TSTP Solution File: SWW271+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW271+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 00:13:25 EDT 2023
% Result : Theorem 15.40s 15.53s
% Output : CNFRefutation 15.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW271+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 22:53:44 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 15.40/15.46 %-------------------------------------------
% 15.40/15.46 % File :CSE---1.6
% 15.40/15.46 % Problem :theBenchmark
% 15.40/15.46 % Transform :cnf
% 15.40/15.46 % Format :tptp:raw
% 15.40/15.46 % Command :java -jar mcs_scs.jar %d %s
% 15.40/15.46
% 15.40/15.46 % Result :Theorem 14.210000s
% 15.40/15.46 % Output :CNFRefutation 14.210000s
% 15.40/15.46 %-------------------------------------------
% 15.40/15.46 %------------------------------------------------------------------------------
% 15.40/15.46 % File : SWW271+1 : TPTP v8.1.2. Released v5.2.0.
% 15.40/15.46 % Domain : Software Verification
% 15.40/15.46 % Problem : Fundamental Theorem of Algebra 438896, 1000 axioms selected
% 15.40/15.46 % Version : Especial.
% 15.40/15.46 % English :
% 15.40/15.46
% 15.40/15.46 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 15.40/15.46 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 15.40/15.46 % Source : [Bla11]
% 15.40/15.46 % Names : fta_438896.1000.p [Bla11]
% 15.40/15.46
% 15.40/15.46 % Status : Theorem
% 15.40/15.46 % Rating : 0.42 v8.1.0, 0.44 v7.4.0, 0.47 v7.3.0, 0.41 v7.2.0, 0.38 v7.1.0, 0.35 v7.0.0, 0.37 v6.4.0, 0.42 v6.2.0, 0.48 v6.1.0, 0.53 v6.0.0, 0.52 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0
% 15.40/15.46 % Syntax : Number of formulae : 1209 ( 269 unt; 0 def)
% 15.40/15.46 % Number of atoms : 3081 ( 826 equ)
% 15.40/15.46 % Maximal formula atoms : 13 ( 2 avg)
% 15.40/15.46 % Number of connectives : 2079 ( 207 ~; 63 |; 140 &)
% 15.40/15.46 % ( 238 <=>;1431 =>; 0 <=; 0 <~>)
% 15.40/15.46 % Maximal formula depth : 14 ( 5 avg)
% 15.40/15.46 % Maximal term depth : 9 ( 2 avg)
% 15.40/15.46 % Number of predicates : 75 ( 74 usr; 1 prp; 0-5 aty)
% 15.40/15.46 % Number of functors : 42 ( 42 usr; 11 con; 0-5 aty)
% 15.40/15.46 % Number of variables : 2905 (2891 !; 14 ?)
% 15.40/15.46 % SPC : FOF_THM_RFO_SEQ
% 15.40/15.46
% 15.40/15.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 15.40/15.46 % 2011-03-01 12:06:05
% 15.40/15.46 %------------------------------------------------------------------------------
% 15.40/15.46 %----Relevant facts (995)
% 15.40/15.46 fof(fact_ext,axiom,
% 15.40/15.46 ! [V_g_2,V_f_2] :
% 15.40/15.46 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 15.40/15.46 => V_f_2 = V_g_2 ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_q0,axiom,
% 15.40/15.46 v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).
% 15.40/15.46
% 15.40/15.46 fof(fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096,axiom,
% 15.40/15.46 hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_one__poly__def,axiom,
% 15.40/15.46 ! [T_a] :
% 15.40/15.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.46 => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_pCons__0__0,axiom,
% 15.40/15.46 ! [T_a] :
% 15.40/15.46 ( class_Groups_Ozero(T_a)
% 15.40/15.46 => c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_pCons__eq__0__iff,axiom,
% 15.40/15.46 ! [V_pb_2,V_aa_2,T_a] :
% 15.40/15.46 ( class_Groups_Ozero(T_a)
% 15.40/15.46 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.46 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.46 & V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 15.40/15.46 ! [V_x,T_a] :
% 15.40/15.46 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.46 => c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_square__eq__1__iff,axiom,
% 15.40/15.46 ! [V_x_2,T_a] :
% 15.40/15.46 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 15.40/15.46 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 15.40/15.46 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 15.40/15.46 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_mult__poly__0__left,axiom,
% 15.40/15.46 ! [V_q,T_a] :
% 15.40/15.46 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.46 => 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)) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_mult__poly__0__right,axiom,
% 15.40/15.46 ! [V_p,T_a] :
% 15.40/15.46 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.46 => 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)) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_minus__pCons,axiom,
% 15.40/15.46 ! [V_p,V_a,T_a] :
% 15.40/15.46 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.46 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ).
% 15.40/15.46
% 15.40/15.46 fof(fact_minus__poly__code_I2_J,axiom,
% 15.40/15.46 ! [V_p,V_a,T_b] :
% 15.40/15.46 ( class_Groups_Oab__group__add(T_b)
% 15.40/15.47 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_pne,axiom,
% 15.40/15.47 v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__mult__right,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Oring(T_a)
% 15.40/15.47 => c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__mult__left,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Oring(T_a)
% 15.40/15.47 => c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(T_a,V_a)),V_b) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_n0,axiom,
% 15.40/15.47 v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_oa,axiom,
% 15.40/15.47 c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__0__right,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_a,axiom,
% 15.40/15.47 hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_pq0,axiom,
% 15.40/15.47 ! [B_x] :
% 15.40/15.47 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 15.40/15.47 => hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_qa____),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__refl,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__trans,axiom,
% 15.40/15.47 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__0__left,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 15.40/15.47 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult__right,axiom,
% 15.40/15.47 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult__left,axiom,
% 15.40/15.47 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvdI,axiom,
% 15.40/15.47 ! [V_k,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Odvd(T_a)
% 15.40/15.47 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__dvd__mono,axiom,
% 15.40/15.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult,axiom,
% 15.40/15.47 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult2,axiom,
% 15.40/15.47 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__triv__right,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__triv__left,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_one__dvd,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__dvd__iff,axiom,
% 15.40/15.47 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)),V_y_2))
% 15.40/15.47 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__minus__iff,axiom,
% 15.40/15.47 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)))
% 15.40/15.47 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__poly__code_I1_J,axiom,
% 15.40/15.47 ! [T_a] :
% 15.40/15.47 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.47 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult__cancel__left,axiom,
% 15.40/15.47 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.47 ( class_Rings_Oidom(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 15.40/15.47 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2)) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_dvd__mult__cancel__right,axiom,
% 15.40/15.47 ! [V_b_2,V_c_2,V_aa_2,T_a] :
% 15.40/15.47 ( class_Rings_Oidom(T_a)
% 15.40/15.47 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
% 15.40/15.47 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2)) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 15.40/15.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 15.40/15.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 15.40/15.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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))) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 15.40/15.47 ! [V_rx,V_ly,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 15.40/15.47 ! [V_rx,V_ly,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 15.40/15.47 ! [V_ry,V_rx,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 15.40/15.47 ! [V_ry,V_rx,V_lx,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_pCons__eq__iff,axiom,
% 15.40/15.47 ! [V_qb_2,V_b_2,V_pb_2,V_aa_2,T_a] :
% 15.40/15.47 ( class_Groups_Ozero(T_a)
% 15.40/15.47 => ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qb_2)
% 15.40/15.47 <=> ( V_aa_2 = V_b_2
% 15.40/15.47 & V_pb_2 = V_qb_2 ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_divisors__zero,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ono__zero__divisors(T_a)
% 15.40/15.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_no__zero__divisors,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ono__zero__divisors(T_a)
% 15.40/15.47 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__eq__0__iff,axiom,
% 15.40/15.47 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.47 ( class_Rings_Oring__no__zero__divisors(T_a)
% 15.40/15.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.47 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__zero__right,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Omult__zero(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__zero__left,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Omult__zero(T_a)
% 15.40/15.47 => 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) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_zero__neq__one,axiom,
% 15.40/15.47 ! [T_a] :
% 15.40/15.47 ( class_Rings_Ozero__neq__one(T_a)
% 15.40/15.47 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_one__neq__zero,axiom,
% 15.40/15.47 ! [T_a] :
% 15.40/15.47 ( class_Rings_Ozero__neq__one(T_a)
% 15.40/15.47 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_square__eq__iff,axiom,
% 15.40/15.47 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.47 ( class_Rings_Oidom(T_a)
% 15.40/15.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 15.40/15.47 <=> ( V_aa_2 = V_b_2
% 15.40/15.47 | V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__mult__minus,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Oring(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_minus__mult__commute,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_Rings_Oring(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_ap_I1_J,axiom,
% 15.40/15.47 hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_calculation,axiom,
% 15.40/15.47 ( v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 15.40/15.47 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_qa____),v_na____))) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__left_Ominus,axiom,
% 15.40/15.47 ! [V_y,V_x,T_a] :
% 15.40/15.47 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult_Ominus__left,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult__right_Ominus,axiom,
% 15.40/15.47 ! [V_x,V_xa,T_a] :
% 15.40/15.47 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult_Ominus__right,axiom,
% 15.40/15.47 ! [V_b,V_a,T_a] :
% 15.40/15.47 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 15.40/15.47
% 15.40/15.47 fof(fact_mult_Ocomm__neutral,axiom,
% 15.40/15.47 ! [V_a,T_a] :
% 15.40/15.47 ( class_Groups_Ocomm__monoid__mult(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__1__right,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__1,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Ocomm__monoid__mult(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__1__left,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__equal__zero,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
% 15.40/15.48 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__equal__0__iff__equal,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.48 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_assms_I3_J,axiom,
% 15.40/15.48 v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_assms_I1_J,axiom,
% 15.40/15.48 ! [B_x] :
% 15.40/15.48 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_dpn,axiom,
% 15.40/15.48 c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____ ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 15.40/15.48 ! [V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__eq__iff,axiom,
% 15.40/15.48 ! [V_qb_2,V_pb_2,T_a] :
% 15.40/15.48 ( ( class_Int_Oring__char__0(T_a)
% 15.40/15.48 & class_Rings_Oidom(T_a) )
% 15.40/15.48 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qb_2)
% 15.40/15.48 <=> V_pb_2 = V_qb_2 ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 15.40/15.48 ! [V_q,V_p,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__power,axiom,
% 15.40/15.48 ! [V_x,V_n,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 15.40/15.48 ! [V_q,V_y,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 15.40/15.48 ! [V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__zero,axiom,
% 15.40/15.48 ! [V_pb_2,T_a] :
% 15.40/15.48 ( ( class_Int_Oring__char__0(T_a)
% 15.40/15.48 & class_Rings_Oidom(T_a) )
% 15.40/15.48 => ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 15.40/15.48 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_order__root,axiom,
% 15.40/15.48 ! [V_aa_2,V_pb_2,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.48 <=> ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 | c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__0,axiom,
% 15.40/15.48 ! [V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__mult,axiom,
% 15.40/15.48 ! [V_x,V_q,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__minus,axiom,
% 15.40/15.48 ! [V_x,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__ring(T_a)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__1,axiom,
% 15.40/15.48 ! [V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_zero__reorient,axiom,
% 15.40/15.48 ! [V_x_2,T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 15.40/15.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 15.40/15.48 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Groups_Oab__semigroup__mult(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_one__reorient,axiom,
% 15.40/15.48 ! [V_x_2,T_a] :
% 15.40/15.48 ( class_Groups_Oone(T_a)
% 15.40/15.48 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 15.40/15.48 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_minus__minus,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_equation__minus__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 15.40/15.48 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_minus__equation__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
% 15.40/15.48 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2 ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__equal__iff__equal,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 15.40/15.48 <=> V_aa_2 = V_b_2 ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_order__1,axiom,
% 15.40/15.48 ! [V_p,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult_Ozero__left,axiom,
% 15.40/15.48 ! [V_b,T_a] :
% 15.40/15.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__left_Ozero,axiom,
% 15.40/15.48 ! [V_y,T_a] :
% 15.40/15.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult_Ozero__right,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__right_Ozero,axiom,
% 15.40/15.48 ! [V_x,T_a] :
% 15.40/15.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_poly__eq__0__iff__dvd,axiom,
% 15.40/15.48 ! [V_c_2,V_pb_2,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_c_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.48 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_dvd__iff__poly__eq__0,axiom,
% 15.40/15.48 ! [V_pb_2,V_c_2,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2))
% 15.40/15.48 <=> hAPP(c_Polynomial_Opoly(T_a,V_pb_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_minus__zero,axiom,
