/19.55 [33]~E(x331,x332)+E(f95(x333,x331),f95(x333,x332))
% 19.29/19.55 [34]~E(x341,x342)+E(f105(x341,x343,x344),f105(x342,x343,x344))
% 19.29/19.55 [35]~E(x351,x352)+E(f105(x353,x351,x354),f105(x353,x352,x354))
% 19.29/19.55 [36]~E(x361,x362)+E(f105(x363,x364,x361),f105(x363,x364,x362))
% 19.29/19.55 [37]~E(x371,x372)+E(f89(x371,x373),f89(x372,x373))
% 19.29/19.55 [38]~E(x381,x382)+E(f89(x383,x381),f89(x383,x382))
% 19.29/19.55 [39]~E(x391,x392)+E(f107(x391,x393,x394),f107(x392,x393,x394))
% 19.29/19.55 [40]~E(x401,x402)+E(f107(x403,x401,x404),f107(x403,x402,x404))
% 19.29/19.55 [41]~E(x411,x412)+E(f107(x413,x414,x411),f107(x413,x414,x412))
% 19.29/19.55 [42]~E(x421,x422)+E(f83(x421),f83(x422))
% 19.29/19.55 [43]~E(x431,x432)+E(f28(x431,x433),f28(x432,x433))
% 19.29/19.55 [44]~E(x441,x442)+E(f28(x443,x441),f28(x443,x442))
% 19.29/19.55 [45]~E(x451,x452)+E(f61(x451,x453),f61(x452,x453))
% 19.29/19.55 [46]~E(x461,x462)+E(f61(x463,x461),f61(x463,x462))
% 19.29/19.55 [47]~E(x471,x472)+E(f109(x471,x473,x474),f109(x472,x473,x474))
% 19.29/19.55 [48]~E(x481,x482)+E(f109(x483,x481,x484),f109(x483,x482,x484))
% 19.29/19.55 [49]~E(x491,x492)+E(f109(x493,x494,x491),f109(x493,x494,x492))
% 19.29/19.55 [50]~E(x501,x502)+E(f29(x501,x503,x504),f29(x502,x503,x504))
% 19.29/19.55 [51]~E(x511,x512)+E(f29(x513,x511,x514),f29(x513,x512,x514))
% 19.29/19.55 [52]~E(x521,x522)+E(f29(x523,x524,x521),f29(x523,x524,x522))
% 19.29/19.55 [53]~E(x531,x532)+E(f8(x531,x533),f8(x532,x533))
% 19.29/19.55 [54]~E(x541,x542)+E(f8(x543,x541),f8(x543,x542))
% 19.29/19.55 [55]~E(x551,x552)+E(f81(x551),f81(x552))
% 19.29/19.55 [56]~E(x561,x562)+E(f21(x561,x563,x564),f21(x562,x563,x564))
% 19.29/19.55 [57]~E(x571,x572)+E(f21(x573,x571,x574),f21(x573,x572,x574))
% 19.29/19.55 [58]~E(x581,x582)+E(f21(x583,x584,x581),f21(x583,x584,x582))
% 19.29/19.55 [59]~E(x591,x592)+E(f102(x591,x593,x594,x595),f102(x592,x593,x594,x595))
% 19.29/19.55 [60]~E(x601,x602)+E(f102(x603,x601,x604,x605),f102(x603,x602,x604,x605))
% 19.29/19.55 [61]~E(x611,x612)+E(f102(x613,x614,x611,x615),f102(x613,x614,x612,x615))
% 19.29/19.55 [62]~E(x621,x622)+E(f102(x623,x624,x625,x621),f102(x623,x624,x625,x622))
% 19.29/19.55 [63]~E(x631,x632)+E(f55(x631),f55(x632))
% 19.29/19.55 [64]~E(x641,x642)+E(f90(x641,x643,x644),f90(x642,x643,x644))
% 19.29/19.55 [65]~E(x651,x652)+E(f90(x653,x651,x654),f90(x653,x652,x654))
% 19.29/19.55 [66]~E(x661,x662)+E(f90(x663,x664,x661),f90(x663,x664,x662))
% 19.29/19.55 [67]~E(x671,x672)+E(f58(x671,x673),f58(x672,x673))
% 19.29/19.55 [68]~E(x681,x682)+E(f58(x683,x681),f58(x683,x682))
% 19.29/19.55 [69]~E(x691,x692)+E(f103(x691,x693),f103(x692,x693))
% 19.29/19.55 [70]~E(x701,x702)+E(f103(x703,x701),f103(x703,x702))
% 19.29/19.55 [71]~E(x711,x712)+E(f118(x711,x713),f118(x712,x713))
% 19.29/19.55 [72]~E(x721,x722)+E(f118(x723,x721),f118(x723,x722))
% 19.29/19.55 [73]~E(x731,x732)+E(f110(x731,x733,x734),f110(x732,x733,x734))
% 19.29/19.55 [74]~E(x741,x742)+E(f110(x743,x741,x744),f110(x743,x742,x744))
% 19.29/19.55 [75]~E(x751,x752)+E(f110(x753,x754,x751),f110(x753,x754,x752))
% 19.29/19.55 [76]~E(x761,x762)+E(f12(x761,x763),f12(x762,x763))
% 19.29/19.55 [77]~E(x771,x772)+E(f12(x773,x771),f12(x773,x772))
% 19.29/19.55 [78]~E(x781,x782)+E(f42(x781,x783),f42(x782,x783))
% 19.29/19.55 [79]~E(x791,x792)+E(f42(x793,x791),f42(x793,x792))
% 19.29/19.55 [80]~E(x801,x802)+E(f98(x801,x803,x804),f98(x802,x803,x804))
% 19.29/19.55 [81]~E(x811,x812)+E(f98(x813,x811,x814),f98(x813,x812,x814))
% 19.29/19.55 [82]~E(x821,x822)+E(f98(x823,x824,x821),f98(x823,x824,x822))
% 19.29/19.55 [83]~E(x831,x832)+E(f85(x831,x833),f85(x832,x833))
% 19.29/19.55 [84]~E(x841,x842)+E(f85(x843,x841),f85(x843,x842))
% 19.29/19.55 [85]~E(x851,x852)+E(f76(x851),f76(x852))
% 19.29/19.55 [86]~E(x861,x862)+E(f47(x861,x863),f47(x862,x863))
% 19.29/19.55 [87]~E(x871,x872)+E(f47(x873,x871),f47(x873,x872))
% 19.29/19.55 [88]~E(x881,x882)+E(f88(x881,x883),f88(x882,x883))
% 19.29/19.55 [89]~E(x891,x892)+E(f88(x893,x891),f88(x893,x892))
% 19.29/19.55 [90]~E(x901,x902)+E(f65(x901,x903,x904),f65(x902,x903,x904))
% 19.29/19.55 [91]~E(x911,x912)+E(f65(x913,x911,x914),f65(x913,x912,x914))
% 19.29/19.55 [92]~E(x921,x922)+E(f65(x923,x924,x921),f65(x923,x924,x922))
% 19.29/19.55 [93]~E(x931,x932)+E(f84(x931,x933,x934),f84(x932,x933,x934))
% 19.29/19.55 [94]~E(x941,x942)+E(f84(x943,x941,x944),f84(x943,x942,x944))
% 19.29/19.55 [95]~E(x951,x952)+E(f84(x953,x954,x951),f84(x953,x954,x952))
% 19.29/19.55 [96]~E(x961,x962)+E(f19(x961,x963),f19(x962,x963))
% 19.29/19.55 [97]~E(x971,x972)+E(f19(x973,x971),f19(x973,x972))
% 19.29/19.55 [98]~E(x981,x982)+E(f43(x981,x983,x984,x985),f43(x982,x983,x984,x985))
% 19.29/19.55 [99]~E(x991,x992)+E(f43(x993,x991,x994,x995),f43(x993,x992,x994,x995))
% 19.29/19.55 [100]~E(x1001,x1002)+E(f43(x1003,x1004,x1001,x1005),f43(x1003,x1004,x1002,x1005))
% 19.29/19.55 [101]~E(x1011,x1012)+E(f43(x1013,x1014,x1015,x1011),f43(x1013,x1014,x1015,x1012))
% 19.29/19.55 [102]~E(x1021,x1022)+E(f64(x1021,x1023),f64(x1022,x1023))
% 19.29/19.55 [103]~E(x1031,x1032)+E(f64(x1033,x1031),f64(x1033,x1032))
% 19.29/19.55 [104]~E(x1041,x1042)+E(f30(x1041,x1043),f30(x1042,x1043))
% 19.29/19.55 [105]~E(x1051,x1052)+E(f30(x1053,x1051),f30(x1053,x1052))
% 19.29/19.55 [106]~E(x1061,x1062)+E(f46(x1061,x1063),f46(x1062,x1063))
% 19.29/19.55 [107]~E(x1071,x1072)+E(f46(x1073,x1071),f46(x1073,x1072))
% 19.29/19.55 [108]~E(x1081,x1082)+E(f60(x1081,x1083,x1084),f60(x1082,x1083,x1084))
% 19.29/19.55 [109]~E(x1091,x1092)+E(f60(x1093,x1091,x1094),f60(x1093,x1092,x1094))
% 19.29/19.55 [110]~E(x1101,x1102)+E(f60(x1103,x1104,x1101),f60(x1103,x1104,x1102))
% 19.29/19.55 [111]~E(x1111,x1112)+E(f45(x1111,x1113),f45(x1112,x1113))
% 19.29/19.55 [112]~E(x1121,x1122)+E(f45(x1123,x1121),f45(x1123,x1122))
% 19.29/19.55 [113]~E(x1131,x1132)+E(f91(x1131,x1133),f91(x1132,x1133))
% 19.29/19.55 [114]~E(x1141,x1142)+E(f91(x1143,x1141),f91(x1143,x1142))
% 19.29/19.55 [115]~E(x1151,x1152)+E(f57(x1151,x1153,x1154),f57(x1152,x1153,x1154))
% 19.29/19.55 [116]~E(x1161,x1162)+E(f57(x1163,x1161,x1164),f57(x1163,x1162,x1164))
% 19.29/19.55 [117]~E(x1171,x1172)+E(f57(x1173,x1174,x1171),f57(x1173,x1174,x1172))
% 19.29/19.55 [118]~E(x1181,x1182)+E(f59(x1181,x1183),f59(x1182,x1183))
% 19.29/19.55 [119]~E(x1191,x1192)+E(f59(x1193,x1191),f59(x1193,x1192))
% 19.29/19.55 [120]~E(x1201,x1202)+E(f33(x1201,x1203),f33(x1202,x1203))
% 19.29/19.55 [121]~E(x1211,x1212)+E(f33(x1213,x1211),f33(x1213,x1212))
% 19.29/19.55 [122]~E(x1221,x1222)+E(f48(x1221,x1223,x1224),f48(x1222,x1223,x1224))
% 19.29/19.55 [123]~E(x1231,x1232)+E(f48(x1233,x1231,x1234),f48(x1233,x1232,x1234))
% 19.29/19.55 [124]~E(x1241,x1242)+E(f48(x1243,x1244,x1241),f48(x1243,x1244,x1242))
% 19.29/19.55 [125]~E(x1251,x1252)+E(f101(x1251,x1253,x1254),f101(x1252,x1253,x1254))
% 19.29/19.55 [126]~E(x1261,x1262)+E(f101(x1263,x1261,x1264),f101(x1263,x1262,x1264))
% 19.29/19.55 [127]~E(x1271,x1272)+E(f101(x1273,x1274,x1271),f101(x1273,x1274,x1272))
% 19.29/19.55 [128]~E(x1281,x1282)+E(f78(x1281,x1283,x1284),f78(x1282,x1283,x1284))
% 19.29/19.55 [129]~E(x1291,x1292)+E(f78(x1293,x1291,x1294),f78(x1293,x1292,x1294))
% 19.29/19.55 [130]~E(x1301,x1302)+E(f78(x1303,x1304,x1301),f78(x1303,x1304,x1302))
% 19.29/19.55 [131]~E(x1311,x1312)+E(f99(x1311,x1313,x1314),f99(x1312,x1313,x1314))
% 19.29/19.55 [132]~E(x1321,x1322)+E(f99(x1323,x1321,x1324),f99(x1323,x1322,x1324))
% 19.29/19.55 [133]~E(x1331,x1332)+E(f99(x1333,x1334,x1331),f99(x1333,x1334,x1332))
% 19.29/19.55 [134]~E(x1341,x1342)+E(f24(x1341,x1343,x1344),f24(x1342,x1343,x1344))
% 19.29/19.55 [135]~E(x1351,x1352)+E(f24(x1353,x1351,x1354),f24(x1353,x1352,x1354))
% 19.29/19.55 [136]~E(x1361,x1362)+E(f24(x1363,x1364,x1361),f24(x1363,x1364,x1362))
% 19.29/19.55 [137]~E(x1371,x1372)+E(f87(x1371,x1373),f87(x1372,x1373))
% 19.29/19.55 [138]~E(x1381,x1382)+E(f87(x1383,x1381),f87(x1383,x1382))
% 19.29/19.55 [139]~E(x1391,x1392)+E(f39(x1391,x1393),f39(x1392,x1393))
% 19.29/19.55 [140]~E(x1401,x1402)+E(f39(x1403,x1401),f39(x1403,x1402))
% 19.29/19.55 [141]~E(x1411,x1412)+E(f23(x1411,x1413,x1414),f23(x1412,x1413,x1414))
% 19.29/19.55 [142]~E(x1421,x1422)+E(f23(x1423,x1421,x1424),f23(x1423,x1422,x1424))
% 19.29/19.55 [143]~E(x1431,x1432)+E(f23(x1433,x1434,x1431),f23(x1433,x1434,x1432))
% 19.29/19.55 [144]~E(x1441,x1442)+E(f117(x1441),f117(x1442))
% 19.29/19.55 [145]~E(x1451,x1452)+E(f38(x1451,x1453),f38(x1452,x1453))
% 19.29/19.55 [146]~E(x1461,x1462)+E(f38(x1463,x1461),f38(x1463,x1462))
% 19.29/19.55 [147]~E(x1471,x1472)+E(f79(x1471),f79(x1472))
% 19.29/19.55 [148]~E(x1481,x1482)+E(f108(x1481,x1483,x1484,x1485),f108(x1482,x1483,x1484,x1485))
% 19.29/19.55 [149]~E(x1491,x1492)+E(f108(x1493,x1491,x1494,x1495),f108(x1493,x1492,x1494,x1495))
% 19.29/19.55 [150]~E(x1501,x1502)+E(f108(x1503,x1504,x1501,x1505),f108(x1503,x1504,x1502,x1505))
% 19.29/19.55 [151]~E(x1511,x1512)+E(f108(x1513,x1514,x1515,x1511),f108(x1513,x1514,x1515,x1512))
% 19.29/19.55 [152]~E(x1521,x1522)+E(f74(x1521,x1523,x1524),f74(x1522,x1523,x1524))
% 19.29/19.55 [153]~E(x1531,x1532)+E(f74(x1533,x1531,x1534),f74(x1533,x1532,x1534))