% 15.40/15.48 ! [T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__0__equal__iff__equal,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.48 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 15.40/15.48 <=> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2 ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_equal__neg__zero,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.48 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
% 15.40/15.48 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_ap_I2_J,axiom,
% 15.40/15.48 ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_oop,axiom,
% 15.40/15.48 ! [V_a] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,V_a,v_pa____),v_na____) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__minus,axiom,
% 15.40/15.48 ! [V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oring__1(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__0__left,axiom,
% 15.40/15.48 ! [V_n,T_a] :
% 15.40/15.48 ( ( class_Power_Opower(T_a)
% 15.40/15.48 & class_Rings_Osemiring__0(T_a) )
% 15.40/15.48 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.48 => 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) )
% 15.40/15.48 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.48 => 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) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__0,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Power_Opower(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__eq__0__iff,axiom,
% 15.40/15.48 ! [V_nb_2,V_aa_2,T_a] :
% 15.40/15.48 ( ( class_Power_Opower(T_a)
% 15.40/15.48 & class_Rings_Omult__zero(T_a)
% 15.40/15.48 & class_Rings_Ono__zero__divisors(T_a)
% 15.40/15.48 & class_Rings_Ozero__neq__one(T_a) )
% 15.40/15.48 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.48 <=> ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.48 & V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_order__2,axiom,
% 15.40/15.48 ! [V_a,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_order,axiom,
% 15.40/15.48 ! [V_a,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))
% 15.40/15.48 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_dvd__power__same,axiom,
% 15.40/15.48 ! [V_n,V_y,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 15.40/15.48 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__one,axiom,
% 15.40/15.48 ! [V_n,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_assms_I2_J,axiom,
% 15.40/15.48 c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = v_n ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__Suc__0,axiom,
% 15.40/15.48 ! [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)) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 15.40/15.48 ! [V_m_2,V_x_2] :
% 15.40/15.48 ( 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))
% 15.40/15.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.48 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_nat__one__le__power,axiom,
% 15.40/15.48 ! [V_n,V_i] :
% 15.40/15.48 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__pCons__le,axiom,
% 15.40/15.48 ! [V_p,V_a,T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__power__le,axiom,
% 15.40/15.48 ! [V_n,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__inject__base,axiom,
% 15.40/15.48 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( 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))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.48 => V_a = V_b ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__le__imp__le__base,axiom,
% 15.40/15.48 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( 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)))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__increasing,axiom,
% 15.40/15.48 ! [V_a,V_N,V_n,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__pCons__eq,axiom,
% 15.40/15.48 ! [V_a,V_p,T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_dvd__imp__degree__le,axiom,
% 15.40/15.48 ! [V_q,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
% 15.40/15.48 => ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__decreasing,axiom,
% 15.40/15.48 ! [V_a,V_N,V_n,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.48 => 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)) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_order__degree,axiom,
% 15.40/15.48 ! [V_a,V_p,T_a] :
% 15.40/15.48 ( class_Rings_Oidom(T_a)
% 15.40/15.48 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => 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)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_le__imp__neg__le,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__le__iff__le,axiom,
% 15.40/15.48 ! [V_aa_2,V_b_2,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_minus__le__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_le__minus__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__minus,axiom,
% 15.40/15.48 ! [V_p,T_a] :
% 15.40/15.48 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Polynomial_Odegree(T_a,V_p) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__0__Suc,axiom,
% 15.40/15.48 ! [V_n,T_a] :
% 15.40/15.48 ( ( class_Power_Opower(T_a)
% 15.40/15.48 & class_Rings_Osemiring__0(T_a) )
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__Suc2,axiom,
% 15.40/15.48 ! [V_n,V_a,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__Suc,axiom,
% 15.40/15.48 ! [V_n,V_a,T_a] :
% 15.40/15.48 ( class_Power_Opower(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__mono,axiom,
% 15.40/15.48 ! [V_n,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_zero__le__power,axiom,
% 15.40/15.48 ! [V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => 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)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_one__le__power,axiom,
% 15.40/15.48 ! [V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.48 => 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)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__le__dvd,axiom,
% 15.40/15.48 ! [V_m,V_b,V_n,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.48 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_dvd__power__le,axiom,
% 15.40/15.48 ! [V_m,V_n,V_y,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.48 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_le__imp__power__dvd,axiom,
% 15.40/15.48 ! [V_a,V_n,V_m,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.48 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__pCons__eq__if,axiom,
% 15.40/15.48 ! [V_a,V_p,T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.48 & ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__0,axiom,
% 15.40/15.48 ! [T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_split__mult__neg__le,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 15.40/15.48 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 15.40/15.48 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 15.40/15.48 => 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)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_split__mult__pos__le,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.48 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 15.40/15.48 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 15.40/15.48 => 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)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__mono,axiom,
% 15.40/15.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.48 => 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)) ) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__mono_H,axiom,
% 15.40/15.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.48 => 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)) ) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__left__mono__neg,axiom,
% 15.40/15.48 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__right__mono__neg,axiom,
% 15.40/15.48 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__mult__left__mono,axiom,
% 15.40/15.48 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__comm__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__left__mono,axiom,
% 15.40/15.48 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__right__mono,axiom,
% 15.40/15.48 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__nonpos__nonpos,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__nonpos__nonneg,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__nonneg__nonpos2,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__nonneg__nonpos,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__nonneg__nonneg,axiom,
% 15.40/15.48 ! [V_b,V_a,T_a] :
% 15.40/15.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.48 => 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)) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__le__0__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 15.40/15.48 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_zero__le__mult__iff,axiom,
% 15.40/15.48 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.48 => ( 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_aa_2),V_b_2))
% 15.40/15.48 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 15.40/15.48 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_zero__le__square,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__ring(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_zero__le__one,axiom,
% 15.40/15.48 ! [T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_not__one__le__zero,axiom,
% 15.40/15.48 ! [T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.48 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 15.40/15.48 ! [V_q,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 15.40/15.48 ! [V_q,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 15.40/15.48 ! [V_q,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => 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)) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_minus__le__self__iff,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__le__0__iff__le,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_le__minus__self__iff,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_neg__0__le__iff__le,axiom,
% 15.40/15.48 ! [V_aa_2,T_a] :
% 15.40/15.48 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.48 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__1,axiom,
% 15.40/15.48 ! [T_a] :
% 15.40/15.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__pCons__0,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Ozero(T_a)
% 15.40/15.48 => c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__left__le__one__le,axiom,
% 15.40/15.48 ! [V_y,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_mult__right__le__one__le,axiom,
% 15.40/15.48 ! [V_y,V_x,T_a] :
% 15.40/15.48 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 15.40/15.48 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.48 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__mult,axiom,
% 15.40/15.48 ! [V_n,V_m,V_a,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => 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) ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_power__one__right,axiom,
% 15.40/15.48 ! [V_a,T_a] :
% 15.40/15.48 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.48 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 15.40/15.48
% 15.40/15.48 fof(fact_degree__linear__power,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.49 => c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_field__power__not__zero,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 15.40/15.49 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.49 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__mult__distrib,axiom,
% 15.40/15.49 ! [V_n,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Groups_Ocomm__monoid__mult(T_a)
% 15.40/15.49 => 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)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__commutes,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.49 => 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)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le0,axiom,
% 15.40/15.49 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__1__left,axiom,
% 15.40/15.49 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_realpow__Suc__le__self,axiom,
% 15.40/15.49 ! [V_n,V_r,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.49 => 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) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_IH,axiom,
% 15.40/15.49 ! [B_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,v_na____)
% 15.40/15.49 => ! [B_p,B_q] :
% 15.40/15.49 ( ! [B_x] :
% 15.40/15.49 ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 15.40/15.49 => hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
% 15.40/15.49 => ( c_Polynomial_Odegree(tc_Complex_Ocomplex,B_p) = B_m
% 15.40/15.49 => ( B_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_q),B_m))) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_one__le__mult__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_realpow__two__disj,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.49 ( class_Rings_Oidom(T_a)
% 15.40/15.49 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),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_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 15.40/15.49 <=> ( V_x_2 = V_y_2
% 15.40/15.49 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__eq__self__implies__10,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 15.40/15.49 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 15.40/15.49 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__mult__le__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_One__nat__def,axiom,
% 15.40/15.49 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oorder__refl,axiom,
% 15.40/15.49 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__zeroE,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__mono,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_lessI,axiom,
% 15.40/15.49 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_zero__less__Suc,axiom,
% 15.40/15.49 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oeq__iff,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2] :
% 15.40/15.49 ( V_x_2 = V_y_2
% 15.40/15.49 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Ole__less,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 15.40/15.49 | V_x_2 = V_y_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__le,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 15.40/15.49 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 & V_x_2 != V_y_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oneq__le__trans,axiom,
% 15.40/15.49 ! [V_b,V_a] :
% 15.40/15.49 ( V_a != V_b
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oeq__refl,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( V_x = V_y
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oantisym__conv,axiom,
% 15.40/15.49 ! [V_x_2,V_y_2] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.49 <=> V_x_2 = V_y_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 | V_x = V_y ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Ole__neq__trans,axiom,
% 15.40/15.49 ! [V_b,V_a] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 => ( V_a != V_b
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a] :
% 15.40/15.49 ( V_a = V_b
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 => ( V_b = V_c
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__antisym,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 15.40/15.49 => V_m = V_n ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oantisym,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 15.40/15.49 => V_x = V_y ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oorder__trans,axiom,
% 15.40/15.49 ! [V_z,V_y,V_x] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a] :
% 15.40/15.49 ( V_a = V_b
% 15.40/15.49 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Ole__less__trans,axiom,
% 15.40/15.49 ! [V_z,V_y,V_x] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__imp__neq,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => V_x != V_y ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__not__sym,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__imp__le,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__imp__not__less,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => V_x != V_y ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => V_y != V_x ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 15.40/15.49 => ( V_b = V_c
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__le__trans,axiom,
% 15.40/15.49 ! [V_z,V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__asym_H,axiom,
% 15.40/15.49 ! [V_b,V_a] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 15.40/15.49 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__trans,axiom,
% 15.40/15.49 ! [V_z,V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd_Oless__asym,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.40/15.49 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 15.40/15.49 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_linorder__neqE__linordered__idom,axiom,
% 15.40/15.49 ! [V_y,V_x,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.49 => ( V_x != V_y
% 15.40/15.49 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__less__cases,axiom,
% 15.40/15.49 ! [V_P_2,V_nb_2,V_m_2] :
% 15.40/15.49 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 15.40/15.49 => ( ( V_m_2 = V_nb_2
% 15.40/15.49 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 15.40/15.49 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 15.40/15.49 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 15.40/15.49 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__not__refl3,axiom,
% 15.40/15.49 ! [V_t,V_s] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 15.40/15.49 => V_s != V_t ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__not__refl2,axiom,
% 15.40/15.49 ! [V_m,V_n] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 15.40/15.49 => V_m != V_n ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__irrefl__nat,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_linorder__neqE__nat,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( V_x != V_y
% 15.40/15.49 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__neq__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( V_m_2 != V_nb_2
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__not__refl,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__less0,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_neq0__conv,axiom,
% 15.40/15.49 ! [V_nb_2] :
% 15.40/15.49 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__nat__zero__code,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__dvd__not__less,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_gr__implies__not0,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_gr0I,axiom,
% 15.40/15.49 ! [V_n] :
% 15.40/15.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__less__SucD,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__lessD,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__SucE,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 15.40/15.49 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => V_m = V_n ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__trans__Suc,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__lessI,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => ( c_Nat_OSuc(V_m) != V_n
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__SucI,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__antisym,axiom,
% 15.40/15.49 ! [V_m,V_n] :
% 15.40/15.49 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 15.40/15.49 => V_m = V_n ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__less__less__Suc__eq,axiom,
% 15.40/15.49 ! [V_m_2,V_nb_2] :
% 15.40/15.49 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 15.40/15.49 <=> V_nb_2 = V_m_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__less__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__Suc__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 | V_m_2 = V_nb_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__less__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__or__eq__imp__le,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 | V_m = V_n )
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__neq__implies__less,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => ( V_m != V_n
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__imp__le__nat,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__eq__less__or__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 | V_m_2 = V_nb_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__less__le,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 & V_m_2 != V_nb_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__strict__increasing__iff,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 15.40/15.49 => ( 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))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__less__imp__less__exp,axiom,
% 15.40/15.49 ! [V_n,V_m,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__strict__increasing,axiom,
% 15.40/15.49 ! [V_a,V_N,V_n,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__minus__iff,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_minus__less__iff,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_neg__less__iff__less,axiom,
% 15.40/15.49 ! [V_aa_2,V_b_2,T_a] :
% 15.40/15.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__power__less__imp__less,axiom,
% 15.40/15.49 ! [V_n,V_m,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__zero__less__power__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_x_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 15.40/15.49 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__Suc__eq__0__disj,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 15.40/15.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 | ? [B_j] :
% 15.40/15.49 ( V_m_2 = c_Nat_OSuc(B_j)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__Suc0,axiom,
% 15.40/15.49 ! [V_nb_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 15.40/15.49 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_gr0__conv__Suc,axiom,
% 15.40/15.49 ! [V_nb_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
% 15.40/15.49 <=> ? [B_m] : V_nb_2 = c_Nat_OSuc(B_m) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__imp__le,axiom,
% 15.40/15.49 ! [V_n,V_k] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__le__lessD,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__less__Suc__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 15.40/15.49 <=> V_nb_2 = V_m_2 ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__leI,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__imp__less__Suc,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__le__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__Suc__eq__le,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__eq__Suc__le,axiom,
% 15.40/15.49 ! [V_m_2,V_nb_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__0__less__mult__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel2,axiom,
% 15.40/15.49 ! [V_nb_2,V_k_2,V_m_2] :
% 15.40/15.49 ( 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_nb_2),V_k_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__mono1,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 15.40/15.49 => 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)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__mono2,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 15.40/15.49 => 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)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__mult__cancel,axiom,
% 15.40/15.49 ! [V_n,V_m,V_k] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__mult__less__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__strict__decreasing,axiom,
% 15.40/15.49 ! [V_a,V_N,V_n,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.49 => 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)) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_one__less__power,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__strict__mono,axiom,
% 15.40/15.49 ! [V_n,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.49 => 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)) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__square__less__zero,axiom,
% 15.40/15.49 ! [V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring(T_a)
% 15.40/15.49 => ~ 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)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel__right__disj,axiom,
% 15.40/15.49 ! [V_b_2,V_c_2,V_aa_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
% 15.40/15.49 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 15.40/15.49 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel__left__disj,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 15.40/15.49 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 15.40/15.49 & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
% 15.40/15.49 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel__left__pos,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__pos__pos,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__pos__neg,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__pos__neg2,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_zero__less__mult__pos,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_zero__less__mult__pos2,axiom,
% 15.40/15.49 ! [V_a,V_b,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__cancel__left__neg,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__neg__pos,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__neg__neg,axiom,
% 15.40/15.49 ! [V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__right__mono,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__left__mono,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_comm__mult__strict__left__mono,axiom,
% 15.40/15.49 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__right__mono__neg,axiom,
% 15.40/15.49 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__left__mono__neg,axiom,
% 15.40/15.49 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__one__less__zero,axiom,
% 15.40/15.49 ! [T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_zero__less__one,axiom,
% 15.40/15.49 ! [T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_neg__0__less__iff__less,axiom,
% 15.40/15.49 ! [V_aa_2,T_a] :
% 15.40/15.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_neg__less__0__iff__less,axiom,
% 15.40/15.49 ! [V_aa_2,T_a] :
% 15.40/15.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_neg__less__nonneg,axiom,
% 15.40/15.49 ! [V_aa_2,T_a] :
% 15.40/15.49 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__minus__self__iff,axiom,
% 15.40/15.49 ! [V_aa_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__1__mult,axiom,
% 15.40/15.49 ! [V_n,V_m,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_zero__less__power,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => 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)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__inject__exp,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_aa_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
% 15.40/15.49 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2)
% 15.40/15.49 <=> V_m_2 = V_nb_2 ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_one__less__mult,axiom,
% 15.40/15.49 ! [V_m,V_n] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 15.40/15.49 => 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)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_n__less__n__mult__m,axiom,
% 15.40/15.49 ! [V_m,V_n] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_n__less__m__mult__n,axiom,
% 15.40/15.49 ! [V_m,V_n] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__cancel2,axiom,
% 15.40/15.49 ! [V_nb_2,V_k_2,V_m_2] :
% 15.40/15.49 ( 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_nb_2),V_k_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__mult__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)),V_m_2))
% 15.40/15.49 <=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__mult__cancel2,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_m_2)),V_m_2))
% 15.40/15.49 <=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__dvd__imp__le,axiom,
% 15.40/15.49 ! [V_n,V_m,V_i] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__cancel__left__pos,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__cancel__left__neg,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__mono,axiom,
% 15.40/15.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__strict__mono_H,axiom,
% 15.40/15.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__le__imp__less,axiom,
% 15.40/15.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__less__imp__less,axiom,
% 15.40/15.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => 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)) ) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__right__less__imp__less,axiom,
% 15.40/15.49 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__imp__less__right,axiom,
% 15.40/15.49 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__left__less__imp__less,axiom,
% 15.40/15.49 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__less__imp__less__left,axiom,
% 15.40/15.49 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__right__le__imp__le,axiom,
% 15.40/15.49 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__left__le__imp__le,axiom,
% 15.40/15.49 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semiring__strict(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__less__imp__less__base,axiom,
% 15.40/15.49 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.49 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__gt1__lemma,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => 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))) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__less__power__Suc,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => 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))) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__gt1,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => 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))) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__inject,axiom,
% 15.40/15.49 ! [V_y,V_x] :
% 15.40/15.49 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 15.40/15.49 => V_x = V_y ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat_Oinject,axiom,
% 15.40/15.49 ! [V_nat_H_2,V_nat_2] :
% 15.40/15.49 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 15.40/15.49 <=> V_nat_2 = V_nat_H_2 ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__n__not__n,axiom,
% 15.40/15.49 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 15.40/15.49
% 15.40/15.49 fof(fact_n__not__Suc__n,axiom,
% 15.40/15.49 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__antisym,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.49 => V_m = V_n ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__trans,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_eq__imp__le,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( V_m = V_n
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__le__linear,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__refl,axiom,
% 15.40/15.49 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__commute,axiom,
% 15.40/15.49 ! [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) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__assoc,axiom,
% 15.40/15.49 ! [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)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__dvd__1__iff__1,axiom,
% 15.40/15.49 ! [V_m_2] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 15.40/15.49 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__Suc__less,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__Suc__less__one,axiom,
% 15.40/15.49 ! [V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.49 => 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)) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__le__imp__le__exp,axiom,