% 19.29/19.55 [154]~E(x1541,x1542)+E(f74(x1543,x1544,x1541),f74(x1543,x1544,x1542))
% 19.29/19.55 [155]~E(x1551,x1552)+E(f80(x1551,x1553),f80(x1552,x1553))
% 19.29/19.55 [156]~E(x1561,x1562)+E(f80(x1563,x1561),f80(x1563,x1562))
% 19.29/19.55 [157]~E(x1571,x1572)+E(f37(x1571,x1573),f37(x1572,x1573))
% 19.29/19.55 [158]~E(x1581,x1582)+E(f37(x1583,x1581),f37(x1583,x1582))
% 19.29/19.55 [159]~E(x1591,x1592)+E(f104(x1591,x1593),f104(x1592,x1593))
% 19.29/19.55 [160]~E(x1601,x1602)+E(f104(x1603,x1601),f104(x1603,x1602))
% 19.29/19.55 [161]~E(x1611,x1612)+E(f72(x1611,x1613),f72(x1612,x1613))
% 19.29/19.55 [162]~E(x1621,x1622)+E(f72(x1623,x1621),f72(x1623,x1622))
% 19.29/19.55 [163]~E(x1631,x1632)+E(f93(x1631,x1633,x1634),f93(x1632,x1633,x1634))
% 19.29/19.55 [164]~E(x1641,x1642)+E(f93(x1643,x1641,x1644),f93(x1643,x1642,x1644))
% 19.29/19.55 [165]~E(x1651,x1652)+E(f93(x1653,x1654,x1651),f93(x1653,x1654,x1652))
% 19.29/19.55 [166]~E(x1661,x1662)+E(f53(x1661),f53(x1662))
% 19.29/19.55 [167]~E(x1671,x1672)+E(f32(x1671,x1673),f32(x1672,x1673))
% 19.29/19.55 [168]~E(x1681,x1682)+E(f32(x1683,x1681),f32(x1683,x1682))
% 19.29/19.55 [169]~E(x1691,x1692)+E(f71(x1691,x1693),f71(x1692,x1693))
% 19.29/19.55 [170]~E(x1701,x1702)+E(f71(x1703,x1701),f71(x1703,x1702))
% 19.29/19.55 [171]~E(x1711,x1712)+E(f50(x1711,x1713,x1714),f50(x1712,x1713,x1714))
% 19.29/19.55 [172]~E(x1721,x1722)+E(f50(x1723,x1721,x1724),f50(x1723,x1722,x1724))
% 19.29/19.55 [173]~E(x1731,x1732)+E(f50(x1733,x1734,x1731),f50(x1733,x1734,x1732))
% 19.29/19.55 [174]~E(x1741,x1742)+E(f67(x1741),f67(x1742))
% 19.29/19.55 [175]~E(x1751,x1752)+E(f77(x1751),f77(x1752))
% 19.29/19.55 [176]~E(x1761,x1762)+E(f36(x1761,x1763),f36(x1762,x1763))
% 19.29/19.55 [177]~E(x1771,x1772)+E(f36(x1773,x1771),f36(x1773,x1772))
% 19.29/19.55 [178]~E(x1781,x1782)+E(f100(x1781,x1783,x1784),f100(x1782,x1783,x1784))
% 19.29/19.55 [179]~E(x1791,x1792)+E(f100(x1793,x1791,x1794),f100(x1793,x1792,x1794))
% 19.29/19.55 [180]~E(x1801,x1802)+E(f100(x1803,x1804,x1801),f100(x1803,x1804,x1802))
% 19.29/19.55 [181]~E(x1811,x1812)+E(f96(x1811,x1813),f96(x1812,x1813))
% 19.29/19.55 [182]~E(x1821,x1822)+E(f96(x1823,x1821),f96(x1823,x1822))
% 19.29/19.55 [183]~E(x1831,x1832)+E(f34(x1831,x1833),f34(x1832,x1833))
% 19.29/19.55 [184]~E(x1841,x1842)+E(f34(x1843,x1841),f34(x1843,x1842))
% 19.29/19.55 [185]~E(x1851,x1852)+E(f82(x1851,x1853),f82(x1852,x1853))
% 19.29/19.55 [186]~E(x1861,x1862)+E(f82(x1863,x1861),f82(x1863,x1862))
% 19.29/19.55 [187]~E(x1871,x1872)+E(f97(x1871),f97(x1872))
% 19.29/19.55 [188]~E(x1881,x1882)+E(f49(x1881,x1883),f49(x1882,x1883))
% 19.29/19.55 [189]~E(x1891,x1892)+E(f49(x1893,x1891),f49(x1893,x1892))
% 19.29/19.55 [190]~E(x1901,x1902)+E(f54(x1901,x1903),f54(x1902,x1903))
% 19.29/19.55 [191]~E(x1911,x1912)+E(f54(x1913,x1911),f54(x1913,x1912))
% 19.29/19.55 [192]~E(x1921,x1922)+E(f35(x1921,x1923,x1924),f35(x1922,x1923,x1924))
% 19.29/19.55 [193]~E(x1931,x1932)+E(f35(x1933,x1931,x1934),f35(x1933,x1932,x1934))
% 19.29/19.55 [194]~E(x1941,x1942)+E(f35(x1943,x1944,x1941),f35(x1943,x1944,x1942))
% 19.29/19.55 [195]~E(x1951,x1952)+E(f68(x1951),f68(x1952))
% 19.29/19.55 [196]~E(x1961,x1962)+E(f25(x1961,x1963,x1964),f25(x1962,x1963,x1964))
% 19.29/19.55 [197]~E(x1971,x1972)+E(f25(x1973,x1971,x1974),f25(x1973,x1972,x1974))
% 19.29/19.55 [198]~E(x1981,x1982)+E(f25(x1983,x1984,x1981),f25(x1983,x1984,x1982))
% 19.29/19.55 [199]~E(x1991,x1992)+E(f40(x1991,x1993,x1994),f40(x1992,x1993,x1994))
% 19.29/19.55 [200]~E(x2001,x2002)+E(f40(x2003,x2001,x2004),f40(x2003,x2002,x2004))
% 19.29/19.55 [201]~E(x2011,x2012)+E(f40(x2013,x2014,x2011),f40(x2013,x2014,x2012))
% 19.29/19.55 [202]~E(x2021,x2022)+E(f44(x2021,x2023,x2024),f44(x2022,x2023,x2024))
% 19.29/19.55 [203]~E(x2031,x2032)+E(f44(x2033,x2031,x2034),f44(x2033,x2032,x2034))
% 19.29/19.55 [204]~E(x2041,x2042)+E(f44(x2043,x2044,x2041),f44(x2043,x2044,x2042))
% 19.29/19.55 [205]~E(x2051,x2052)+E(f111(x2051,x2053),f111(x2052,x2053))
% 19.29/19.55 [206]~E(x2061,x2062)+E(f111(x2063,x2061),f111(x2063,x2062))
% 19.29/19.55 [207]~E(x2071,x2072)+E(f63(x2071,x2073),f63(x2072,x2073))
% 19.29/19.55 [208]~E(x2081,x2082)+E(f63(x2083,x2081),f63(x2083,x2082))
% 19.29/19.55 [209]~E(x2091,x2092)+E(f62(x2091,x2093,x2094),f62(x2092,x2093,x2094))
% 19.29/19.55 [210]~E(x2101,x2102)+E(f62(x2103,x2101,x2104),f62(x2103,x2102,x2104))
% 19.29/19.55 [211]~E(x2111,x2112)+E(f62(x2113,x2114,x2111),f62(x2113,x2114,x2112))
% 19.29/19.55 [212]~E(x2121,x2122)+E(f75(x2121),f75(x2122))
% 19.29/19.55 [213]~E(x2131,x2132)+E(f66(x2131),f66(x2132))
% 19.29/19.55 [214]~E(x2141,x2142)+E(f56(x2141),f56(x2142))
% 19.29/19.55 [215]~E(x2151,x2152)+E(f86(x2151),f86(x2152))
% 19.29/19.55 [216]~E(x2161,x2162)+E(f69(x2161),f69(x2162))
% 19.29/19.55 [217]~E(x2171,x2172)+E(f94(x2171,x2173),f94(x2172,x2173))
% 19.29/19.55 [218]~E(x2181,x2182)+E(f94(x2183,x2181),f94(x2183,x2182))
% 19.29/19.55 [219]~E(x2191,x2192)+E(f73(x2191,x2193),f73(x2192,x2193))
% 19.29/19.55 [220]~E(x2201,x2202)+E(f73(x2203,x2201),f73(x2203,x2202))
% 19.29/19.55 [221]~E(x2211,x2212)+E(f92(x2211,x2213),f92(x2212,x2213))
% 19.29/19.55 [222]~E(x2221,x2222)+E(f92(x2223,x2221),f92(x2223,x2222))
% 19.29/19.55 [223]~E(x2231,x2232)+E(f106(x2231,x2233,x2234),f106(x2232,x2233,x2234))
% 19.29/19.55 [224]~E(x2241,x2242)+E(f106(x2243,x2241,x2244),f106(x2243,x2242,x2244))
% 19.29/19.55 [225]~E(x2251,x2252)+E(f106(x2253,x2254,x2251),f106(x2253,x2254,x2252))
% 19.29/19.55 [226]~E(x2261,x2262)+E(f31(x2261,x2263),f31(x2262,x2263))
% 19.29/19.55 [227]~E(x2271,x2272)+E(f31(x2273,x2271),f31(x2273,x2272))
% 19.29/19.55 [228]~E(x2281,x2282)+E(f52(x2281),f52(x2282))
% 19.29/19.55 [229]~E(x2291,x2292)+E(f26(x2291,x2293,x2294,x2295,x2296),f26(x2292,x2293,x2294,x2295,x2296))
% 19.29/19.55 [230]~E(x2301,x2302)+E(f26(x2303,x2301,x2304,x2305,x2306),f26(x2303,x2302,x2304,x2305,x2306))
% 19.29/19.55 [231]~E(x2311,x2312)+E(f26(x2313,x2314,x2311,x2315,x2316),f26(x2313,x2314,x2312,x2315,x2316))
% 19.29/19.55 [232]~E(x2321,x2322)+E(f26(x2323,x2324,x2325,x2321,x2326),f26(x2323,x2324,x2325,x2322,x2326))
% 19.29/19.55 [233]~E(x2331,x2332)+E(f26(x2333,x2334,x2335,x2336,x2331),f26(x2333,x2334,x2335,x2336,x2332))
% 19.29/19.55 [234]~P1(x2341)+P1(x2342)+~E(x2341,x2342)
% 19.29/19.55 [235]~P80(x2351)+P80(x2352)+~E(x2351,x2352)
% 19.29/19.55 [236]~P2(x2361)+P2(x2362)+~E(x2361,x2362)
% 19.29/19.55 [237]~P12(x2371)+P12(x2372)+~E(x2371,x2372)
% 19.29/19.55 [238]P3(x2382,x2383,x2384)+~E(x2381,x2382)+~P3(x2381,x2383,x2384)
% 19.29/19.55 [239]P3(x2393,x2392,x2394)+~E(x2391,x2392)+~P3(x2393,x2391,x2394)
% 19.29/19.55 [240]P3(x2403,x2404,x2402)+~E(x2401,x2402)+~P3(x2403,x2404,x2401)
% 19.29/19.55 [241]~P30(x2411)+P30(x2412)+~E(x2411,x2412)
% 19.29/19.55 [242]~P73(x2421)+P73(x2422)+~E(x2421,x2422)
% 19.29/19.55 [243]~P17(x2431)+P17(x2432)+~E(x2431,x2432)
% 19.29/19.55 [244]~P58(x2441)+P58(x2442)+~E(x2441,x2442)
% 19.29/19.55 [245]~P31(x2451)+P31(x2452)+~E(x2451,x2452)
% 19.29/19.55 [246]~P33(x2461)+P33(x2462)+~E(x2461,x2462)
% 19.29/19.55 [247]~P27(x2471)+P27(x2472)+~E(x2471,x2472)
% 19.29/19.55 [248]~P48(x2481)+P48(x2482)+~E(x2481,x2482)
% 19.29/19.55 [249]~P37(x2491)+P37(x2492)+~E(x2491,x2492)
% 19.29/19.55 [250]~P39(x2501)+P39(x2502)+~E(x2501,x2502)
% 19.29/19.55 [251]P8(x2512,x2513)+~E(x2511,x2512)+~P8(x2511,x2513)
% 19.29/19.55 [252]P8(x2523,x2522)+~E(x2521,x2522)+~P8(x2523,x2521)
% 19.29/19.55 [253]P81(x2532,x2533,x2534)+~E(x2531,x2532)+~P81(x2531,x2533,x2534)
% 19.29/19.55 [254]P81(x2543,x2542,x2544)+~E(x2541,x2542)+~P81(x2543,x2541,x2544)
% 19.29/19.55 [255]P81(x2553,x2554,x2552)+~E(x2551,x2552)+~P81(x2553,x2554,x2551)
% 19.29/19.55 [256]~P54(x2561)+P54(x2562)+~E(x2561,x2562)
% 19.29/19.55 [257]~P50(x2571)+P50(x2572)+~E(x2571,x2572)
% 19.29/19.55 [258]~P44(x2581)+P44(x2582)+~E(x2581,x2582)
% 19.29/19.55 [259]~P40(x2591)+P40(x2592)+~E(x2591,x2592)
% 19.29/19.55 [260]~P14(x2601)+P14(x2602)+~E(x2601,x2602)
% 19.29/19.55 [261]~P18(x2611)+P18(x2612)+~E(x2611,x2612)
% 19.29/19.55 [262]~P59(x2621)+P59(x2622)+~E(x2621,x2622)
% 19.29/19.55 [263]~P13(x2631)+P13(x2632)+~E(x2631,x2632)
% 19.29/19.55 [264]~P32(x2641)+P32(x2642)+~E(x2641,x2642)
% 19.29/19.55 [265]~P6(x2651)+P6(x2652)+~E(x2651,x2652)
% 19.29/19.55 [266]~P62(x2661)+P62(x2662)+~E(x2661,x2662)
% 19.29/19.55 [267]~P75(x2671)+P75(x2672)+~E(x2671,x2672)
% 19.29/19.55 [268]P7(x2682,x2683,x2684,x2685,x2686)+~E(x2681,x2682)+~P7(x2681,x2683,x2684,x2685,x2686)
% 19.29/19.55 [269]P7(x2693,x2692,x2694,x2695,x2696)+~E(x2691,x2692)+~P7(x2693,x2691,x2694,x2695,x2696)
% 19.29/19.55 [270]P7(x2703,x2704,x2702,x2705,x2706)+~E(x2701,x2702)+~P7(x2703,x2704,x2701,x2705,x2706)
% 19.29/19.55 [271]P7(x2713,x2714,x2715,x2712,x2716)+~E(x2711,x2712)+~P7(x2713,x2714,x2715,x2711,x2716)
% 19.29/19.55 [272]P7(x2723,x2724,x2725,x2726,x2722)+~E(x2721,x2722)+~P7(x2723,x2724,x2725,x2726,x2721)
% 19.29/19.55 [273]~P47(x2731)+P47(x2732)+~E(x2731,x2732)
% 19.29/19.55 [274]~P82(x2741)+P82(x2742)+~E(x2741,x2742)
% 19.29/19.55 [275]~P22(x2751)+P22(x2752)+~E(x2751,x2752)
% 19.29/19.55 [276]~P60(x2761)+P60(x2762)+~E(x2761,x2762)
% 19.29/19.55 [277]~P43(x2771)+P43(x2772)+~E(x2771,x2772)
% 19.29/19.55 [278]~P15(x2781)+P15(x2782)+~E(x2781,x2782)
% 19.29/19.55 [279]~P55(x2791)+P55(x2792)+~E(x2791,x2792)
% 19.29/19.55 [280]~P74(x2801)+P74(x2802)+~E(x2801,x2802)
% 19.29/19.55 [281]~P69(x2811)+P69(x2812)+~E(x2811,x2812)
% 19.29/19.55 [282]~P68(x2821)+P68(x2822)+~E(x2821,x2822)
% 19.29/19.55 [283]~P64(x2831)+P64(x2832)+~E(x2831,x2832)
% 19.29/19.55 [284]~P53(x2841)+P53(x2842)+~E(x2841,x2842)
% 19.29/19.55 [285]~P56(x2851)+P56(x2852)+~E(x2851,x2852)
% 19.29/19.55 [286]~P67(x2861)+P67(x2862)+~E(x2861,x2862)
% 19.29/19.55 [287]~P41(x2871)+P41(x2872)+~E(x2871,x2872)
% 19.29/19.55 [288]~P23(x2881)+P23(x2882)+~E(x2881,x2882)
% 19.29/19.55 [289]~P42(x2891)+P42(x2892)+~E(x2891,x2892)
% 19.29/19.55 [290]~P49(x2901)+P49(x2902)+~E(x2901,x2902)
% 19.29/19.55 [291]~P38(x2911)+P38(x2912)+~E(x2911,x2912)
% 19.29/19.55 [292]~P61(x2921)+P61(x2922)+~E(x2921,x2922)
% 19.29/19.55 [293]~P16(x2931)+P16(x2932)+~E(x2931,x2932)
% 19.29/19.55 [294]~P36(x2941)+P36(x2942)+~E(x2941,x2942)
% 19.29/19.55 [295]~P52(x2951)+P52(x2952)+~E(x2951,x2952)
% 19.29/19.55 [296]~P79(x2961)+P79(x2962)+~E(x2961,x2962)
% 19.29/19.55 [297]~P35(x2971)+P35(x2972)+~E(x2971,x2972)
% 19.29/19.55 [298]~P28(x2981)+P28(x2982)+~E(x2981,x2982)
% 19.29/19.55 [299]~P24(x2991)+P24(x2992)+~E(x2991,x2992)
% 19.29/19.55 [300]~P63(x3001)+P63(x3002)+~E(x3001,x3002)
% 19.29/19.55 [301]~P26(x3011)+P26(x3012)+~E(x3011,x3012)
% 19.29/19.55 [302]~P19(x3021)+P19(x3022)+~E(x3021,x3022)
% 19.29/19.55 [303]~P66(x3031)+P66(x3032)+~E(x3031,x3032)
% 19.29/19.55 [304]~P46(x3041)+P46(x3042)+~E(x3041,x3042)
% 19.29/19.55 [305]~P21(x3051)+P21(x3052)+~E(x3051,x3052)
% 19.29/19.55 [306]~P76(x3061)+P76(x3062)+~E(x3061,x3062)
% 19.29/19.55 [307]~P78(x3071)+P78(x3072)+~E(x3071,x3072)
% 19.29/19.55 [308]~P20(x3081)+P20(x3082)+~E(x3081,x3082)
% 19.29/19.55 [309]P10(x3092,x3093)+~E(x3091,x3092)+~P10(x3091,x3093)
% 19.29/19.55 [310]P10(x3103,x3102)+~E(x3101,x3102)+~P10(x3103,x3101)
% 19.29/19.55 [311]~P65(x3111)+P65(x3112)+~E(x3111,x3112)
% 19.29/19.55 [312]P5(x3122,x3123,x3124)+~E(x3121,x3122)+~P5(x3121,x3123,x3124)
% 19.29/19.55 [313]P5(x3133,x3132,x3134)+~E(x3131,x3132)+~P5(x3133,x3131,x3134)
% 19.29/19.55 [314]P5(x3143,x3144,x3142)+~E(x3141,x3142)+~P5(x3143,x3144,x3141)
% 19.29/19.55 [315]~P51(x3151)+P51(x3152)+~E(x3151,x3152)
% 19.29/19.55 [316]P11(x3162,x3163)+~E(x3161,x3162)+~P11(x3161,x3163)
% 19.29/19.55 [317]P11(x3173,x3172)+~E(x3171,x3172)+~P11(x3173,x3171)
% 19.29/19.55 [318]~P71(x3181)+P71(x3182)+~E(x3181,x3182)
% 19.29/19.55 [319]~P34(x3191)+P34(x3192)+~E(x3191,x3192)
% 19.29/19.55 [320]~P77(x3201)+P77(x3202)+~E(x3201,x3202)
% 19.29/19.55 [321]~P70(x3211)+P70(x3212)+~E(x3211,x3212)
% 19.29/19.55 [322]~P25(x3221)+P25(x3222)+~E(x3221,x3222)
% 19.29/19.55 [323]~P72(x3231)+P72(x3232)+~E(x3231,x3232)
% 19.29/19.55 [324]~P29(x3241)+P29(x3242)+~E(x3241,x3242)
% 19.29/19.55 [325]P4(x3252,x3253,x3254,x3255)+~E(x3251,x3252)+~P4(x3251,x3253,x3254,x3255)
% 19.29/19.55 [326]P4(x3263,x3262,x3264,x3265)+~E(x3261,x3262)+~P4(x3263,x3261,x3264,x3265)
% 19.29/19.55 [327]P4(x3273,x3274,x3272,x3275)+~E(x3271,x3272)+~P4(x3273,x3274,x3271,x3275)
% 19.29/19.55 [328]P4(x3283,x3284,x3285,x3282)+~E(x3281,x3282)+~P4(x3283,x3284,x3285,x3281)
% 19.29/19.55 [329]~P57(x3291)+P57(x3292)+~E(x3291,x3292)
% 19.29/19.55 [330]P9(x3302,x3303)+~E(x3301,x3302)+~P9(x3301,x3303)
% 19.29/19.55 [331]P9(x3313,x3312)+~E(x3311,x3312)+~P9(x3313,x3311)
% 19.29/19.55 [332]~P45(x3321)+P45(x3322)+~E(x3321,x3322)
% 19.29/19.55
% 19.29/19.55 %-------------------------------------------
% 19.56/19.59 cnf(2060,plain,
% 19.56/19.59 (~P3(a1,x20601,x20601)),
% 19.56/19.59 inference(scs_inference,[],[338,545,2,916])).
% 19.56/19.59 cnf(2071,plain,
% 19.56/19.59 (~P3(a114,f15(a114,x20711,x20712),x20712)),
% 19.56/19.59 inference(rename_variables,[],[714])).
% 19.56/19.59 cnf(2074,plain,
% 19.56/19.59 (E(f15(a114,x20741,x20742),f15(a114,x20742,x20741))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2077,plain,
% 19.56/19.59 (E(f15(a112,x20771,x20772),f15(a112,x20772,x20771))),
% 19.56/19.59 inference(rename_variables,[],[599])).
% 19.56/19.59 cnf(2082,plain,
% 19.56/19.59 (E(f15(a114,x20821,x20822),f15(a114,x20822,x20821))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2085,plain,
% 19.56/19.59 (P3(a114,x20851,f15(a114,f15(a114,x20852,x20851),f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[664])).
% 19.56/19.59 cnf(2090,plain,
% 19.56/19.59 (~P3(a114,f15(a114,x20901,x20902),x20902)),
% 19.56/19.59 inference(rename_variables,[],[714])).
% 19.56/19.59 cnf(2093,plain,
% 19.56/19.59 (~P3(a114,f15(a114,x20931,x20932),x20932)),
% 19.56/19.59 inference(rename_variables,[],[714])).
% 19.56/19.59 cnf(2096,plain,
% 19.56/19.59 (~P3(a114,f15(a114,x20961,x20962),x20962)),
% 19.56/19.59 inference(rename_variables,[],[714])).
% 19.56/19.59 cnf(2099,plain,
% 19.56/19.59 (~P3(a114,f15(a114,x20991,x20992),x20992)),
% 19.56/19.59 inference(rename_variables,[],[714])).
% 19.56/19.59 cnf(2102,plain,
% 19.56/19.59 (P80(f51(f18(a114,f11(a114,x21021,x21022)),x21021))),
% 19.56/19.59 inference(rename_variables,[],[681])).
% 19.56/19.59 cnf(2104,plain,
% 19.56/19.59 (~E(f15(a114,x21041,f15(a114,f6(a114),f7(a114))),x21041)),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,714,2071,2090,2093,2096,598,2074,599,609,705,664,637,681,616,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900])).
% 19.56/19.59 cnf(2105,plain,
% 19.56/19.59 (~E(f15(a114,x21051,f7(a114)),x21051)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2114,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x21141,f7(a114))),x21141))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2117,plain,
% 19.56/19.59 (P80(f51(f18(a114,x21171),x21171))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2120,plain,
% 19.56/19.59 (P80(f51(f18(a1,x21201),f51(f4(a114),f17(x21201))))),
% 19.56/19.59 inference(rename_variables,[],[610])).
% 19.56/19.59 cnf(2123,plain,
% 19.56/19.59 (P80(f51(f18(a112,x21231),x21231))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2126,plain,
% 19.56/19.59 (P80(f51(f18(a114,x21261),f15(a114,x21261,x21262)))),
% 19.56/19.59 inference(rename_variables,[],[640])).
% 19.56/19.59 cnf(2130,plain,
% 19.56/19.59 (P3(a112,f13(a112,x21301,f7(a112)),x21301)),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,714,2071,2090,2093,2096,598,2074,599,609,705,586,587,2123,664,637,640,681,616,569,718,610,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589])).
% 19.56/19.59 cnf(2131,plain,
% 19.56/19.59 (P80(f51(f18(a112,x21311),x21311))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2140,plain,
% 19.56/19.59 (P80(f51(f18(a1,x21401),x21401))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2143,plain,
% 19.56/19.59 (P80(f51(f18(a1,x21431),x21431))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2154,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x21541,f7(a114))),x21541))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2159,plain,
% 19.56/19.59 (~E(f15(a114,x21591,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(2167,plain,
% 19.56/19.59 (P3(a112,f6(a112),f15(a112,f7(a112),f7(a112)))),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,588,558,595,714,2071,2090,2093,2096,598,2074,599,609,705,585,2140,586,587,2123,664,637,713,711,640,681,616,569,718,2114,610,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304])).
% 19.56/19.59 cnf(2172,plain,
% 19.56/19.59 (P80(f51(f18(a114,x21721),x21721))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2174,plain,
% 19.56/19.59 (P81(f18(a1,f11(a112,x21741,x21742)),x21742,x21741)),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,588,558,595,714,2071,2090,2093,2096,598,2074,599,609,705,585,2140,2143,586,2117,587,2123,664,637,713,711,640,681,616,569,718,2114,610,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492])).
% 19.56/19.59 cnf(2175,plain,
% 19.56/19.59 (P80(f51(f18(a1,x21751),x21751))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2191,plain,
% 19.56/19.59 (~P81(f18(a114,f15(a114,f11(a112,x21911,x21912),f7(a114))),x21912,x21911)),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,588,558,595,714,2071,2090,2093,2096,598,2074,599,609,705,585,2140,2143,586,2117,587,2123,664,637,713,711,640,681,616,569,718,2114,2154,610,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336])).
% 19.56/19.59 cnf(2192,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x21921,f7(a114))),x21921))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2203,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22031),x22031))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2206,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x22061,f7(a114))),x22061))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2210,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x22101,f15(a114,x22102,f7(a114)))),x22102))),
% 19.56/19.59 inference(scs_inference,[],[338,545,580,546,588,558,595,714,2071,2090,2093,2096,598,2074,599,609,705,585,2140,2143,2175,586,2117,587,2123,664,637,713,711,639,640,681,2102,616,569,718,2114,2154,2192,2206,605,610,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856])).