% 15.40/15.49 ! [V_n,V_m,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 15.40/15.49 => ( 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))
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__increasing__iff,axiom,
% 15.40/15.49 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 15.40/15.49 => ( 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))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_power__eq__imp__eq__base,axiom,
% 15.40/15.49 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.49 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.49 => ( 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)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.49 => V_a = V_b ) ) ) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__power,axiom,
% 15.40/15.49 ! [V_x,V_n,T_a] :
% 15.40/15.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.49 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.49 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 15.40/15.49 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Zero__not__Suc,axiom,
% 15.40/15.49 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat_Osimps_I2_J,axiom,
% 15.40/15.49 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__not__Zero,axiom,
% 15.40/15.49 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat_Osimps_I3_J,axiom,
% 15.40/15.49 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_dvd__1__iff__1,axiom,
% 15.40/15.49 ! [V_m_2] :
% 15.40/15.49 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 15.40/15.49 <=> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Zero__neq__Suc,axiom,
% 15.40/15.49 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__neq__Zero,axiom,
% 15.40/15.49 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 15.40/15.49 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__0__eq,axiom,
% 15.40/15.49 ! [V_nb_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.49 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__leD,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__SucE,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 15.40/15.49 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__SucI,axiom,
% 15.40/15.49 ! [V_n,V_m] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.49 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__le__mono,axiom,
% 15.40/15.49 ! [V_m_2,V_nb_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__Suc__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 15.40/15.49 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 | V_m_2 = c_Nat_OSuc(V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_not__less__eq__eq,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__n__not__le__n,axiom,
% 15.40/15.49 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__0,axiom,
% 15.40/15.49 ! [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) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__0__right,axiom,
% 15.40/15.49 ! [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) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__is__0,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.49 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2)
% 15.40/15.49 <=> ( V_m_2 = V_nb_2
% 15.40/15.49 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__cancel2,axiom,
% 15.40/15.49 ! [V_nb_2,V_k_2,V_m_2] :
% 15.40/15.49 ( 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_nb_2),V_k_2)
% 15.40/15.49 <=> ( V_m_2 = V_nb_2
% 15.40/15.49 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_Suc__mult__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( 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_nb_2)
% 15.40/15.49 <=> V_m_2 = V_nb_2 ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__square,axiom,
% 15.40/15.49 ! [V_m] : 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)) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_le__cube,axiom,
% 15.40/15.49 ! [V_m] : 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))) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__mono1,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => 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)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__mono2,axiom,
% 15.40/15.49 ! [V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => 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)) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__le__mono,axiom,
% 15.40/15.49 ! [V_l,V_k,V_j,V_i] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.49 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 15.40/15.49 => 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)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__1,axiom,
% 15.40/15.49 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__1__eq__mult__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)
% 15.40/15.49 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 15.40/15.49 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__1__right,axiom,
% 15.40/15.49 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__eq__1__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 15.40/15.49 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 15.40/15.49 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_mult__eq__1__iff,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2] :
% 15.40/15.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.49 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.49 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__le__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 => ( 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_nb_2))
% 15.40/15.49 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_nat__mult__dvd__cancel1,axiom,
% 15.40/15.49 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.49 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.49 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_nb_2)))
% 15.40/15.49 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2)) ) ) ).
% 15.40/15.49
% 15.40/15.49 fof(fact_pow__divides__eq__nat,axiom,
% 15.40/15.49 ! [V_b_2,V_aa_2,V_nb_2] :
% 15.40/15.49 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_nb_2)))
% 15.40/15.50 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_aa_2),V_b_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pow__divides__pow__nat,axiom,
% 15.40/15.50 ! [V_b,V_n,V_a] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)))
% 15.40/15.50 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zero__less__power__nat__eq,axiom,
% 15.40/15.50 ! [V_nb_2,V_x_2] :
% 15.40/15.50 ( 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_nb_2))
% 15.40/15.50 <=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 15.40/15.50 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_nb_2)))
% 15.40/15.50 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_nat__mult__eq__cancel1,axiom,
% 15.40/15.50 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.50 => ( 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_nb_2)
% 15.40/15.50 <=> V_m_2 = V_nb_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_nat__mult__less__cancel1,axiom,
% 15.40/15.50 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 15.40/15.50 => ( 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_nb_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pow__divides__pow__int,axiom,
% 15.40/15.50 ! [V_b,V_n,V_a] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)))
% 15.40/15.50 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pow__divides__eq__int,axiom,
% 15.40/15.50 ! [V_b_2,V_aa_2,V_nb_2] :
% 15.40/15.50 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_nb_2)))
% 15.40/15.50 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_b_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
% 15.40/15.50 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 15.40/15.50 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.50 ( 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_nb_2)
% 15.40/15.50 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 | V_m_2 = V_nb_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
% 15.40/15.50 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 15.40/15.50 ! [V_x] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 15.40/15.50 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_dvd__pos__nat,axiom,
% 15.40/15.50 ! [V_m,V_n] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 15.40/15.50 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_psize__def,axiom,
% 15.40/15.50 ! [V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.50 & ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 => c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__refl,axiom,
% 15.40/15.50 ! [V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_power__power__power,axiom,
% 15.40/15.50 ! [T_a] :
% 15.40/15.50 ( class_Power_Opower(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_degree__pcompose__le,axiom,
% 15.40/15.50 ! [V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => 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))) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pcompose__0,axiom,
% 15.40/15.50 ! [V_q,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__pcompose,axiom,
% 15.40/15.50 ! [V_x,V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_power_Opower_Opower__0,axiom,
% 15.40/15.50 ! [V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 15.40/15.50
% 15.40/15.50 fof(fact_power_Opower_Opower__Suc,axiom,
% 15.40/15.50 ! [V_nb_2,V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Nat_OSuc(V_nb_2)) = hAPP(hAPP(V_times_2,V_aa_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),V_nb_2)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__le__cases,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_le__funE,axiom,
% 15.40/15.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 15.40/15.50 ( class_Orderings_Oord(T_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I6_J,axiom,
% 15.40/15.50 ! [V_z,V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I5_J,axiom,
% 15.40/15.50 ! [V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => V_x = V_y ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__trans,axiom,
% 15.40/15.50 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__antisym,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => V_x = V_y ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I4_J,axiom,
% 15.40/15.50 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.50 => ( V_b = V_c
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_ord__le__eq__trans,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oord(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => ( V_b = V_c
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I3_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( V_a = V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_ord__eq__le__trans,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oord(T_a)
% 15.40/15.50 => ( V_a = V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__antisym__conv,axiom,
% 15.40/15.50 ! [V_x_2,V_y_2,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_le__funD,axiom,
% 15.40/15.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 15.40/15.50 ( class_Orderings_Oord(T_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__eq__refl,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( V_x = V_y
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__eq__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( V_x_2 = V_y_2
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__linear,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_le__fun__def,axiom,
% 15.40/15.50 ! [V_g_2,V_f_2,T_a,T_b] :
% 15.40/15.50 ( class_Orderings_Oord(T_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 15.40/15.50 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__cases,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ( V_x != V_y
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__asym,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I10_J,axiom,
% 15.40/15.50 ! [V_z,V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__trans,axiom,
% 15.40/15.50 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I2_J,axiom,
% 15.40/15.50 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 15.40/15.50 => ( V_b = V_c
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_ord__less__eq__trans,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oord(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => ( V_b = V_c
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I1_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( V_a = V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_ord__eq__less__trans,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oord(T_a)
% 15.40/15.50 => ( V_a = V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I9_J,axiom,
% 15.40/15.50 ! [V_a,V_b,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__asym_H,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__imp__not__eq2,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => V_y != V_x ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__imp__not__eq,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => V_x != V_y ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__imp__not__less,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__not__sym,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_less__imp__neq,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => V_x != V_y ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__neqE,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( V_x != V_y
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__antisym__conv3,axiom,
% 15.40/15.50 ! [V_x_2,V_y_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__less__linear,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 | V_x = V_y
% 15.40/15.50 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_not__less__iff__gr__or__eq,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 15.40/15.50 | V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__neq__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( V_x_2 != V_y_2
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__irrefl,axiom,
% 15.40/15.50 ! [V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_psize__eq__0__iff,axiom,
% 15.40/15.50 ! [V_pb_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__not__less,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__not__le,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__le__less__linear,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__le,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 & V_x_2 != V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_less__le__not__le,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__le__less,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 | V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_leI,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_not__leE,axiom,
% 15.40/15.50 ! [V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__antisym__conv1,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__neq__le__trans,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( V_a != V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I12_J,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( V_a != V_b
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_leD,axiom,
% 15.40/15.50 ! [V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__imp__le,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_linorder__antisym__conv2,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Orderings_Olinorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 15.40/15.50 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__le__imp__less__or__eq,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 | V_x = V_y ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__le__neq__trans,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => ( V_a != V_b
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I11_J,axiom,
% 15.40/15.50 ! [V_a,V_b,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.50 => ( V_a != V_b
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__less__le__trans,axiom,