% 19.56/19.59 cnf(2211,plain,
% 19.56/19.59 (P80(f51(f18(a114,x22111),f15(a114,x22112,x22111)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2214,plain,
% 19.56/19.59 (P80(f51(f18(a114,x22141),f15(a114,x22142,x22141)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2217,plain,
% 19.56/19.59 (P80(f51(f18(a114,x22171),f15(a114,x22172,x22171)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2224,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22241),f51(f4(a114),f17(x22241))))),
% 19.56/19.59 inference(rename_variables,[],[610])).
% 19.56/19.59 cnf(2229,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22291),x22291))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2232,plain,
% 19.56/19.59 (~P3(a114,x22321,x22321)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2235,plain,
% 19.56/19.59 (~P3(a114,x22351,x22351)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2238,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x22381,f7(a114))),x22381))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2245,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22451),x22451))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2266,plain,
% 19.56/19.59 (P80(f51(f18(a114,x22661),x22661))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2273,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22731),x22731))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2276,plain,
% 19.56/19.59 (P80(f51(f18(a1,x22761),x22761))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2291,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x22911,x22912),x22912),x22911)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2294,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x22941,x22942),x22942),x22941)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2295,plain,
% 19.56/19.59 (P81(f18(a1,f11(a112,f4(a114),x22951)),x22951,f5(a1))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,338,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,606,2291,705,585,2140,2143,2175,2203,2229,2245,2273,586,2117,2172,2266,587,2123,664,637,713,711,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255])).
% 19.56/19.59 cnf(2298,plain,
% 19.56/19.59 (~E(f15(a114,f15(a114,x22981,x22982),f7(a114)),x22981)),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,338,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,606,2291,705,585,2140,2143,2175,2203,2229,2245,2273,586,2117,2172,2266,587,2123,664,665,637,713,711,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240])).
% 19.56/19.59 cnf(2299,plain,
% 19.56/19.59 (P3(a114,x22991,f15(a114,f15(a114,x22991,x22992),f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[665])).
% 19.56/19.59 cnf(2301,plain,
% 19.56/19.59 (~P3(a114,x23011,x23011)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2303,plain,
% 19.56/19.59 (~P3(a114,x23031,f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[703])).
% 19.56/19.59 cnf(2305,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x23051,x23052),x23052),x23051)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2307,plain,
% 19.56/19.59 (~E(f15(a114,x23071,f7(a114)),x23071)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2310,plain,
% 19.56/19.59 (~P3(a112,f7(a112),f6(a112))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,338,348,353,703,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,606,2291,2294,705,2105,585,2140,2143,2175,2203,2229,2245,2273,586,2117,2172,2266,587,2123,664,2085,665,637,713,711,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083])).
% 19.56/19.59 cnf(2313,plain,
% 19.56/19.59 (~P3(a114,x23131,f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[703])).
% 19.56/19.59 cnf(2320,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x23201,f7(a114))),x23201))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2322,plain,
% 19.56/19.59 (P3(a1,f6(a1),f96(a3,x23221))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,335,338,346,348,353,703,2303,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,606,2291,2294,705,2105,585,2140,2143,2175,2203,2229,2245,2273,586,2117,2172,2266,587,2123,664,2085,665,637,713,711,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908])).
% 19.56/19.59 cnf(2325,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x23251,x23252),x23252),x23251)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2330,plain,
% 19.56/19.59 (P3(a114,x23301,f15(a114,x23301,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2331,plain,
% 19.56/19.59 (P3(a114,x23311,f15(a114,f15(a114,x23312,x23311),f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[664])).
% 19.56/19.59 cnf(2334,plain,
% 19.56/19.59 (P3(a114,x23341,f15(a114,x23341,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2336,plain,
% 19.56/19.59 (~E(f7(a114),f6(a114))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,335,338,346,348,353,703,2303,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,2330,606,2291,2294,2305,705,2105,585,2140,2143,2175,2203,2229,2245,2273,586,2117,2172,2266,587,2123,664,2085,665,637,713,711,2159,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830])).
% 19.56/19.59 cnf(2337,plain,
% 19.56/19.59 (~E(f15(a114,x23371,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(2340,plain,
% 19.56/19.59 (P3(a114,x23401,f15(a114,x23401,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2341,plain,
% 19.56/19.59 (~P3(a114,x23411,x23411)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2350,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x23501,f7(a114))),x23501))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2353,plain,
% 19.56/19.59 (P80(f51(f18(a1,x23531),x23531))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2356,plain,
% 19.56/19.59 (~P3(a114,x23561,x23561)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2359,plain,
% 19.56/19.59 (~P3(a114,x23591,x23591)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2362,plain,
% 19.56/19.59 (P3(a114,x23621,f15(a114,x23621,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2365,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x23651,x23652),x23652),x23651)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2368,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x23681,x23682),x23682),x23681)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2371,plain,
% 19.56/19.59 (~E(f15(a114,x23711,f7(a114)),x23711)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2374,plain,
% 19.56/19.59 (~E(f15(a114,x23741,f7(a114)),x23741)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2377,plain,
% 19.56/19.59 (~E(f15(a114,x23771,f7(a114)),x23771)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2380,plain,
% 19.56/19.59 (P80(f51(f18(a1,x23801),x23801))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2385,plain,
% 19.56/19.59 (P80(f51(f18(a112,x23851),x23851))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2390,plain,
% 19.56/19.59 (P80(f51(f18(a1,x23901),x23901))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2393,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x23931,f7(a114))),x23931))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2400,plain,
% 19.56/19.59 (P3(a114,f6(a114),f15(a114,x24001,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[611])).
% 19.56/19.59 cnf(2403,plain,
% 19.56/19.59 (E(f15(a114,f6(a114),x24031),x24031)),
% 19.56/19.59 inference(rename_variables,[],[576])).
% 19.56/19.59 cnf(2404,plain,
% 19.56/19.59 (P3(a114,x24041,f15(a114,x24041,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2408,plain,
% 19.56/19.59 (~P3(a112,x24081,x24081)),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,335,338,339,340,346,348,353,354,363,410,703,2303,698,545,580,546,588,556,558,595,714,2071,2090,2093,2096,598,2074,599,609,2330,2334,2340,2362,606,2291,2294,2305,2325,2365,576,705,2105,2307,2371,2374,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,586,2117,2172,2266,587,2123,2131,2385,664,2085,665,637,713,611,711,2159,639,2211,2214,2217,640,681,2102,616,569,718,2114,2154,2192,2206,2238,2320,2350,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159])).
% 19.56/19.59 cnf(2419,plain,
% 19.56/19.59 (E(f13(a114,x24191,f15(a114,x24191,x24192)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[608])).
% 19.56/19.59 cnf(2424,plain,
% 19.56/19.59 (P80(f51(f18(a114,x24241),x24241))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2427,plain,
% 19.56/19.59 (P3(a114,x24271,f15(a114,x24271,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2428,plain,
% 19.56/19.59 (~E(f15(a114,x24281,f7(a114)),x24281)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2431,plain,
% 19.56/19.59 (~P3(a114,x24311,x24311)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2434,plain,
% 19.56/19.59 (P80(f51(f18(a112,x24341),x24341))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2435,plain,
% 19.56/19.59 (P3(a114,x24351,f15(a114,x24351,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2440,plain,
% 19.56/19.59 (P80(f51(f18(a1,x24401),x24401))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2443,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x24431,f7(a114))),x24431))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2448,plain,
% 19.56/19.59 (~E(f15(a114,x24481,f7(a114)),x24481)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2451,plain,
% 19.56/19.59 (P80(f51(f18(a1,x24511),x24511))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2452,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x24521,x24522),x24522),x24521)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2455,plain,
% 19.56/19.59 (P80(f51(f18(a112,x24551),x24551))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2456,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x24561,x24562),x24562),x24561)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2459,plain,
% 19.56/19.59 (P80(f51(f18(a112,x24591),x24591))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2462,plain,
% 19.56/19.59 (P80(f51(f18(a112,x24621),x24621))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2463,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x24631,x24632),x24632),x24631)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2468,plain,
% 19.56/19.59 (~E(f15(a114,x24681,f7(a114)),x24681)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2471,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x24711,x24712),x24712),x24711)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2474,plain,
% 19.56/19.59 (P80(f51(f18(a1,x24741),x24741))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2475,plain,
% 19.56/19.59 (P3(a114,x24751,f15(a114,x24751,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2478,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x24781,f7(a114))),x24781))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2481,plain,
% 19.56/19.59 (P80(f51(f18(a1,x24811),x24811))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2484,plain,
% 19.56/19.59 (P80(f51(f18(a1,x24841),x24841))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2489,plain,
% 19.56/19.59 (P3(a1,x24891,f15(a1,f51(f4(a114),f27(x24891)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2498,plain,
% 19.56/19.59 (P80(f51(f18(a114,f13(a114,x24981,x24982)),x24981))),
% 19.56/19.59 inference(rename_variables,[],[680])).
% 19.56/19.59 cnf(2499,plain,
% 19.56/19.59 (P3(a114,f6(a114),f15(a114,x24991,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[611])).
% 19.56/19.59 cnf(2502,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x25021),f7(a1)),x25021)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2507,plain,
% 19.56/19.59 (~P3(a114,x25071,f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[703])).
% 19.56/19.59 cnf(2510,plain,
% 19.56/19.59 (~P3(a114,x25101,x25101)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2511,plain,
% 19.56/19.59 (P3(a114,x25111,f15(a114,x25111,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2514,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x25141,f7(a114))),x25141))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2517,plain,
% 19.56/19.59 (P80(f51(f18(a112,x25171),x25171))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2520,plain,
% 19.56/19.59 (~E(f15(a114,x25201,f7(a114)),x25201)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2522,plain,
% 19.56/19.59 (P80(f51(f18(a1,f13(a114,f15(a114,x25221,x25222),x25222)),x25221))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,335,338,339,340,342,346,347,348,353,354,363,410,470,492,493,498,506,703,2303,2313,698,545,580,696,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,599,609,2330,2334,2340,2362,2404,2427,2435,2475,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,576,705,2105,2307,2371,2374,2377,2428,2448,2468,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,586,2117,2172,2266,587,2123,2131,2385,2434,2455,2459,2462,664,2085,665,717,637,713,611,2400,608,711,2159,639,2211,2214,2217,640,680,681,2102,616,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,634,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565])).
% 19.56/19.59 cnf(2523,plain,
% 19.56/19.59 (P80(f51(f18(a1,x25231),x25231))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2532,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x25321,f7(a114))),x25321))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2535,plain,
% 19.56/19.59 (P80(f51(f18(a114,x25351),x25351))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2542,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x25421),f7(a1)),x25421)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2546,plain,
% 19.56/19.59 (~P80(f51(f18(a112,f7(a112)),f6(a112)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,335,338,339,340,342,346,347,348,353,354,363,369,371,410,470,482,492,493,498,506,703,2303,2313,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,599,609,2330,2334,2340,2362,2404,2427,2435,2475,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,576,705,2105,2307,2371,2374,2377,2428,2448,2468,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,586,2117,2172,2266,2424,587,2123,2131,2385,2434,2455,2459,2462,664,2085,665,717,2502,637,712,713,611,2400,608,711,2159,639,2211,2214,2217,640,680,681,2102,616,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,634,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205])).
% 19.56/19.59 cnf(2549,plain,
% 19.56/19.59 (P80(f51(f18(a114,f11(a114,x25491,x25492)),x25491))),
% 19.56/19.59 inference(rename_variables,[],[681])).
% 19.56/19.59 cnf(2550,plain,
% 19.56/19.59 (P80(f51(f18(a114,f6(a114)),x25501))),
% 19.56/19.59 inference(rename_variables,[],[590])).
% 19.56/19.59 cnf(2555,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x25551,x25552),x25552),x25551)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2565,plain,
% 19.56/19.59 (~E(f15(a114,x25651,f7(a114)),x25651)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2570,plain,
% 19.56/19.59 (P80(f51(f18(a112,x25701),x25701))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2573,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x25731,f7(a114))),x25731))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2574,plain,
% 19.56/19.59 (~E(f15(a114,x25741,f7(a114)),x25741)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2579,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x25791,f7(a114))),x25791))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2580,plain,
% 19.56/19.59 (~E(f15(a114,x25801,f7(a114)),x25801)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2583,plain,
% 19.56/19.59 (P80(f51(f18(a1,x25831),x25831))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2584,plain,
% 19.56/19.59 (~E(f15(a114,x25841,f7(a114)),x25841)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2587,plain,
% 19.56/19.59 (P80(f51(f18(a1,x25871),x25871))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2590,plain,
% 19.56/19.59 (P80(f51(f18(a1,x25901),x25901))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2593,plain,
% 19.56/19.59 (P3(a114,x25931,f15(a114,x25931,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2594,plain,
% 19.56/19.59 (~P3(a114,x25941,f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[703])).
% 19.56/19.59 cnf(2597,plain,
% 19.56/19.59 (P3(a1,x25971,f15(a1,f51(f4(a114),f27(x25971)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2600,plain,
% 19.56/19.59 (P80(f51(f18(a1,x26001),x26001))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2601,plain,
% 19.56/19.59 (~P3(a114,x26011,f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[703])).
% 19.56/19.59 cnf(2604,plain,
% 19.56/19.59 (P80(f51(f18(a1,x26041),x26041))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2609,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26091,f7(a114))),x26091))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2610,plain,
% 19.56/19.59 (P80(f51(f18(a114,x26101),x26101))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2613,plain,
% 19.56/19.59 (P80(f51(f18(a1,x26131),x26131))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2614,plain,
% 19.56/19.59 (~E(f15(a114,x26141,f7(a114)),x26141)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2617,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26171,f7(a114))),x26171))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2620,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26201,f7(a114))),x26201))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2623,plain,
% 19.56/19.59 (P80(f51(f18(a112,x26231),x26231))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2628,plain,
% 19.56/19.59 (P80(f51(f18(a114,x26281),x26281))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2631,plain,
% 19.56/19.59 (P80(f51(f18(a114,x26311),x26311))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2632,plain,
% 19.56/19.59 (P3(a114,x26321,f15(a114,x26321,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2643,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26431,f7(a114))),x26431))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2646,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26461,f7(a114))),x26461))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2648,plain,
% 19.56/19.59 (~P80(f51(f18(a112,f15(a112,f7(a112),f7(a112))),f6(a112)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,335,337,338,339,340,342,346,347,348,353,354,363,369,371,401,409,410,427,470,482,483,492,493,496,498,506,526,532,703,2303,2313,2507,2594,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,599,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,586,2117,2172,2266,2424,2535,2610,2628,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,664,2085,665,717,2502,637,712,713,611,2400,608,2419,711,2159,639,2211,2214,2217,640,680,681,2102,590,616,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,634,2489,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851])).