% 15.40/15.50 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I7_J,axiom,
% 15.40/15.50 ! [V_z,V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_order__le__less__trans,axiom,
% 15.40/15.50 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.50 ( class_Orderings_Opreorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_xt1_I8_J,axiom,
% 15.40/15.50 ! [V_z,V_x,V_y,T_a] :
% 15.40/15.50 ( class_Orderings_Oorder(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zpower__zpower,axiom,
% 15.40/15.50 ! [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)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_termination__basic__simps_I5_J,axiom,
% 15.40/15.50 ! [V_y,V_x] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__poly__pCons,axiom,
% 15.40/15.50 ! [V_pb_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
% 15.40/15.50 <=> ( c_Polynomial_Opos__poly(T_a,V_pb_2)
% 15.40/15.50 | ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_compl__le__compl__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Lattices_Oboolean__algebra(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_compl__mono,axiom,
% 15.40/15.50 ! [V_y,V_x,T_a] :
% 15.40/15.50 ( class_Lattices_Oboolean__algebra(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_less__fun__def,axiom,
% 15.40/15.50 ! [V_g_2,V_f_2,T_a,T_b] :
% 15.40/15.50 ( class_Orderings_Oord(T_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 15.40/15.50 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_not__pos__poly__0,axiom,
% 15.40/15.50 ! [T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__poly__mult,axiom,
% 15.40/15.50 ! [V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 15.40/15.50 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult__left__idem,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 15.40/15.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult__idem,axiom,
% 15.40/15.50 ! [V_x,T_a] :
% 15.40/15.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 15.40/15.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_times_Oidem,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 15.40/15.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_compl__eq__compl__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Lattices_Oboolean__algebra(T_a)
% 15.40/15.50 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_uminus__apply,axiom,
% 15.40/15.50 ! [V_x_2,V_A_2,T_b,T_a] :
% 15.40/15.50 ( class_Groups_Ouminus(T_a)
% 15.40/15.50 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_double__compl,axiom,
% 15.40/15.50 ! [V_x,T_a] :
% 15.40/15.50 ( class_Lattices_Oboolean__algebra(T_a)
% 15.40/15.50 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zdvd__antisym__nonneg,axiom,
% 15.40/15.50 ! [V_n,V_m] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 15.40/15.50 => V_m = V_n ) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zdvd__mult__cancel,axiom,
% 15.40/15.50 ! [V_n,V_m,V_k] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
% 15.40/15.50 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zdvd__imp__le,axiom,
% 15.40/15.50 ! [V_n,V_z] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zdvd__not__zless,axiom,
% 15.40/15.50 ! [V_n,V_m] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
% 15.40/15.50 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__poly__total,axiom,
% 15.40/15.50 ! [V_p,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 | c_Polynomial_Opos__poly(T_a,V_p)
% 15.40/15.50 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__replicate__append,axiom,
% 15.40/15.50 ! [V_x,V_p,V_n,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__rec__pCons,axiom,
% 15.40/15.50 ! [V_pb_2,V_aa_2,T_a,V_z_2,V_f_2,T_b] :
% 15.40/15.50 ( class_Groups_Ozero(T_b)
% 15.40/15.50 => ( 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
% 15.40/15.50 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_synthetic__div__eq__0__iff,axiom,
% 15.40/15.50 ! [V_c_2,V_pb_2,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => ( c_Polynomial_Osynthetic__div(T_a,V_pb_2,V_c_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 <=> c_Polynomial_Odegree(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_eq__zero__or__degree__less,axiom,
% 15.40/15.50 ! [V_n,V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.50 => ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) ) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zle__refl,axiom,
% 15.40/15.50 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zle__linear,axiom,
% 15.40/15.50 ! [V_w,V_z] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 15.40/15.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zle__trans,axiom,
% 15.40/15.50 ! [V_k,V_j,V_i] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zle__antisym,axiom,
% 15.40/15.50 ! [V_w,V_z] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 15.40/15.50 => V_z = V_w ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zminus__0,axiom,
% 15.40/15.50 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__1,axiom,
% 15.40/15.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__1__right,axiom,
% 15.40/15.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__commute,axiom,
% 15.40/15.50 ! [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) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__zminus,axiom,
% 15.40/15.50 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__assoc,axiom,
% 15.40/15.50 ! [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)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_int__0__neq__1,axiom,
% 15.40/15.50 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zless__linear,axiom,
% 15.40/15.50 ! [V_y,V_x] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 15.40/15.50 | V_x = V_y
% 15.40/15.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zless__le,axiom,
% 15.40/15.50 ! [V_w_2,V_z_2] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 15.40/15.50 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2)
% 15.40/15.50 & V_z_2 != V_w_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zmult__zless__mono2,axiom,
% 15.40/15.50 ! [V_k,V_j,V_i] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__zmult__eq__1__iff,axiom,
% 15.40/15.50 ! [V_nb_2,V_m_2] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 15.40/15.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 15.40/15.50 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 15.40/15.50 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_int__one__le__iff__zero__less,axiom,
% 15.40/15.50 ! [V_z_2] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_int__0__less__1,axiom,
% 15.40/15.50 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__monom,axiom,
% 15.40/15.50 ! [V_a,V_n,V_m,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( ( V_m = V_n
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = V_a )
% 15.40/15.50 & ( V_m != V_n
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_expand__poly__eq,axiom,
% 15.40/15.50 ! [V_qb_2,V_pb_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( V_pb_2 = V_qb_2
% 15.40/15.50 <=> ! [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_qb_2),B_n) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__inject,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2)
% 15.40/15.50 <=> V_x_2 = V_y_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_monom__eq__iff,axiom,
% 15.40/15.50 ! [V_b_2,V_nb_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Polynomial_Omonom(T_a,V_b_2,V_nb_2)
% 15.40/15.50 <=> V_aa_2 = V_b_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__0,axiom,
% 15.40/15.50 ! [V_n,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__pCons__0,axiom,
% 15.40/15.50 ! [V_p,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__pCons__Suc,axiom,
% 15.40/15.50 ! [V_n,V_p,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(V_n)) = hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_synthetic__div__0,axiom,
% 15.40/15.50 ! [V_c,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__minus,axiom,
% 15.40/15.50 ! [V_n,V_p,T_a] :
% 15.40/15.50 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__dvd__antisym,axiom,
% 15.40/15.50 ! [V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Oidom(T_a)
% 15.40/15.50 => ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) = hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_q),V_p))
% 15.40/15.50 => V_p = V_q ) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_monom__eq__0,axiom,
% 15.40/15.50 ! [V_n,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_monom__eq__0__iff,axiom,
% 15.40/15.50 ! [V_nb_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_degree__monom__eq,axiom,
% 15.40/15.50 ! [V_n,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 => c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)) = V_n ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_degree__monom__le,axiom,
% 15.40/15.50 ! [V_n,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_minus__monom,axiom,
% 15.40/15.50 ! [V_n,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.50 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__eq__0,axiom,
% 15.40/15.50 ! [V_n,V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_le__degree,axiom,
% 15.40/15.50 ! [V_n,V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_leading__coeff__0__iff,axiom,
% 15.40/15.50 ! [V_pb_2,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 <=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_leading__coeff__neq__0,axiom,
% 15.40/15.50 ! [V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_monom__Suc,axiom,
% 15.40/15.50 ! [V_n,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__monom,axiom,
% 15.40/15.50 ! [V_x,V_n,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_monom__0,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ozero(T_a)
% 15.40/15.50 => c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_synthetic__div__pCons,axiom,
% 15.40/15.50 ! [V_c,V_p,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__rec__0,axiom,
% 15.40/15.50 ! [T_a,V_z_2,V_f_2,T_b] :
% 15.40/15.50 ( class_Groups_Ozero(T_b)
% 15.40/15.50 => ( 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
% 15.40/15.50 => 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 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__1,axiom,
% 15.40/15.50 ! [V_n,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 15.40/15.50 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__poly__def,axiom,
% 15.40/15.50 ! [V_pb_2,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,V_pb_2)
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2))) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__linear__power,axiom,
% 15.40/15.50 ! [V_n,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__rec_Osimps,axiom,
% 15.40/15.50 ! [V_pb_2,V_aa_2,V_f_2,V_z_2,T_a,T_b] :
% 15.40/15.50 ( class_Groups_Ozero(T_b)
% 15.40/15.50 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_If(T_a,c_fequal(V_pb_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2))) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 15.40/15.50 ! [V_n,V_x] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zdvd__mono,axiom,
% 15.40/15.50 ! [V_t_2,V_m_2,V_k_2] :
% 15.40/15.50 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 15.40/15.50 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 15.40/15.50 ! [V_y,V_x] :
% 15.40/15.50 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_synthetic__div__correct_H,axiom,
% 15.40/15.50 ! [V_p,V_c,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zminus__zminus,axiom,
% 15.40/15.50 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 15.40/15.50
% 15.40/15.50 fof(fact_double__eq__0__iff,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__le__cancel__right,axiom,
% 15.40/15.50 ! [V_b_2,V_c_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__le__cancel__left,axiom,
% 15.40/15.50 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__right__mono,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__left__mono,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__mono,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__le__imp__le__right,axiom,
% 15.40/15.50 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( 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))
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__le__imp__le__left,axiom,
% 15.40/15.50 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( 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))
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__poly__code_I2_J,axiom,
% 15.40/15.50 ! [V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__poly__code_I1_J,axiom,
% 15.40/15.50 ! [V_q,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult__poly__add__left,axiom,
% 15.40/15.50 ! [V_r,V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__0__iff,axiom,
% 15.40/15.50 ! [V_aa_2,V_b_2,T_a] :
% 15.40/15.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 15.40/15.50 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
% 15.40/15.50 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add_Ocomm__neutral,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__0__right,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Groups_Omonoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_double__zero__sym,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
% 15.40/15.50 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__0,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__0__left,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Groups_Omonoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__less__imp__less__left,axiom,
% 15.40/15.50 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( 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))
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__less__imp__less__right,axiom,
% 15.40/15.50 ! [V_b,V_c,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( 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))
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__strict__mono,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__strict__left__mono,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__strict__right__mono,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => 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)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__less__cancel__left,axiom,
% 15.40/15.50 ! [V_b_2,V_aa_2,V_c_2,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__less__cancel__right,axiom,
% 15.40/15.50 ! [V_b_2,V_c_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_crossproduct__eq,axiom,
% 15.40/15.50 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 15.40/15.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 15.40/15.50 => ( 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))
% 15.40/15.50 <=> ( V_w_2 = V_x_2
% 15.40/15.50 | V_y_2 = V_z_2 ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_combine__common__factor,axiom,
% 15.40/15.50 ! [V_c,V_b,V_e,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Osemiring(T_a)
% 15.40/15.50 => 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) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 15.40/15.50 ! [V_b,V_m,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__class_Odistrib,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_crossproduct__noteq,axiom,
% 15.40/15.50 ! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 15.40/15.50 => ( ( V_aa_2 != V_b_2
% 15.40/15.50 & V_c_2 != V_d_2 )
% 15.40/15.50 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 15.40/15.50 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult__left_Oadd,axiom,
% 15.40/15.50 ! [V_ya,V_y,V_x,T_a] :
% 15.40/15.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult_Oadd__left,axiom,
% 15.40/15.50 ! [V_b,V_a_H,V_a,T_a] :
% 15.40/15.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult__right_Oadd,axiom,
% 15.40/15.50 ! [V_y,V_x,V_xa,T_a] :
% 15.40/15.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_mult_Oadd__right,axiom,
% 15.40/15.50 ! [V_b_H,V_b,V_a,T_a] :