% 19.56/19.59 cnf(2653,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26531,f7(a114))),x26531))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2656,plain,
% 19.56/19.59 (P80(f51(f18(a114,x26561),x26561))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2659,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26591,f7(a114))),x26591))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2660,plain,
% 19.56/19.59 (P80(f51(f18(a114,f6(a114)),x26601))),
% 19.56/19.59 inference(rename_variables,[],[590])).
% 19.56/19.59 cnf(2667,plain,
% 19.56/19.59 (~P3(a114,x26671,x26671)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2678,plain,
% 19.56/19.59 (E(f15(a114,x26781,x26782),f15(a114,x26782,x26781))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2681,plain,
% 19.56/19.59 (E(f15(a114,x26811,x26812),f15(a114,x26812,x26811))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2684,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x26841,f7(a114))),x26841))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2691,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x26911),f7(a1)),x26911)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2696,plain,
% 19.56/19.59 (~E(f15(a114,x26961,f7(a114)),x26961)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2699,plain,
% 19.56/19.59 (P80(f51(f18(a1,x26991),x26991))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2702,plain,
% 19.56/19.59 (P3(a114,x27021,f15(a114,f15(a114,x27021,x27022),f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[665])).
% 19.56/19.59 cnf(2705,plain,
% 19.56/19.59 (P3(a114,x27051,f15(a114,x27051,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2712,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27121),f7(a1)),x27121)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2715,plain,
% 19.56/19.59 (~P3(a114,x27151,x27151)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2718,plain,
% 19.56/19.59 (P3(a1,x27181,f15(a1,f51(f4(a114),f27(x27181)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2721,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27211),f7(a1)),x27211)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2723,plain,
% 19.56/19.59 (E(x27231,f15(a114,f51(f51(f14(a114),f13(a114,x27232,x27232)),x27233),x27231))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,335,337,338,339,340,342,346,347,348,353,354,363,369,371,401,409,410,427,451,470,482,483,492,493,496,498,506,516,526,532,703,2303,2313,2507,2594,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,599,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,664,2085,665,2299,2702,717,2502,2542,2691,2712,637,712,713,611,2400,608,2419,711,2159,639,2211,2214,2217,640,680,681,2102,2549,590,2550,616,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,617,634,2489,2597,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121])).
% 19.56/19.59 cnf(2724,plain,
% 19.56/19.59 (P80(f51(f18(a114,x27241),f15(a114,x27242,x27241)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2729,plain,
% 19.56/19.59 (P80(f51(f18(a114,x27291),f15(a114,x27292,x27291)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2734,plain,
% 19.56/19.59 (~E(f15(a114,x27341,f7(a114)),x27341)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2735,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x27351,x27352),x27352),x27351)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2738,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27381),f7(a1)),x27381)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2741,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x27411,x27412),x27412),x27411)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2742,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x27421,x27422),x27422),x27421)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2745,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27451),f7(a1)),x27451)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2746,plain,
% 19.56/19.59 (P3(a1,x27461,f15(a1,f51(f4(a114),f27(x27461)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2751,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27511),f7(a1)),x27511)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2754,plain,
% 19.56/19.59 (P80(f51(f18(a114,f13(a114,x27541,x27542)),x27541))),
% 19.56/19.59 inference(rename_variables,[],[680])).
% 19.56/19.59 cnf(2755,plain,
% 19.56/19.59 (P80(f51(f18(a114,x27551),x27551))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2770,plain,
% 19.56/19.59 (P80(f51(f18(a114,f13(a114,x27701,x27702)),x27701))),
% 19.56/19.59 inference(rename_variables,[],[680])).
% 19.56/19.59 cnf(2773,plain,
% 19.56/19.59 (~E(f15(a114,x27731,f7(a114)),x27731)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2776,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x27761,x27762),x27762),x27761)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2784,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x27841,f7(a114))),x27841))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(2785,plain,
% 19.56/19.59 (P80(f51(f18(a114,x27851),x27851))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2786,plain,
% 19.56/19.59 (P80(f51(f18(a114,x27861),x27861))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2793,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x27931),f7(a1)),x27931)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2802,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28021),x28021))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2805,plain,
% 19.56/19.59 (P80(f51(f18(a112,x28051),x28051))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2808,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28081),x28081))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2811,plain,
% 19.56/19.59 (P80(f51(f18(a114,x28111),x28111))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2816,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28161),x28161))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2819,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28191),x28191))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2822,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28221),x28221))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2825,plain,
% 19.56/19.59 (P80(f51(f18(a112,x28251),x28251))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2830,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28301),x28301))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2833,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28331),x28331))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2835,plain,
% 19.56/19.59 (P80(f51(f18(a1,f11(a114,f15(a114,f6(a114),f51(f51(f14(a114),f15(a114,f6(a114),f7(a114))),x28351)),f15(a114,f6(a114),f7(a114)))),x28351))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,335,337,338,339,340,342,346,347,348,353,354,363,369,371,401,409,410,427,446,447,448,451,461,465,468,470,482,483,492,493,496,498,506,513,515,516,526,532,536,703,2303,2313,2507,2594,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,599,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,639,2211,2214,2217,2724,640,680,2498,2754,681,2102,2549,590,2550,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,617,634,2489,2597,2718,605,610,2120,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755])).
% 19.56/19.59 cnf(2836,plain,
% 19.56/19.59 (E(f15(a114,x28361,x28362),f15(a114,x28362,x28361))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2837,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28371),x28371))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2838,plain,
% 19.56/19.59 (~E(f15(a114,x28381,f7(a114)),x28381)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2839,plain,
% 19.56/19.59 (P3(a114,x28391,f15(a114,x28391,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2842,plain,
% 19.56/19.59 (E(f15(a114,x28421,x28422),f15(a114,x28422,x28421))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(2843,plain,
% 19.56/19.59 (~E(f15(a114,x28431,f7(a114)),x28431)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2846,plain,
% 19.56/19.59 (P3(a114,x28461,f15(a114,x28461,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(2847,plain,
% 19.56/19.59 (P3(a1,x28471,f15(a1,f51(f4(a114),f27(x28471)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2850,plain,
% 19.56/19.59 (P80(f51(f18(a114,f6(a114)),x28501))),
% 19.56/19.59 inference(rename_variables,[],[590])).
% 19.56/19.59 cnf(2851,plain,
% 19.56/19.59 (P80(f51(f18(a114,x28511),x28511))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(2854,plain,
% 19.56/19.59 (~E(f15(a114,x28541,f7(a114)),x28541)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2855,plain,
% 19.56/19.59 (~E(f15(a114,x28551,f7(a114)),x28551)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2856,plain,
% 19.56/19.59 (~P3(a114,x28561,x28561)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(2859,plain,
% 19.56/19.59 (E(f13(a114,x28591,f6(a114)),x28591)),
% 19.56/19.59 inference(rename_variables,[],[573])).
% 19.56/19.59 cnf(2860,plain,
% 19.56/19.59 (~E(f15(a114,x28601,f7(a114)),x28601)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(2861,plain,
% 19.56/19.59 (E(f13(a114,f15(a114,x28611,x28612),x28612),x28611)),
% 19.56/19.59 inference(rename_variables,[],[606])).
% 19.56/19.59 cnf(2868,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28681),f51(f4(a114),f17(x28681))))),
% 19.56/19.59 inference(rename_variables,[],[610])).
% 19.56/19.59 cnf(2869,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28691),x28691))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2870,plain,
% 19.56/19.59 (~P3(a1,f15(a1,f10(a1,x28701),f7(a1)),x28701)),
% 19.56/19.59 inference(rename_variables,[],[717])).
% 19.56/19.59 cnf(2873,plain,
% 19.56/19.59 (P80(f51(f18(a112,x28731),x28731))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2874,plain,
% 19.56/19.59 (E(f15(a112,x28741,x28742),f15(a112,x28742,x28741))),
% 19.56/19.59 inference(rename_variables,[],[599])).
% 19.56/19.59 cnf(2877,plain,
% 19.56/19.59 (P80(f51(f18(a112,x28771),x28771))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(2878,plain,
% 19.56/19.59 (E(f15(a112,x28781,x28782),f15(a112,x28782,x28781))),
% 19.56/19.59 inference(rename_variables,[],[599])).
% 19.56/19.59 cnf(2881,plain,
% 19.56/19.59 (P80(f51(f18(a1,x28811),x28811))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(2884,plain,
% 19.56/19.59 (P3(a1,x28841,f15(a1,f51(f4(a114),f27(x28841)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2885,plain,
% 19.56/19.59 (P3(a1,x28851,f15(a1,f51(f4(a114),f27(x28851)),f7(a1)))),
% 19.56/19.59 inference(rename_variables,[],[634])).
% 19.56/19.59 cnf(2888,plain,
% 19.56/19.59 (P80(f51(f18(a114,x28881),f15(a114,x28882,x28881)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(2889,plain,
% 19.56/19.59 (E(f15(a114,x28891,f6(a114)),x28891)),
% 19.56/19.59 inference(rename_variables,[],[574])).
% 19.56/19.59 cnf(3033,plain,
% 19.56/19.59 (P3(a112,f13(a112,x30331,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x30331,x30332)),f7(a112))),f7(a112))),x30332)),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043])).
% 19.56/19.59 cnf(3035,plain,
% 19.56/19.59 (P3(a112,x30351,f15(a112,x30352,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x30352,x30351)),f7(a112))),f7(a112))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042])).
% 19.56/19.59 cnf(3038,plain,
% 19.56/19.59 (P3(a114,x30381,f15(a114,x30381,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3041,plain,
% 19.56/19.59 (P3(a114,x30411,f15(a114,x30411,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3044,plain,
% 19.56/19.59 (~E(f15(a114,x30441,f7(a114)),x30441)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3047,plain,
% 19.56/19.59 (~E(f15(a114,x30471,f7(a114)),x30471)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3050,plain,
% 19.56/19.59 (P3(a114,x30501,f15(a114,x30501,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3056,plain,
% 19.56/19.59 (~P80(f51(f18(a112,f7(a112)),f11(a112,f6(a112),f7(a112))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125])).
% 19.56/19.59 cnf(3058,plain,
% 19.56/19.59 (P80(f51(f18(a112,f7(a112)),f15(a112,f51(f5(a112),f15(a114,x30581,f7(a114))),f51(f5(a112),f51(a16,f6(a112))))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068])).
% 19.56/19.59 cnf(3061,plain,
% 19.56/19.59 (P3(a114,x30611,f15(a114,x30611,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3069,plain,
% 19.56/19.59 (~E(f15(a114,f15(a114,f6(a114),f7(a114)),x30691),f6(a114))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910])).
% 19.56/19.59 cnf(3070,plain,
% 19.56/19.59 (~E(f15(a114,x30701,f7(a114)),x30701)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3081,plain,
% 19.56/19.59 (~E(f15(a114,x30811,f7(a114)),x30811)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3084,plain,
% 19.56/19.59 (~E(f15(a114,x30841,f7(a114)),x30841)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3097,plain,
% 19.56/19.59 (~E(f15(a114,x30971,f7(a114)),x30971)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3100,plain,
% 19.56/19.59 (~E(f15(a114,x31001,f7(a114)),x31001)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3107,plain,
% 19.56/19.59 (~P3(a114,x31071,x31071)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(3116,plain,
% 19.56/19.59 (P3(a114,x31161,f15(a114,x31161,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3119,plain,
% 19.56/19.59 (~P3(a114,x31191,x31191)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(3121,plain,
% 19.56/19.59 (~P3(a1,f6(a1),f51(f4(a114),f6(a114)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,435,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126])).
% 19.56/19.59 cnf(3122,plain,
% 19.56/19.59 (~P3(a114,x31221,x31221)),
% 19.56/19.59 inference(rename_variables,[],[700])).
% 19.56/19.59 cnf(3127,plain,
% 19.56/19.59 (P3(a114,x31271,f15(a114,x31271,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3140,plain,
% 19.56/19.59 (~E(f15(a114,x31401,f7(a114)),x31401)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3143,plain,
% 19.56/19.59 (E(f15(a114,x31431,x31432),f15(a114,x31432,x31431))),
% 19.56/19.59 inference(rename_variables,[],[598])).
% 19.56/19.59 cnf(3375,plain,
% 19.56/19.59 (~P80(f51(f18(a114,f15(a114,x33751,f7(a114))),x33751))),
% 19.56/19.59 inference(rename_variables,[],[718])).
% 19.56/19.59 cnf(3379,plain,
% 19.56/19.59 (P3(a114,f51(f51(f14(a114),f15(a114,x33791,f7(a114))),x33792),f51(f51(f14(a114),f15(a114,x33791,f7(a114))),f15(a114,x33792,f7(a114))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,435,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,2842,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914])).
% 19.56/19.59 cnf(3405,plain,
% 19.56/19.59 (P3(a114,f15(a114,f6(a114),f7(a114)),f51(a16,f15(a112,f7(a112),f7(a112))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,363,364,369,371,401,409,410,412,415,427,428,435,437,446,447,448,451,459,461,465,468,470,471,482,483,484,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,2842,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,637,712,713,611,2400,608,2419,711,2159,2337,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275])).
% 19.56/19.59 cnf(3420,plain,
% 19.56/19.59 (P80(f51(f18(a1,x34201),x34201))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(3479,plain,
% 19.56/19.59 (E(f15(a1,f6(a1),x34791),x34791)),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,379,401,409,410,412,415,427,428,435,437,439,444,446,447,448,451,459,461,465,468,470,471,482,483,484,488,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,598,2074,2082,2678,2681,2836,2842,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839])).
% 19.56/19.59 cnf(3532,plain,
% 19.56/19.59 (~E(f15(a114,x35321,f7(a114)),x35321)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3537,plain,
% 19.56/19.59 (~E(f15(a114,x35371,f7(a114)),x35371)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3544,plain,
% 19.56/19.59 (~E(f15(a114,x35441,f7(a114)),x35441)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3549,plain,
% 19.56/19.59 (P3(a114,x35491,f15(a114,x35491,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3555,plain,
% 19.56/19.59 (~P3(a114,f6(a114),f13(a114,x35551,f15(a114,x35552,x35551)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,379,386,399,401,408,409,410,412,415,427,428,429,435,437,439,444,446,447,448,451,459,461,465,468,470,471,482,483,484,486,488,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,599,2077,2874,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302])).
% 19.56/19.59 cnf(3562,plain,
% 19.56/19.59 (P3(a114,x35621,f15(a114,x35621,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3565,plain,
% 19.56/19.59 (P3(a114,x35651,f15(a114,x35651,f7(a114)))),
% 19.56/19.59 inference(rename_variables,[],[609])).
% 19.56/19.59 cnf(3572,plain,
% 19.56/19.59 (~E(f15(a114,x35721,f7(a114)),x35721)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3615,plain,
% 19.56/19.59 (E(f15(a112,x36151,x36152),f15(a112,x36152,x36151))),
% 19.56/19.59 inference(rename_variables,[],[599])).
% 19.56/19.59 cnf(3633,plain,
% 19.56/19.59 (P80(f51(f18(a1,f6(a1)),f7(a1)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,386,399,401,408,409,410,412,415,427,428,429,435,437,438,439,444,446,447,448,451,459,461,465,468,470,471,482,483,484,486,488,492,493,496,498,506,513,514,515,516,523,526,532,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973])).
% 19.56/19.59 cnf(3731,plain,
% 19.56/19.59 (~P80(f51(f18(a112,f51(f5(a112),f15(a114,x37311,f7(a114)))),f51(f5(a112),x37311)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,386,392,399,401,408,409,410,412,415,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,482,483,484,486,488,492,493,496,498,506,513,514,515,516,523,526,527,528,532,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578])).
% 19.56/19.59 cnf(3834,plain,
% 19.56/19.59 (P80(f51(f18(a114,x38341),x38341))),
% 19.56/19.59 inference(rename_variables,[],[586])).
% 19.56/19.59 cnf(3864,plain,
% 19.56/19.59 (~E(a1,x38641)+P45(x38641)),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332])).
% 19.56/19.59 cnf(3877,plain,
% 19.56/19.59 (~E(f15(a114,x38771,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(3883,plain,
% 19.56/19.59 (P80(f51(f18(a114,x38831),f106(a3,x38832,x38831)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292])).
% 19.56/19.59 cnf(3891,plain,
% 19.56/19.59 (P6(f51(f51(f14(a1),f13(a1,f15(a1,f7(a1),f10(a1,x38911)),f6(a1))),f13(a1,f15(a1,f7(a1),f10(a1,x38911)),f6(a1))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945])).
% 19.56/19.59 cnf(3906,plain,
% 19.56/19.59 (~E(f15(a114,x39061,f7(a114)),x39061)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3909,plain,
% 19.56/19.59 (~E(f15(a114,x39091,f7(a114)),x39091)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3913,plain,
% 19.56/19.59 (~P3(a112,f6(a112),f51(f51(f20(a112),f10(a112,f51(f5(a112),f6(a114)))),f15(a114,f6(a114),f7(a114))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421])).
% 19.56/19.59 cnf(3914,plain,
% 19.56/19.59 (~E(f15(a114,x39141,f7(a114)),x39141)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3924,plain,
% 19.56/19.59 (~P3(a1,f28(a2,f13(a2,f117(f51(a3,f106(a3,x39241,x39242))),x39241)),f96(a3,x39241))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032])).
% 19.56/19.59 cnf(3927,plain,
% 19.56/19.59 (~E(f15(a114,x39271,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(3930,plain,
% 19.56/19.59 (~E(f15(a114,x39301,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(3933,plain,
% 19.56/19.59 (~E(f15(a114,x39331,f7(a114)),x39331)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3940,plain,
% 19.56/19.59 (P80(f51(f18(a1,x39401),x39401))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(3943,plain,
% 19.56/19.59 (P80(f51(f18(a112,x39431),x39431))),
% 19.56/19.59 inference(rename_variables,[],[587])).
% 19.56/19.59 cnf(3946,plain,
% 19.56/19.59 (P80(f51(f18(a1,x39461),x39461))),
% 19.56/19.59 inference(rename_variables,[],[585])).
% 19.56/19.59 cnf(3949,plain,
% 19.56/19.59 (~E(f15(a114,x39491,f7(a114)),x39491)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3964,plain,
% 19.56/19.59 (~E(f15(a114,x39641,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(3967,plain,
% 19.56/19.59 (~E(f15(a114,x39671,f7(a114)),x39671)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(3968,plain,
% 19.56/19.59 (~E(f15(a114,x39681,f7(a114)),f6(a114))),
% 19.56/19.59 inference(rename_variables,[],[711])).
% 19.56/19.59 cnf(3975,plain,
% 19.56/19.59 (P80(f51(f18(a114,x39751),f15(a114,x39752,x39751)))),
% 19.56/19.59 inference(rename_variables,[],[639])).
% 19.56/19.59 cnf(3991,plain,
% 19.56/19.59 (~P80(f51(f18(a112,f15(a112,f15(a112,f7(a112),f51(f5(a112),f15(a114,f6(a114),f7(a114)))),f51(f5(a112),f15(a114,f6(a114),f7(a114))))),f6(a112)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,507,509,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062])).
% 19.56/19.59 cnf(4032,plain,
% 19.56/19.59 (~E(f15(a114,x40321,f7(a114)),x40321)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4037,plain,
% 19.56/19.59 (~E(f15(a114,x40371,f7(a114)),x40371)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4043,plain,
% 19.56/19.59 (~E(f15(a114,x40431,f7(a114)),x40431)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4047,plain,
% 19.56/19.59 (P3(a114,f13(a114,f15(a114,f15(a114,f15(a114,x40471,f6(a114)),f7(a114)),f7(a114)),f15(a114,f15(a114,f15(a114,x40471,f6(a114)),f7(a114)),f7(a114))),f13(a114,f15(a114,f15(a114,f15(a114,x40471,f6(a114)),f7(a114)),f7(a114)),f15(a114,f15(a114,x40471,f6(a114)),f7(a114))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,337,338,339,340,341,342,346,347,348,349,353,354,357,360,363,364,369,371,372,373,377,379,381,385,386,392,399,401,408,409,410,412,415,424,427,428,429,435,436,437,438,439,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,507,509,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,574,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,640,680,2498,2754,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,605,610,2120,2224,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490])).
% 19.56/19.59 cnf(4070,plain,
% 19.56/19.59 (~E(f15(a114,x40701,f7(a114)),x40701)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4137,plain,
% 19.56/19.59 (~E(f15(a114,x41371,f7(a114)),x41371)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4139,plain,
% 19.56/19.59 (~P80(f51(f18(f118(x41391,a114),f51(f14(a114),f15(a114,f7(a112),f7(a114)))),f51(f14(a114),f7(a112))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,336,337,338,339,340,341,342,346,347,348,349,350,353,354,357,360,363,364,365,366,369,371,372,373,377,379,381,385,386,392,399,401,404,408,409,410,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,507,509,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,575,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,605,610,2120,2224,2868,635,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620])).
% 19.56/19.59 cnf(4160,plain,
% 19.56/19.59 (~E(f15(a114,x41601,f7(a114)),x41601)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4172,plain,
% 19.56/19.59 (P80(f51(f18(a114,f41(f7(a114),f18(a114,f7(a114)))),f7(a114)))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,336,337,338,339,340,341,342,346,347,348,349,350,353,354,357,360,363,364,365,366,369,370,371,372,373,377,379,381,385,386,392,399,401,404,408,409,410,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,496,498,501,506,507,509,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,575,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,4137,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,3946,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,2785,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,605,603,610,2120,2224,2868,635,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620,1553,1505,1258,1257,1256,1203,1191,1050,1049,958,930,867,866,1639,1335,1244])).
% 19.56/19.59 cnf(4196,plain,
% 19.56/19.59 (P3(a1,f6(a1),f15(a1,f51(f51(f14(a1),x41961),x41961),f51(f51(f14(a1),f7(a1)),f7(a1))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,336,337,338,339,340,341,342,346,347,348,349,350,353,354,357,360,363,364,365,366,369,370,371,372,373,377,379,381,385,386,392,399,401,404,408,409,410,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,494,495,496,498,501,506,507,509,513,514,515,516,523,526,527,528,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,575,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,4137,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,3946,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,2785,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,3943,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,605,603,610,2120,2224,2868,635,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620,1553,1505,1258,1257,1256,1203,1191,1050,1049,958,930,867,866,1639,1335,1244,1150,2015,1599,1546,1915,1647,1822,1821,1819,1723,1666,1665])).
% 19.56/19.59 cnf(4230,plain,
% 19.56/19.59 (P80(f51(f18(f118(x42301,a113),x42302),x42302))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,336,337,338,339,340,341,342,346,347,348,349,350,352,353,354,357,360,363,364,365,366,369,370,371,372,373,377,379,381,385,386,392,399,401,404,408,409,410,411,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,451,459,461,465,468,470,471,478,482,483,484,486,488,492,493,494,495,496,498,501,506,507,509,513,514,515,516,523,526,527,528,529,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,548,552,588,556,558,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,575,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,4137,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,3946,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,2785,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,3943,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,605,603,610,2120,2224,2868,635,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620,1553,1505,1258,1257,1256,1203,1191,1050,1049,958,930,867,866,1639,1335,1244,1150,2015,1599,1546,1915,1647,1822,1821,1819,1723,1666,1665,1561,1560,1488,1487,1340,1338,1274,1189,1734,2027,2026,1617,1622,1621,1374,1373,2057])).
% 19.56/19.59 cnf(4279,plain,
% 19.56/19.59 (~P9(a114,f51(f14(a114),f15(a114,f15(a114,x42791,f6(a114)),f7(a114))))),
% 19.56/19.59 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,335,336,337,338,339,340,341,342,346,347,348,349,350,352,353,354,357,360,363,364,365,366,369,370,371,372,373,377,379,381,385,386,392,399,401,404,408,409,410,411,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,451,452,459,461,465,468,470,471,478,482,483,484,486,488,492,493,494,495,496,498,501,506,507,509,513,514,515,516,518,523,526,527,528,529,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,548,552,588,556,558,559,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,3615,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,2889,575,576,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,4137,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,3946,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,2785,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,3943,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,2770,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,605,603,610,2120,2224,2868,635,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620,1553,1505,1258,1257,1256,1203,1191,1050,1049,958,930,867,866,1639,1335,1244,1150,2015,1599,1546,1915,1647,1822,1821,1819,1723,1666,1665,1561,1560,1488,1487,1340,1338,1274,1189,1734,2027,2026,1617,1622,1621,1374,1373,2057,2055,2017,2016,2009,1923,1922,2054,2049,2046,2036,2035,968,1164,1003,1925,1100,1129,1463,1262,888,1579,1805,1804,1423])).
% 19.56/19.59 cnf(4290,plain,
% 19.56/19.59 (~E(f15(a114,x42901,f7(a114)),x42901)),
% 19.56/19.59 inference(rename_variables,[],[705])).
% 19.56/19.59 cnf(4349,plain,
% 19.56/19.59 (E(f15(a114,f6(a114),x43491),x43491)),
% 19.56/19.59 inference(rename_variables,[],[576])).