% 15.40/15.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_minus__add__cancel,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__minus__cancel,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_minus__add,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.50 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_minus__add__distrib,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.50 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_coeff__add,axiom,
% 15.40/15.50 ! [V_n,V_q,V_p,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__monom,axiom,
% 15.40/15.50 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_dvd__add,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.50 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 15.40/15.50 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__right__imp__eq,axiom,
% 15.40/15.50 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.50 ( class_Groups_Ocancel__semigroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 15.40/15.50 => V_b = V_c ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__imp__eq,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 15.40/15.50 => V_b = V_c ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__left__imp__eq,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocancel__semigroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 15.40/15.50 => V_b = V_c ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__right__cancel,axiom,
% 15.40/15.50 ! [V_c_2,V_aa_2,V_b_2,T_a] :
% 15.40/15.50 ( class_Groups_Ocancel__semigroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2)
% 15.40/15.50 <=> V_b_2 = V_c_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__left__cancel,axiom,
% 15.40/15.50 ! [V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Ocancel__semigroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2)
% 15.40/15.50 <=> V_b_2 = V_c_2 ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oab__semigroup__add(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 15.40/15.50 ! [V_d,V_c,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 15.40/15.50 ! [V_d,V_c,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => 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)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 15.40/15.50 ! [V_c,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_poly__add,axiom,
% 15.40/15.50 ! [V_x,V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.50 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__pCons,axiom,
% 15.40/15.50 ! [V_q,V_b,V_p,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.50 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__poly__add,axiom,
% 15.40/15.50 ! [V_q,V_p,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 15.40/15.50 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 15.40/15.50 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__nonneg__nonneg,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__nonneg__eq__0__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__increasing,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__increasing2,axiom,
% 15.40/15.50 ! [V_a,V_b,V_c,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 15.40/15.50 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__nonpos__nonpos,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_even__less__0__iff,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 15.40/15.50 ! [V_aa_2,T_a] :
% 15.40/15.50 ( class_Groups_Olinordered__ab__group__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__pos__pos,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__neg__neg,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_pos__add__strict,axiom,
% 15.40/15.50 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 15.40/15.50 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_unity__coeff__ex,axiom,
% 15.40/15.50 ! [V_l_2,V_P_2,T_a] :
% 15.40/15.50 ( ( class_Rings_Odvd(T_a)
% 15.40/15.50 & class_Rings_Osemiring__0(T_a) )
% 15.40/15.50 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 15.40/15.50 <=> ? [B_x] :
% 15.40/15.50 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l_2),c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))))
% 15.40/15.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__less__le__mono,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__le__less__mono,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 15.40/15.50 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_add__scale__eq__noteq,axiom,
% 15.40/15.50 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 15.40/15.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 15.40/15.50 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 => ( ( V_a = V_b
% 15.40/15.50 & V_c != V_d )
% 15.40/15.50 => 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)) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_sum__squares__eq__zero__iff,axiom,
% 15.40/15.50 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.50 => ( 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)
% 15.40/15.50 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_less__add__one,axiom,
% 15.40/15.50 ! [V_a,T_a] :
% 15.40/15.50 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.50 => 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))) ) ).
% 15.40/15.50
% 15.40/15.50 fof(fact_minus__unique,axiom,
% 15.40/15.50 ! [V_b,V_a,T_a] :
% 15.40/15.50 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.50 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.50 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_ab__left__minus,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_left__minus,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 15.40/15.51 <=> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_right__minus,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__eq__0__iff,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.51 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 15.40/15.51 ! [V_m,V_a,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 15.40/15.51 ! [V_a,V_m,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 15.40/15.51 ! [V_m,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__add__less,axiom,
% 15.40/15.51 ! [V_q,V_n,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 15.40/15.51 => 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) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__add__eq__right,axiom,
% 15.40/15.51 ! [V_q,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
% 15.40/15.51 => 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__add__eq__left,axiom,
% 15.40/15.51 ! [V_p,V_q,T_a] :
% 15.40/15.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))
% 15.40/15.51 => 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__add__le,axiom,
% 15.40/15.51 ! [V_q,V_n,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 15.40/15.51 => 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) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__pos__nonneg,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__nonneg__pos,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__strict__increasing,axiom,
% 15.40/15.51 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__strict__increasing2,axiom,
% 15.40/15.51 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__neg__nonpos,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__nonpos__neg,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_sum__squares__le__zero__iff,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.51 => ( 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))
% 15.40/15.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_sum__squares__ge__zero,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__ring(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_sum__squares__gt__zero__iff,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__ring__strict(T_a)
% 15.40/15.51 => ( 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)))
% 15.40/15.51 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.51 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_not__sum__squares__lt__zero,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__ring(T_a)
% 15.40/15.51 => ~ 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zero__less__two,axiom,
% 15.40/15.51 ! [T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__semidom(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__pCons,axiom,
% 15.40/15.51 ! [V_x,V_p,V_a,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 15.40/15.51 ! [V_t_2,V_d_2] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 15.40/15.51 ! [V_t_2,V_d_2] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_convex__bound__le,axiom,
% 15.40/15.51 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__semiring__1(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 15.40/15.51 => 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) ) ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_convex__bound__lt,axiom,
% 15.40/15.51 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 15.40/15.51 => 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) ) ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pcompose__pCons,axiom,
% 15.40/15.51 ! [V_q,V_p,V_a,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 15.40/15.51 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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 15.40/15.51 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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__def,axiom,
% 15.40/15.51 ! [V_r_2,V_qb_2,V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_qb_2,V_r_2)
% 15.40/15.51 <=> ( 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_qb_2),V_y_2),V_r_2)
% 15.40/15.51 & ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 => V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.51 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 => ( V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2)) ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__le,axiom,
% 15.40/15.51 ! [V_p,V_n,T_a] :
% 15.40/15.51 ( class_Groups_Ozero(T_a)
% 15.40/15.51 => ( ! [B_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i)
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) = c_Groups_Ozero__class_Ozero(T_a) )
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__monic,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Ozero__class_Ozero(T_a) )
% 15.40/15.51 & ( ~ ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__degree__imp,axiom,
% 15.40/15.51 ! [V_p,V_n,T_a] :
% 15.40/15.51 ( class_Groups_Ozero(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))
% 15.40/15.51 => ? [B_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i)
% 15.40/15.51 & hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__dvd2,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_y)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__dvd1,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_x)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__leE,axiom,
% 15.40/15.51 ! [V_n,V_k,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 15.40/15.51 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__leD1,axiom,
% 15.40/15.51 ! [V_n,V_k,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__leD2,axiom,
% 15.40/15.51 ! [V_n,V_k,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__le__mono,axiom,
% 15.40/15.51 ! [V_l,V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__le__mono1,axiom,
% 15.40/15.51 ! [V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_trans__le__add2,axiom,
% 15.40/15.51 ! [V_m,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_trans__le__add1,axiom,
% 15.40/15.51 ! [V_m,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__left__cancel__le,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( 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_nb_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__iff__add,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.51 <=> ? [B_k] : V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add1,axiom,
% 15.40/15.51 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add2,axiom,
% 15.40/15.51 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__left__mono,axiom,
% 15.40/15.51 ! [V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_termination__basic__simps_I4_J,axiom,
% 15.40/15.51 ! [V_y,V_z,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_termination__basic__simps_I3_J,axiom,
% 15.40/15.51 ! [V_z,V_y,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__0,axiom,
% 15.40/15.51 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__0__right,axiom,
% 15.40/15.51 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zminus__zadd__distrib,axiom,
% 15.40/15.51 ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__zmult__distrib2,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__zmult__distrib,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_termination__basic__simps_I1_J,axiom,
% 15.40/15.51 ! [V_z,V_y,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_termination__basic__simps_I2_J,axiom,
% 15.40/15.51 ! [V_y,V_z,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__strict__right__mono,axiom,
% 15.40/15.51 ! [V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__eq__self__zero,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 15.40/15.51 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__is__0,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Nat_Oadd__0__right,axiom,
% 15.40/15.51 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 15.40/15.51
% 15.40/15.51 fof(fact_plus__nat_Oadd__0,axiom,
% 15.40/15.51 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 15.40/15.51
% 15.40/15.51 fof(fact_left__add__mult__distrib,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__mult__distrib,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__mult__distrib2,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_not__add__less1,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_not__add__less2,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__left__cancel__less,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( 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_nb_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_trans__less__add1,axiom,
% 15.40/15.51 ! [V_m,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_trans__less__add2,axiom,
% 15.40/15.51 ! [V_m,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__less__mono1,axiom,
% 15.40/15.51 ! [V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__less__mono,axiom,
% 15.40/15.51 ! [V_l,V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__add__eq__less,axiom,
% 15.40/15.51 ! [V_n,V_m,V_l,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__lessD1,axiom,
% 15.40/15.51 ! [V_k,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__reduce,axiom,
% 15.40/15.51 ! [V_nb_2,V_k_2] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_nb_2)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__Suc__shift,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__Suc,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__Suc__right,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__zero__iff,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__0__0,axiom,
% 15.40/15.51 ! [T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd_Ocommute,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,V_a,V_b) = c_Polynomial_Opoly__gcd(T_a,V_b,V_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd_Oleft__commute,axiom,
% 15.40/15.51 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c)) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd_Oassoc,axiom,
% 15.40/15.51 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__unique__div,axiom,
% 15.40/15.51 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 15.40/15.51 => V_q1 = V_q2 ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__unique__mod,axiom,
% 15.40/15.51 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 15.40/15.51 => V_r1 = V_r2 ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__unique,axiom,
% 15.40/15.51 ! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
% 15.40/15.51 => ( V_q1 = V_q2
% 15.40/15.51 & V_r1 = V_r2 ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__0__iff,axiom,
% 15.40/15.51 ! [V_r_2,V_qb_2,V_y_2,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_qb_2,V_r_2)
% 15.40/15.51 <=> ( V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__by__0__iff,axiom,
% 15.40/15.51 ! [V_r_2,V_qb_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_qb_2,V_r_2)
% 15.40/15.51 <=> ( V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_r_2 = V_x_2 ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__0,axiom,
% 15.40/15.51 ! [V_y,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__by__0,axiom,
% 15.40/15.51 ! [V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__greatest,axiom,
% 15.40/15.51 ! [V_y,V_x,V_k,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_x))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_y))
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__poly__gcd__iff,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,V_k_2,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)))
% 15.40/15.51 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_x_2))
% 15.40/15.51 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_y_2)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__minus__left,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__minus__right,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__1__right,axiom,
% 15.40/15.51 ! [V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__1__left,axiom,
% 15.40/15.51 ! [V_y,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 15.40/15.51 ! [V_q,V_p,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_power__add,axiom,
% 15.40/15.51 ! [V_n,V_m,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__is__1,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.51 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.51 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.51 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_one__is__add,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.51 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.40/15.51 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.51 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__gr__0,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( 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_nb_2))
% 15.40/15.51 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 15.40/15.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 15.40/15.51 ! [V_y,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__add__Suc1,axiom,
% 15.40/15.51 ! [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))) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__add__Suc2,axiom,
% 15.40/15.51 ! [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))) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__iff__Suc__add,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 15.40/15.51 <=> ? [B_k] : V_nb_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_odd__nonzero,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__zless__mono,axiom,
% 15.40/15.51 ! [V_z,V_z_H,V_w,V_w_H] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__Suc__right,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__Suc,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zless__add1__eq,axiom,
% 15.40/15.51 ! [V_z_2,V_w_2] :
% 15.40/15.51 ( 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)))
% 15.40/15.51 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 15.40/15.51 | V_w_2 = V_z_2 ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__eq__plus1__left,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__eq__plus1,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__zminus__inverse2,axiom,
% 15.40/15.51 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdvd__period,axiom,
% 15.40/15.51 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_aa_2] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_d_2))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2)),V_t_2))) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdvd__reduce,axiom,
% 15.40/15.51 ! [V_m_2,V_nb_2,V_k_2] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_nb_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_nb_2)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zpower__zadd__distrib,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_odd__less__0,axiom,
% 15.40/15.51 ! [V_z_2] :
% 15.40/15.51 ( 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))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zle__add1__eq__le,axiom,
% 15.40/15.51 ! [V_z_2,V_w_2] :
% 15.40/15.51 ( 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)))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add1__zle__eq,axiom,
% 15.40/15.51 ! [V_z_2,V_w_2] :
% 15.40/15.51 ( 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)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zless__imp__add1__zle,axiom,
% 15.40/15.51 ! [V_z,V_w] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pdivmod__rel__mult,axiom,
% 15.40/15.51 ! [V_r_H,V_q_H,V_z,V_r,V_q,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
% 15.40/15.51 => ( c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__mult__le,axiom,
% 15.40/15.51 ! [V_q,V_p,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__mult__eq,axiom,
% 15.40/15.51 ! [V_q,V_p,T_a] :
% 15.40/15.51 ( class_Rings_Oidom(T_a)
% 15.40/15.51 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 => ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__monom,axiom,
% 15.40/15.51 ! [V_n,V_b,V_m,V_a,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__imp__0__less,axiom,
% 15.40/15.51 ! [V_z] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_coeff__mult__degree__sum,axiom,
% 15.40/15.51 ! [V_q,V_p,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_self__quotient__aux1,axiom,
% 15.40/15.51 ! [V_q,V_r,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 15.40/15.51 => ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_self__quotient__aux2,axiom,
% 15.40/15.51 ! [V_q,V_r,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 15.40/15.51 => ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 15.40/15.51 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 15.40/15.51 ( 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)
% 15.40/15.51 => ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__right__cancel,axiom,
% 15.40/15.51 ! [V_nb_2,V_k_2,V_m_2] :
% 15.40/15.51 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)
% 15.40/15.51 <=> V_m_2 = V_nb_2 ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__left__cancel,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( 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_nb_2)
% 15.40/15.51 <=> V_m_2 = V_nb_2 ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__assoc,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__left__commute,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__add__commute,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__assoc,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__left__commute,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zadd__commute,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_q__pos__lemma,axiom,
% 15.40/15.51 ! [V_r_H,V_q_H,V_b_H] :
% 15.40/15.51 ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_q__neg__lemma,axiom,
% 15.40/15.51 ! [V_r_H,V_q_H,V_b_H] :
% 15.40/15.51 ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_unique__quotient__lemma,axiom,
% 15.40/15.51 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 15.40/15.51 ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono2__lemma,axiom,
% 15.40/15.51 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 15.40/15.51 ( 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)
% 15.40/15.51 => ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_unique__quotient__lemma__neg,axiom,
% 15.40/15.51 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 15.40/15.51 ( 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))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__gcd__unique,axiom,
% 15.40/15.51 ! [V_y,V_x,V_d,T_a] :
% 15.40/15.51 ( class_Fields_Ofield(T_a)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))
% 15.40/15.51 => ( ! [B_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_x))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_y))
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_d)) ) )
% 15.40/15.51 => ( ( ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Ozero__class_Ozero(T_a) )
% 15.40/15.51 & ( ~ ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.51 & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Oone__class_Oone(T_a) ) )
% 15.40/15.51 => c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = V_d ) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__Suc__ex__iff,axiom,
% 15.40/15.51 ! [V_l_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 15.40/15.51 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_incr__mult__lemma,axiom,
% 15.40/15.51 ! [V_k_2,V_P_2,V_d_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
% 15.40/15.51 => ( ! [B_x] :
% 15.40/15.51 ( hBOOL(hAPP(V_P_2,B_x))
% 15.40/15.51 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 15.40/15.51 => ! [B_x] :
% 15.40/15.51 ( hBOOL(hAPP(V_P_2,B_x))
% 15.40/15.51 => 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)))) ) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_ex__least__nat__less,axiom,
% 15.40/15.51 ! [V_nb_2,V_P_2] :
% 15.40/15.51 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 15.40/15.51 => ( hBOOL(hAPP(V_P_2,V_nb_2))
% 15.40/15.51 => ? [B_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_nb_2)
% 15.40/15.51 & ! [B_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 15.40/15.51 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 15.40/15.51 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_realpow__minus__mult,axiom,
% 15.40/15.51 ! [V_x,V_n,T_a] :
% 15.40/15.51 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd_OmonoD,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,V_f_2,T_a] :
% 15.40/15.51 ( class_Orderings_Oorder(T_a)
% 15.40/15.51 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_a,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 15.40/15.51 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__diff__right,axiom,
% 15.40/15.51 ! [V_i,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__diff__conv,axiom,
% 15.40/15.51 ! [V_i_2,V_k_2,V_j_2] :
% 15.40/15.51 ( 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)
% 15.40/15.51 <=> 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add__diff,axiom,
% 15.40/15.51 ! [V_m,V_n,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add__diff__inverse,axiom,
% 15.40/15.51 ! [V_m,V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__diff__assoc,axiom,
% 15.40/15.51 ! [V_i,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__diff__conv2,axiom,
% 15.40/15.51 ! [V_i_2,V_j_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 15.40/15.51 => ( 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))
% 15.40/15.51 <=> 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add__diff__inverse2,axiom,
% 15.40/15.51 ! [V_m,V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__imp__diff__is__add,axiom,
% 15.40/15.51 ! [V_k_2,V_j_2,V_i_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 15.40/15.51 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__assoc,axiom,
% 15.40/15.51 ! [V_i,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__diff__assoc2,axiom,
% 15.40/15.51 ! [V_i,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__assoc2,axiom,
% 15.40/15.51 ! [V_i,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__diff__inverse,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__diff__conv,axiom,
% 15.40/15.51 ! [V_k_2,V_j_2,V_i_2] :
% 15.40/15.51 ( 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))
% 15.40/15.51 <=> 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__0,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__cancel2,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__cancel,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__diff__left,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__inverse,axiom,
% 15.40/15.51 ! [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 ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__inverse2,axiom,
% 15.40/15.51 ! [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 ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__diff__cancel,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__add__cancel,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__diff__mult,axiom,
% 15.40/15.51 ! [V_b,V_a,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Oring(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_eq__add__iff2,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oring(T_a)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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)
% 15.40/15.51 <=> 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_aa_2)),V_e_2),V_d_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_eq__add__iff1,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oring(T_a)
% 15.40/15.51 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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)
% 15.40/15.51 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2) = V_d_2 ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult_Oprod__diff__prod,axiom,
% 15.40/15.51 ! [V_b,V_a,V_y,V_x,T_a] :
% 15.40/15.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__minus__eq__add,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_ab__diff__minus,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__def,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zero__less__diff,axiom,
% 15.40/15.51 ! [V_m_2,V_nb_2] :
% 15.40/15.51 ( 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_nb_2,V_m_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__less,axiom,
% 15.40/15.51 ! [V_m,V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__less__Suc,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__is__0__eq,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2] :
% 15.40/15.51 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__is__0__eq_H,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__diff__le,axiom,
% 15.40/15.51 ! [V_m,V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__diff__iff,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 15.40/15.51 => ( 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_nb_2,V_k_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__less__mono,axiom,
% 15.40/15.51 ! [V_c,V_b,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__diffD1,axiom,
% 15.40/15.51 ! [V_n,V_m,V_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__diffD,axiom,
% 15.40/15.51 ! [V_n,V_m,V_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__1,axiom,
% 15.40/15.51 ! [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 ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_minus__diff__eq,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_minus__apply,axiom,
% 15.40/15.51 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 15.40/15.51 ( class_Groups_Ominus(T_a)
% 15.40/15.51 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__Suc,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__diff__diff,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__pCons,axiom,
% 15.40/15.51 ! [V_q,V_b,V_p,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_poly__diff,axiom,
% 15.40/15.51 ! [V_x,V_q,V_p,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__ring(T_a)
% 15.40/15.51 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__eq__diff__eq,axiom,
% 15.40/15.51 ! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 15.40/15.51 => ( V_aa_2 = V_b_2
% 15.40/15.51 <=> V_c_2 = V_d_2 ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__commute,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__diff__nat,axiom,
% 15.40/15.51 ! [V_n,V_m,V_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_dvd__diff,axiom,
% 15.40/15.51 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__monom,axiom,
% 15.40/15.51 ! [V_b,V_n,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_coeff__diff,axiom,