% 19.56/19.59 cnf(4431,plain,
% 19.56/19.59 (~P80(f51(f18(a1,f51(f4(a114),f15(a114,f6(a114),f7(a114)))),f29(a1,x44311,f51(f4(a114),f6(a114)))))),
% 19.56/19.60 inference(scs_inference,[],[693,700,2232,2235,2301,2341,2356,2359,2431,2510,2667,2715,2856,3107,3119,3122,333,334,335,336,337,338,339,340,341,342,346,347,348,349,350,352,353,354,357,360,363,364,365,366,369,370,371,372,373,377,379,381,385,386,392,396,399,401,404,408,409,410,411,412,415,424,427,428,429,435,436,437,438,439,441,444,446,447,448,450,451,452,453,454,456,459,460,461,463,465,468,469,470,471,478,482,483,484,486,488,492,493,494,495,496,498,501,506,507,509,513,514,515,516,518,523,526,527,528,529,530,532,534,536,537,541,703,2303,2313,2507,2594,2601,694,698,545,580,696,697,546,547,548,552,588,556,557,558,559,595,714,2071,2090,2093,2096,2099,598,2074,2082,2678,2681,2836,2842,3143,599,2077,2874,2878,3615,609,2330,2334,2340,2362,2404,2427,2435,2475,2511,2593,2632,2705,2839,2846,3038,3041,3050,3061,3116,3127,3549,3562,3565,606,2291,2294,2305,2325,2365,2368,2452,2456,2463,2471,2555,2735,2742,2776,2861,2741,607,573,2859,574,2889,575,576,2403,4349,705,2105,2307,2371,2374,2377,2428,2448,2468,2520,2565,2574,2580,2584,2614,2696,2734,2773,2838,2843,2855,2860,3044,3047,3070,3081,3084,3097,3100,3140,3532,3537,3544,3572,2854,3906,3909,3914,3933,3949,3967,4032,4037,4043,4070,4137,4160,4290,585,2140,2143,2175,2203,2229,2245,2273,2276,2353,2380,2390,2440,2451,2474,2481,2484,2523,2583,2587,2590,2600,2604,2613,2699,2802,2808,2816,2819,2822,2830,2833,2837,2869,2881,3420,3940,3946,586,2117,2172,2266,2424,2535,2610,2628,2631,2656,2755,2786,2811,2851,3834,2785,587,2123,2131,2385,2434,2455,2459,2462,2517,2570,2623,2805,2825,2873,2877,3943,664,2085,2331,665,2299,2702,717,2502,2542,2691,2712,2721,2738,2745,2751,2793,2870,637,712,713,611,2400,2499,608,2419,711,2159,2337,3877,3927,3930,3964,3968,563,639,2211,2214,2217,2724,2729,2888,3975,640,2126,680,2498,2754,2770,681,2102,2549,590,2550,2660,2850,616,568,569,716,718,2114,2154,2192,2206,2238,2320,2350,2393,2443,2478,2514,2532,2573,2579,2609,2617,2620,2643,2646,2653,2659,2684,2784,3375,617,634,2489,2597,2718,2746,2847,2885,2884,644,605,603,610,2120,2224,2868,635,672,683,688,2,916,898,897,892,905,1044,998,1612,1372,1306,1295,1200,1199,1197,1153,1038,980,900,815,1166,21,1972,1965,1945,1827,1826,1675,1589,1552,1538,1377,1222,1190,1185,1142,1140,1138,1124,1086,1048,1030,880,800,1304,1208,1864,1492,1410,1409,1388,1385,1371,1359,1355,1336,1314,1313,1279,1278,1109,1034,1033,1856,1812,1811,1785,1668,1576,1554,1457,1443,1442,1441,1439,1417,1327,1056,1036,1020,1267,1266,1265,1234,1132,1131,1885,1773,1772,1632,1631,1498,1496,1494,1393,1392,1102,274,265,261,255,254,253,240,239,238,235,3,1084,1083,947,925,924,976,908,1365,1362,1361,1360,830,1405,915,913,1594,1461,1297,1260,1154,1123,805,804,1997,1996,1995,1850,1658,1657,1656,1637,1573,1491,1469,1300,1299,1162,1159,1092,1066,1064,994,934,1985,1761,1370,1383,1376,1357,1298,1276,1273,1095,1078,1077,1076,1075,932,803,797,1534,1712,1643,1642,1570,1558,1556,1540,1458,1415,1398,1397,1238,1616,1067,1408,2003,1565,1016,931,795,1240,1859,1548,1353,1352,1351,1205,1204,1107,1071,1053,937,851,850,849,1542,1437,1910,1694,1690,1942,1823,1698,1697,1531,1420,1419,1040,1907,1730,1729,1549,1236,1235,1695,1919,1917,1844,1820,1528,1527,1851,1574,1953,1911,1886,1635,1433,2013,2007,2006,1935,1934,1898,1897,2052,2047,2045,2008,1892,1891,2056,1178,1177,1808,1563,1271,1270,1269,1268,1121,1115,1113,1000,1993,1384,1926,1515,1251,1477,1752,1432,1261,2048,1567,1566,1382,1381,1022,1015,1013,1627,1233,1709,1708,1707,1706,1705,1430,1679,1678,1908,1871,1869,1803,1801,1799,1798,1667,1649,1648,1755,1586,1682,1813,2002,1966,1510,1509,1936,1720,1669,1751,1775,1468,817,1255,1215,1039,999,984,981,902,823,822,793,792,791,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,754,753,752,751,750,749,748,747,746,745,744,743,742,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,2043,2042,1550,1541,1364,1363,1232,1152,1151,1125,1068,1011,975,955,949,910,909,904,903,887,884,883,843,821,809,807,806,790,789,780,779,1282,1281,1207,1202,1180,1127,1126,1094,1070,1069,1041,1018,1010,960,1165,1133,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,1973,1924,1914,1849,1806,1677,1473,1472,1455,1418,1394,1379,1378,1354,1303,1275,1243,1223,1212,1209,1188,1186,1184,1163,1136,1134,1111,1093,1047,1043,1042,1035,1031,1025,1002,989,988,986,978,959,954,950,938,891,890,889,877,874,864,862,861,839,838,836,835,834,832,831,829,828,827,826,825,824,814,812,810,799,798,788,787,782,781,778,1728,1727,1715,1699,1543,1499,1479,1478,1444,1428,1413,1412,1411,1302,1285,1201,1175,1174,929,927,813,1183,1004,2031,1984,1948,1941,1927,1571,1486,1485,1454,1453,1431,1356,1332,1331,1319,1289,1211,1156,1144,1143,1141,1122,1106,1103,1037,1001,977,973,953,907,906,876,873,872,870,869,857,856,855,854,853,847,846,844,820,784,783,2044,2010,1987,1963,1962,1961,1960,1955,1954,1947,1946,1920,1909,1846,1816,1787,1786,1784,1783,1782,1781,1780,1765,1763,1688,1597,1593,1592,1590,1578,1467,1436,1427,1425,1347,1346,1345,1343,1329,1318,1280,1239,1221,1220,1216,1181,1173,1172,1169,1130,1104,1021,1019,875,2021,1905,1742,1692,1691,1611,1606,1604,1530,1529,1503,1502,1501,1500,1484,1483,1481,1414,1224,2000,1990,1989,1957,1956,1951,1950,1858,1758,1625,1624,1535,974,2011,1888,1369,2050,1906,1660,2051,2018,2023,332,272,271,270,269,268,263,248,1082,948,1743,1994,1350,1292,1312,1311,969,945,1435,1434,1368,1366,1097,1045,886,885,819,1421,1334,1333,1287,1237,2032,1193,1192,1171,1147,1146,1788,1754,1210,1098,842,1732,1731,1290,1288,1264,1195,1194,1149,1148,2012,1998,1626,1247,1158,1128,1090,1089,1062,1061,1058,935,863,841,840,1777,1724,1583,1452,1451,1450,1446,1445,1375,1349,1348,1291,1182,1009,1008,1007,1005,2005,1217,1490,1389,1301,1137,1096,961,852,794,785,2001,1807,1504,997,918,1750,1921,1396,1395,1337,1317,1316,1315,1112,1903,1902,1900,1899,1843,1842,1790,1789,1581,1476,1650,1559,1506,1245,933,859,858,786,1683,1815,1710,1655,1620,1553,1505,1258,1257,1256,1203,1191,1050,1049,958,930,867,866,1639,1335,1244,1150,2015,1599,1546,1915,1647,1822,1821,1819,1723,1666,1665,1561,1560,1488,1487,1340,1338,1274,1189,1734,2027,2026,1617,1622,1621,1374,1373,2057,2055,2017,2016,2009,1923,1922,2054,2049,2046,2036,2035,968,1164,1003,1925,1100,1129,1463,1262,888,1579,1805,1804,1423,1325,1386,1873,1829,942,868,1513,1254,1323,1929,1848,1794,1645,1603,1602,1601,1600,1526,1525,1524,1523,1522,1456,1872,1475,1474,1407,1406,1404,1403,1401,1400,1399,1023,941,940,1952,1654,1653,1615,1614,1949,1714,1696,1978,1977,1933,1932,1931,1854,1889,1857,1779,1284,1733,1879,1878,1877,1866,1865,2030,2004,1975,1876,1796,1718,1717,1716,1687,1685,1629,1387,2022,1968,1744])).
% 19.56/19.60 cnf(4483,plain,
% 19.56/19.60 (E(x44831,f15(a114,f51(f51(f14(a114),f13(a114,x44832,x44832)),x44833),x44831))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4485,plain,
% 19.56/19.60 (E(x44851,f15(a114,f51(f51(f14(a114),f13(a114,x44852,x44852)),x44853),x44851))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4487,plain,
% 19.56/19.60 (E(x44871,f15(a114,f51(f51(f14(a114),f13(a114,x44872,x44872)),x44873),x44871))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4489,plain,
% 19.56/19.60 (E(x44891,f15(a114,f51(f51(f14(a114),f13(a114,x44892,x44892)),x44893),x44891))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4491,plain,
% 19.56/19.60 (E(x44911,f15(a114,f51(f51(f14(a114),f13(a114,x44912,x44912)),x44913),x44911))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4493,plain,
% 19.56/19.60 (E(x44931,f15(a114,f51(f51(f14(a114),f13(a114,x44932,x44932)),x44933),x44931))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4495,plain,
% 19.56/19.60 (E(x44951,f15(a114,f51(f51(f14(a114),f13(a114,x44952,x44952)),x44953),x44951))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4497,plain,
% 19.56/19.60 (E(x44971,f15(a114,f51(f51(f14(a114),f13(a114,x44972,x44972)),x44973),x44971))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4499,plain,
% 19.56/19.60 (E(x44991,f15(a114,f51(f51(f14(a114),f13(a114,x44992,x44992)),x44993),x44991))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4501,plain,
% 19.56/19.60 (E(x45011,f15(a114,f51(f51(f14(a114),f13(a114,x45012,x45012)),x45013),x45011))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4503,plain,
% 19.56/19.60 (E(x45031,f15(a114,f51(f51(f14(a114),f13(a114,x45032,x45032)),x45033),x45031))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4505,plain,
% 19.56/19.60 (E(x45051,f15(a114,f51(f51(f14(a114),f13(a114,x45052,x45052)),x45053),x45051))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4507,plain,
% 19.56/19.60 (E(x45071,f15(a114,f51(f51(f14(a114),f13(a114,x45072,x45072)),x45073),x45071))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4509,plain,
% 19.56/19.60 (E(x45091,f15(a114,f51(f51(f14(a114),f13(a114,x45092,x45092)),x45093),x45091))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4511,plain,
% 19.56/19.60 (E(x45111,f15(a114,f51(f51(f14(a114),f13(a114,x45112,x45112)),x45113),x45111))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4513,plain,
% 19.56/19.60 (E(x45131,f15(a114,f51(f51(f14(a114),f13(a114,x45132,x45132)),x45133),x45131))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4515,plain,
% 19.56/19.60 (E(x45151,f15(a114,f51(f51(f14(a114),f13(a114,x45152,x45152)),x45153),x45151))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4517,plain,
% 19.56/19.60 (E(x45171,f15(a114,f51(f51(f14(a114),f13(a114,x45172,x45172)),x45173),x45171))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4519,plain,
% 19.56/19.60 (E(x45191,f15(a114,f51(f51(f14(a114),f13(a114,x45192,x45192)),x45193),x45191))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4521,plain,
% 19.56/19.60 (E(x45211,f15(a114,f51(f51(f14(a114),f13(a114,x45212,x45212)),x45213),x45211))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4523,plain,
% 19.56/19.60 (E(x45231,f15(a114,f51(f51(f14(a114),f13(a114,x45232,x45232)),x45233),x45231))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4525,plain,
% 19.56/19.60 (E(x45251,f15(a114,f51(f51(f14(a114),f13(a114,x45252,x45252)),x45253),x45251))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4527,plain,
% 19.56/19.60 (E(x45271,f15(a114,f51(f51(f14(a114),f13(a114,x45272,x45272)),x45273),x45271))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4529,plain,
% 19.56/19.60 (E(x45291,f15(a114,f51(f51(f14(a114),f13(a114,x45292,x45292)),x45293),x45291))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4531,plain,
% 19.56/19.60 (E(x45311,f15(a114,f51(f51(f14(a114),f13(a114,x45312,x45312)),x45313),x45311))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4533,plain,
% 19.56/19.60 (E(x45331,f15(a114,f51(f51(f14(a114),f13(a114,x45332,x45332)),x45333),x45331))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4535,plain,
% 19.56/19.60 (E(x45351,f15(a114,f51(f51(f14(a114),f13(a114,x45352,x45352)),x45353),x45351))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4537,plain,
% 19.56/19.60 (E(x45371,f15(a114,f51(f51(f14(a114),f13(a114,x45372,x45372)),x45373),x45371))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4539,plain,
% 19.56/19.60 (E(x45391,f15(a114,f51(f51(f14(a114),f13(a114,x45392,x45392)),x45393),x45391))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4541,plain,
% 19.56/19.60 (E(x45411,f15(a114,f51(f51(f14(a114),f13(a114,x45412,x45412)),x45413),x45411))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4543,plain,
% 19.56/19.60 (E(x45431,f15(a114,f51(f51(f14(a114),f13(a114,x45432,x45432)),x45433),x45431))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4545,plain,
% 19.56/19.60 (E(x45451,f15(a114,f51(f51(f14(a114),f13(a114,x45452,x45452)),x45453),x45451))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4547,plain,
% 19.56/19.60 (E(x45471,f15(a114,f51(f51(f14(a114),f13(a114,x45472,x45472)),x45473),x45471))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4549,plain,
% 19.56/19.60 (E(x45491,f15(a114,f51(f51(f14(a114),f13(a114,x45492,x45492)),x45493),x45491))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4551,plain,
% 19.56/19.60 (E(x45511,f15(a114,f51(f51(f14(a114),f13(a114,x45512,x45512)),x45513),x45511))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4553,plain,
% 19.56/19.60 (E(x45531,f15(a114,f51(f51(f14(a114),f13(a114,x45532,x45532)),x45533),x45531))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4555,plain,
% 19.56/19.60 (E(x45551,f15(a114,f51(f51(f14(a114),f13(a114,x45552,x45552)),x45553),x45551))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4557,plain,
% 19.56/19.60 (E(x45571,f15(a114,f51(f51(f14(a114),f13(a114,x45572,x45572)),x45573),x45571))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4559,plain,
% 19.56/19.60 (E(x45591,f15(a114,f51(f51(f14(a114),f13(a114,x45592,x45592)),x45593),x45591))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4561,plain,
% 19.56/19.60 (E(x45611,f15(a114,f51(f51(f14(a114),f13(a114,x45612,x45612)),x45613),x45611))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4563,plain,
% 19.56/19.60 (E(x45631,f15(a114,f51(f51(f14(a114),f13(a114,x45632,x45632)),x45633),x45631))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4565,plain,
% 19.56/19.60 (E(x45651,f15(a114,f51(f51(f14(a114),f13(a114,x45652,x45652)),x45653),x45651))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4567,plain,
% 19.56/19.60 (E(x45671,f15(a114,f51(f51(f14(a114),f13(a114,x45672,x45672)),x45673),x45671))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4569,plain,
% 19.56/19.60 (E(x45691,f15(a114,f51(f51(f14(a114),f13(a114,x45692,x45692)),x45693),x45691))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4571,plain,
% 19.56/19.60 (E(x45711,f15(a114,f51(f51(f14(a114),f13(a114,x45712,x45712)),x45713),x45711))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4573,plain,
% 19.56/19.60 (E(x45731,f15(a114,f51(f51(f14(a114),f13(a114,x45732,x45732)),x45733),x45731))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4575,plain,
% 19.56/19.60 (E(x45751,f15(a114,f51(f51(f14(a114),f13(a114,x45752,x45752)),x45753),x45751))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4577,plain,
% 19.56/19.60 (E(x45771,f15(a114,f51(f51(f14(a114),f13(a114,x45772,x45772)),x45773),x45771))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4579,plain,
% 19.56/19.60 (E(x45791,f15(a114,f51(f51(f14(a114),f13(a114,x45792,x45792)),x45793),x45791))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4581,plain,
% 19.56/19.60 (E(x45811,f15(a114,f51(f51(f14(a114),f13(a114,x45812,x45812)),x45813),x45811))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4583,plain,
% 19.56/19.60 (E(x45831,f15(a114,f51(f51(f14(a114),f13(a114,x45832,x45832)),x45833),x45831))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4585,plain,
% 19.56/19.60 (E(x45851,f15(a114,f51(f51(f14(a114),f13(a114,x45852,x45852)),x45853),x45851))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4587,plain,
% 19.56/19.60 (E(x45871,f15(a114,f51(f51(f14(a114),f13(a114,x45872,x45872)),x45873),x45871))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4589,plain,
% 19.56/19.60 (E(x45891,f15(a114,f51(f51(f14(a114),f13(a114,x45892,x45892)),x45893),x45891))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4591,plain,
% 19.56/19.60 (E(x45911,f15(a114,f51(f51(f14(a114),f13(a114,x45912,x45912)),x45913),x45911))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4593,plain,
% 19.56/19.60 (E(x45931,f15(a114,f51(f51(f14(a114),f13(a114,x45932,x45932)),x45933),x45931))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4595,plain,
% 19.56/19.60 (E(x45951,f15(a114,f51(f51(f14(a114),f13(a114,x45952,x45952)),x45953),x45951))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4597,plain,
% 19.56/19.60 (E(x45971,f15(a114,f51(f51(f14(a114),f13(a114,x45972,x45972)),x45973),x45971))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4599,plain,
% 19.56/19.60 (E(x45991,f15(a114,f51(f51(f14(a114),f13(a114,x45992,x45992)),x45993),x45991))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4601,plain,
% 19.56/19.60 (E(x46011,f15(a114,f51(f51(f14(a114),f13(a114,x46012,x46012)),x46013),x46011))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4603,plain,
% 19.56/19.60 (E(x46031,f15(a114,f51(f51(f14(a114),f13(a114,x46032,x46032)),x46033),x46031))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4605,plain,
% 19.56/19.60 (E(x46051,f15(a114,f51(f51(f14(a114),f13(a114,x46052,x46052)),x46053),x46051))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4607,plain,
% 19.56/19.60 (E(x46071,f15(a114,f51(f51(f14(a114),f13(a114,x46072,x46072)),x46073),x46071))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4609,plain,
% 19.56/19.60 (E(x46091,f15(a114,f51(f51(f14(a114),f13(a114,x46092,x46092)),x46093),x46091))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4611,plain,
% 19.56/19.60 (E(x46111,f15(a114,f51(f51(f14(a114),f13(a114,x46112,x46112)),x46113),x46111))),
% 19.56/19.60 inference(rename_variables,[],[2723])).
% 19.56/19.60 cnf(4615,plain,
% 19.56/19.60 (P3(a112,f13(a112,x46151,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x46151,x46152)),f7(a112))),f7(a112))),x46152)),
% 19.56/19.60 inference(rename_variables,[],[3033])).
% 19.56/19.60 cnf(4616,plain,
% 19.56/19.60 (P80(f51(f18(a112,x46161),x46161))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4619,plain,
% 19.56/19.60 (P3(a112,f13(a112,x46191,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x46191,x46192)),f7(a112))),f7(a112))),x46192)),
% 19.56/19.60 inference(rename_variables,[],[3033])).
% 19.56/19.60 cnf(4622,plain,
% 19.56/19.60 (P3(a112,f13(a112,x46221,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x46221,x46222)),f7(a112))),f7(a112))),x46222)),
% 19.56/19.60 inference(rename_variables,[],[3033])).
% 19.56/19.60 cnf(4623,plain,
% 19.56/19.60 (P80(f51(f18(a112,x46231),x46231))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4626,plain,
% 19.56/19.60 (~P3(a112,x46261,x46261)),
% 19.56/19.60 inference(rename_variables,[],[2408])).
% 19.56/19.60 cnf(4627,plain,
% 19.56/19.60 (P80(f51(f18(a112,x46271),x46271))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4630,plain,
% 19.56/19.60 (P3(a114,x46301,f15(a114,f15(a114,x46302,x46301),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4633,plain,
% 19.56/19.60 (P80(f51(f18(a1,x46331),x46331))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4634,plain,
% 19.56/19.60 (P80(f51(f18(a112,x46341),x46341))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4646,plain,
% 19.56/19.60 (P80(f51(f18(a1,x46461),x46461))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4649,plain,
% 19.56/19.60 (P80(f51(f18(a1,x46491),x46491))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4652,plain,
% 19.56/19.60 (~P80(f51(f18(a114,f15(a114,x46521,f7(a114))),x46521))),
% 19.56/19.60 inference(rename_variables,[],[718])).
% 19.56/19.60 cnf(4655,plain,
% 19.56/19.60 (~P3(a1,f51(f4(a114),x46551),f6(a1))),
% 19.56/19.60 inference(rename_variables,[],[712])).
% 19.56/19.60 cnf(4661,plain,
% 19.56/19.60 (~P3(a112,x46611,x46611)),
% 19.56/19.60 inference(rename_variables,[],[2408])).
% 19.56/19.60 cnf(4664,plain,
% 19.56/19.60 (P80(f51(f18(a112,x46641),x46641))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4670,plain,
% 19.56/19.60 (~P3(a1,f51(f4(a114),x46701),f6(a1))),
% 19.56/19.60 inference(rename_variables,[],[712])).
% 19.56/19.60 cnf(4686,plain,
% 19.56/19.60 (P80(f51(f18(a114,x46861),x46861))),
% 19.56/19.60 inference(rename_variables,[],[586])).
% 19.56/19.60 cnf(4689,plain,
% 19.56/19.60 (~E(f15(a114,x46891,f7(a114)),x46891)),
% 19.56/19.60 inference(rename_variables,[],[705])).
% 19.56/19.60 cnf(4697,plain,
% 19.56/19.60 (E(f17(f51(f4(a114),x46971)),x46971)),
% 19.56/19.60 inference(rename_variables,[],[561])).
% 19.56/19.60 cnf(4703,plain,
% 19.56/19.60 (P80(f51(f18(a1,x47031),x47031))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4707,plain,
% 19.56/19.60 (P80(f51(f18(a1,f13(a114,f15(a114,x47071,x47072),x47072)),x47071))),
% 19.56/19.60 inference(rename_variables,[],[2522])).
% 19.56/19.60 cnf(4709,plain,
% 19.56/19.60 (P80(f51(f18(a1,x47091),x47091))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4712,plain,
% 19.56/19.60 (~P3(a1,x47121,x47121)),
% 19.56/19.60 inference(rename_variables,[],[2060])).
% 19.56/19.60 cnf(4713,plain,
% 19.56/19.60 (E(f15(a1,f6(a1),x47131),x47131)),
% 19.56/19.60 inference(rename_variables,[],[3479])).
% 19.56/19.60 cnf(4715,plain,
% 19.56/19.60 (P80(f51(f18(a1,x47151),x47151))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4718,plain,
% 19.56/19.60 (P80(f51(f18(a1,x47181),x47181))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4726,plain,
% 19.56/19.60 (P80(f51(f18(a1,x47261),x47261))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4729,plain,
% 19.56/19.60 (~E(f15(a114,x47291,f15(a114,f6(a114),f7(a114))),x47291)),
% 19.56/19.60 inference(rename_variables,[],[2104])).
% 19.56/19.60 cnf(4737,plain,
% 19.56/19.60 (P3(a112,f13(a112,x47371,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x47371,x47372)),f7(a112))),f7(a112))),x47372)),
% 19.56/19.60 inference(rename_variables,[],[3033])).
% 19.56/19.60 cnf(4738,plain,
% 19.56/19.60 (P80(f51(f18(a112,x47381),x47381))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4741,plain,
% 19.56/19.60 (P3(a112,f13(a112,x47411,f51(f51(f14(a112),f15(a112,f10(a112,f13(a112,x47411,x47412)),f7(a112))),f7(a112))),x47412)),
% 19.56/19.60 inference(rename_variables,[],[3033])).
% 19.56/19.60 cnf(4742,plain,
% 19.56/19.60 (P80(f51(f18(a112,x47421),x47421))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4745,plain,
% 19.56/19.60 (P80(f51(f18(a112,x47451),x47451))),
% 19.56/19.60 inference(rename_variables,[],[587])).
% 19.56/19.60 cnf(4751,plain,
% 19.56/19.60 (P3(a114,x47511,f15(a114,f15(a114,x47512,x47511),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4754,plain,
% 19.56/19.60 (P3(a114,x47541,f15(a114,f15(a114,x47542,x47541),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4761,plain,
% 19.56/19.60 (~P3(a112,x47611,x47611)),
% 19.56/19.60 inference(rename_variables,[],[2408])).
% 19.56/19.60 cnf(4780,plain,
% 19.56/19.60 (E(f17(f51(f4(a114),x47801)),x47801)),
% 19.56/19.60 inference(rename_variables,[],[561])).
% 19.56/19.60 cnf(4783,plain,
% 19.56/19.60 (~P80(f51(f18(a114,f15(a114,x47831,f7(a114))),x47831))),
% 19.56/19.60 inference(rename_variables,[],[718])).
% 19.56/19.60 cnf(4788,plain,
% 19.56/19.60 (P3(a114,x47881,f15(a114,f15(a114,x47882,x47881),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4791,plain,
% 19.56/19.60 (E(f17(f51(f4(a114),x47911)),x47911)),
% 19.56/19.60 inference(rename_variables,[],[561])).
% 19.56/19.60 cnf(4797,plain,
% 19.56/19.60 (~E(f15(a114,x47971,f7(a114)),x47971)),
% 19.56/19.60 inference(rename_variables,[],[705])).
% 19.56/19.60 cnf(4811,plain,
% 19.56/19.60 (P3(a1,x48111,f15(a1,f51(f4(a114),f27(x48111)),f7(a1)))),
% 19.56/19.60 inference(rename_variables,[],[634])).
% 19.56/19.60 cnf(4814,plain,
% 19.56/19.60 (P3(a114,x48141,f15(a114,f15(a114,x48142,x48141),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4815,plain,
% 19.56/19.60 (P3(a1,x48151,f15(a1,f51(f4(a114),f27(x48151)),f7(a1)))),
% 19.56/19.60 inference(rename_variables,[],[634])).
% 19.56/19.60 cnf(4819,plain,
% 19.56/19.60 (P80(f51(f18(a1,x48191),x48191))),
% 19.56/19.60 inference(rename_variables,[],[585])).
% 19.56/19.60 cnf(4829,plain,
% 19.56/19.60 (~P80(f51(f18(a114,f15(a114,x48291,f7(a114))),x48291))),
% 19.56/19.60 inference(rename_variables,[],[718])).
% 19.56/19.60 cnf(4835,plain,
% 19.56/19.60 (P3(a114,x48351,f15(a114,f15(a114,x48352,x48351),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4838,plain,
% 19.56/19.60 (P3(a114,x48381,f15(a114,f15(a114,x48382,x48381),f7(a114)))),
% 19.56/19.60 inference(rename_variables,[],[664])).
% 19.56/19.60 cnf(4851,plain,
% 19.56/19.60 ($false),
% 19.56/19.60 inference(scs_inference,[],[343,351,355,361,367,374,378,380,382,387,391,395,402,405,413,416,419,423,430,431,440,442,445,449,455,457,462,466,472,474,479,485,489,497,499,502,508,510,517,519,521,524,531,533,538,542,549,572,561,4697,4780,4791,690,691,689,715,334,340,348,350,352,365,397,411,469,494,529,573,705,4689,4797,585,4633,4646,4649,4703,4709,4715,4718,4726,4819,586,4686,587,4616,4623,4627,4634,4664,4738,4742,4745,664,4630,4751,4754,4788,4814,4835,4838,717,590,718,4652,4783,4829,634,4811,4815,372,483,514,716,605,364,408,460,527,436,515,452,536,335,712,4655,4670,354,713,447,446,697,369,580,2310,2167,4230,3056,2336,4139,4431,3058,2522,4707,3891,2210,2835,2104,4729,2723,4483,4485,4487,4489,4491,4493,4495,4497,4499,4501,4503,4505,4507,4509,4511,4513,4515,4517,4519,4521,4523,4525,4527,4529,4531,4533,4535,4537,4539,4541,4543,4545,4547,4549,4551,4553,4555,4557,4559,4561,4563,4565,4567,4569,4571,4573,4575,4577,4579,4581,4583,4585,4587,4589,4591,4593,4595,4597,4599,4601,4603,4605,4607,4609,4611,2174,3883,3731,2191,3479,4713,3633,2546,2298,2648,4172,3991,2295,2060,4712,2408,4626,4661,4761,3069,3405,3379,3033,4615,4619,4622,4737,4741,3035,2130,4047,3913,3924,3121,4196,3555,2322,4279,3864,329,324,323,322,321,320,319,318,315,311,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289,288,287,286,285,284,283,282,281,280,279,278,277,276,275,273,267,266,264,262,260,259,258,257,256,250,249,247,246,245,244,243,242,241,236,234,1759,1704,1587,1514,1584,1305,1225,1462,1489,1326,1533,1971,1753,967,1937,1168,1884,1641,1596,1595,1644,1520,1519,1661,1964,1294,1747,1746,1967,1904,1867,1974,1912,2019,1145,1863,1672,837,833,1471,1470,1328,1630,1539,2014,897,1612,1039,815,1945,1138,1025,877,1864,1336,1033,1457,1443,1442,976,945,957,943,1435,1434,1045,1333,1237,1788,1754,1461,1210,805,1732,1264,1850,1637,1247,841,1761]),
% 19.56/19.60 ['proof']).
% 19.56/19.60 % SZS output end Proof
% 19.56/19.60 % Total time :18.120000s
%------------------------------------------------------------------------------