% 15.40/15.51 ! [V_n,V_q,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__mult__distrib2,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__mult__distrib,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__less__mono2,axiom,
% 15.40/15.51 ! [V_l,V_n,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__imp__diff__less,axiom,
% 15.40/15.51 ! [V_n,V_k,V_j] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diffs0__imp__equal,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => V_m = V_n ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__self__eq__0,axiom,
% 15.40/15.51 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_minus__nat_Odiff__0,axiom,
% 15.40/15.51 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__0__eq__0,axiom,
% 15.40/15.51 ! [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) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult_Odiff__right,axiom,
% 15.40/15.51 ! [V_b_H,V_b,V_a,T_a] :
% 15.40/15.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__right_Odiff,axiom,
% 15.40/15.51 ! [V_y,V_x,V_xa,T_a] :
% 15.40/15.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult_Odiff__left,axiom,
% 15.40/15.51 ! [V_b,V_a_H,V_a,T_a] :
% 15.40/15.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__left_Odiff,axiom,
% 15.40/15.51 ! [V_ya,V_y,V_x,T_a] :
% 15.40/15.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__eq__diff__less,axiom,
% 15.40/15.51 ! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__0__right,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__self,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_eq__iff__diff__eq__0,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => ( V_aa_2 = V_b_2
% 15.40/15.51 <=> c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_right__minus__eq,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.51 <=> V_aa_2 = V_b_2 ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__eq__diff__less__eq,axiom,
% 15.40/15.51 ! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__le__self,axiom,
% 15.40/15.51 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__le__mono2,axiom,
% 15.40/15.51 ! [V_l,V_n,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__le__mono,axiom,
% 15.40/15.51 ! [V_l,V_n,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__diff__cancel,axiom,
% 15.40/15.51 ! [V_n,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_eq__diff__iff,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 15.40/15.51 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2)
% 15.40/15.51 <=> V_m_2 = V_nb_2 ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Nat_Odiff__diff__eq,axiom,
% 15.40/15.51 ! [V_n,V_m,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 15.40/15.51 => 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__diff__iff,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 15.40/15.51 => ( 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_nb_2,V_k_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__0,axiom,
% 15.40/15.51 ! [V_a,T_a] :
% 15.40/15.51 ( class_Groups_Ogroup__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__iff__diff__less__0,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__iff__diff__le__0,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add__iff1,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.51 => ( 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_aa_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))
% 15.40/15.51 <=> 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_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_le__add__iff2,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.51 => ( 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_aa_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))
% 15.40/15.51 <=> 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_aa_2)),V_e_2),V_d_2)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__add__iff1,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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))
% 15.40/15.51 <=> 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_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__add__iff2,axiom,
% 15.40/15.51 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
% 15.40/15.51 ( class_Rings_Oordered__ring(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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))
% 15.40/15.51 <=> 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_aa_2)),V_e_2),V_d_2)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_real__squared__diff__one__factored,axiom,
% 15.40/15.51 ! [V_x,T_a] :
% 15.40/15.51 ( class_Rings_Oring__1(T_a)
% 15.40/15.51 => 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))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_inf__period_I4_J,axiom,
% 15.40/15.51 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 15.40/15.51 ( ( class_Rings_Ocomm__ring(T_a)
% 15.40/15.51 & class_Rings_Odvd(T_a) )
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
% 15.40/15.51 => ! [B_x,B_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_inf__period_I3_J,axiom,
% 15.40/15.51 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 15.40/15.51 ( ( class_Rings_Ocomm__ring(T_a)
% 15.40/15.51 & class_Rings_Odvd(T_a) )
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
% 15.40/15.51 => ! [B_x,B_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
% 15.40/15.51 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__less,axiom,
% 15.40/15.51 ! [V_i,V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__pred,axiom,
% 15.40/15.51 ! [V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => 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 ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__diff__split__asm,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,V_P_2] :
% 15.40/15.51 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 15.40/15.51 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 15.40/15.51 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 15.40/15.51 | ? [B_d] :
% 15.40/15.51 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 15.40/15.51 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__diff__split,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2,V_P_2] :
% 15.40/15.51 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
% 15.40/15.51 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)
% 15.40/15.51 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 15.40/15.51 & ! [B_d] :
% 15.40/15.51 ( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 15.40/15.51 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__diff__eq2,axiom,
% 15.40/15.51 ! [V_m,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__Suc__diff__eq1,axiom,
% 15.40/15.51 ! [V_m,V_j,V_k] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__le__add__iff1,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 15.40/15.51 => ( 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_nb_2))
% 15.40/15.51 <=> 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_nb_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__diff__add__eq1,axiom,
% 15.40/15.51 ! [V_n,V_m,V_u,V_i,V_j] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__eq__add__iff1,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 15.40/15.51 => ( 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_nb_2)
% 15.40/15.51 <=> 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_nb_2 ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__le__add__iff2,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 15.40/15.51 => ( 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_nb_2))
% 15.40/15.51 <=> 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_nb_2)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__diff__add__eq2,axiom,
% 15.40/15.51 ! [V_n,V_m,V_u,V_j,V_i] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__eq__add__iff2,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 15.40/15.51 => ( 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_nb_2)
% 15.40/15.51 <=> 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_nb_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__synthetic__div,axiom,
% 15.40/15.51 ! [V_c,V_p,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__pred_H,axiom,
% 15.40/15.51 ! [V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Suc__diff__1,axiom,
% 15.40/15.51 ! [V_n] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.51 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_add__eq__if,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 15.40/15.51 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__less__add__iff2,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 15.40/15.51 => ( 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_nb_2))
% 15.40/15.51 <=> 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_nb_2)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nat__less__add__iff1,axiom,
% 15.40/15.51 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 15.40/15.51 => ( 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_nb_2))
% 15.40/15.51 <=> 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_nb_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_mult__eq__if,axiom,
% 15.40/15.51 ! [V_n,V_m] :
% 15.40/15.51 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.51 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_power__eq__if,axiom,
% 15.40/15.51 ! [V_p,V_m] :
% 15.40/15.51 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 15.40/15.51 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => 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)))) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_realpow__two__diff,axiom,
% 15.40/15.51 ! [V_y,V_x,T_a] :
% 15.40/15.51 ( class_Rings_Ocomm__ring__1(T_a)
% 15.40/15.51 => 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_realpow__num__eq__if,axiom,
% 15.40/15.51 ! [V_m,V_n,T_a] :
% 15.40/15.51 ( class_Power_Opower(T_a)
% 15.40/15.51 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 15.40/15.51 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.51 => 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)))) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_lemma__realpow__diff,axiom,
% 15.40/15.51 ! [V_y,V_n,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Omonoid__mult(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
% 15.40/15.51 => 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) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__int__def__symmetric,axiom,
% 15.40/15.51 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__int__def,axiom,
% 15.40/15.51 ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__bin__lemma,axiom,
% 15.40/15.51 ! [V_l_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 15.40/15.51 <=> 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)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__diff__less,axiom,
% 15.40/15.51 ! [V_q,V_n,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 15.40/15.51 => 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) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_degree__diff__le,axiom,
% 15.40/15.51 ! [V_q,V_n,V_p,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
% 15.40/15.51 => 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) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__poly__code_I1_J,axiom,
% 15.40/15.51 ! [V_q,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdvd__zdiffD,axiom,
% 15.40/15.51 ! [V_n,V_m,V_k] :
% 15.40/15.51 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 15.40/15.51 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__eq__poly__def,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 15.40/15.51 <=> ( V_x_2 = V_y_2
% 15.40/15.51 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_less__poly__def,axiom,
% 15.40/15.51 ! [V_y_2,V_x_2,T_a] :
% 15.40/15.51 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 15.40/15.51 <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_diff__poly__code_I2_J,axiom,
% 15.40/15.51 ! [V_p,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiff__zmult__distrib,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiff__zmult__distrib2,axiom,
% 15.40/15.51 ! [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)) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zle__diff1__eq,axiom,
% 15.40/15.51 ! [V_z_2,V_w_2] :
% 15.40/15.51 ( 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)))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_Limits_Ominus__diff__minus,axiom,
% 15.40/15.51 ! [V_b,V_a,T_a] :
% 15.40/15.51 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.51 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_int__power__div__base,axiom,
% 15.40/15.51 ! [V_k,V_m] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 15.40/15.51 => 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)))) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__eq__0__iff,axiom,
% 15.40/15.51 ! [V_k_2,V_i_2] :
% 15.40/15.51 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.51 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.51 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 15.40/15.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 15.40/15.51 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 15.40/15.51 ! [V_aa_2,V_b_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 15.40/15.51 => ( 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_aa_2,V_b_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 15.40/15.51 ! [V_i_2,V_k_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 15.40/15.51 => ( 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))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 15.40/15.51 ! [V_b_2,V_aa_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2)
% 15.40/15.51 => ( 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_aa_2,V_b_2))
% 15.40/15.51 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_aa_2)
% 15.40/15.51 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono2,axiom,
% 15.40/15.51 ! [V_b,V_b_H,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_div__nonneg__neg__le0,axiom,
% 15.40/15.51 ! [V_b,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_div__pos__pos__trivial,axiom,
% 15.40/15.51 ! [V_b,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 15.40/15.51 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 15.40/15.51 ! [V_aa_2,V_b_2] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => ( 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_aa_2,V_b_2))
% 15.40/15.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_div__nonpos__pos__le0,axiom,
% 15.40/15.51 ! [V_b,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono2__neg,axiom,
% 15.40/15.51 ! [V_b,V_b_H,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 15.40/15.51 => 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)) ) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_div__neg__neg__trivial,axiom,
% 15.40/15.51 ! [V_b,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 15.40/15.51 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono1,axiom,
% 15.40/15.51 ! [V_b,V_a_H,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__mono1__neg,axiom,
% 15.40/15.51 ! [V_b,V_a_H,V_a] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.51 => 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)) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_int__div__less__self,axiom,
% 15.40/15.51 ! [V_k,V_x] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.51 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 15.40/15.51 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_zdiv__zmult2__eq,axiom,
% 15.40/15.51 ! [V_b,V_a,V_c] :
% 15.40/15.51 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 15.40/15.51 => 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) ) ).
% 15.40/15.51
% 15.40/15.51 fof(fact_div__add,axiom,
% 15.40/15.51 ! [V_y,V_x,V_z,T_a] :
% 15.40/15.51 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 15.40/15.51 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 15.40/15.52 ! [V_y,V_x] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__mult1,axiom,
% 15.40/15.52 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__mult2,axiom,
% 15.40/15.52 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self1__is__id,axiom,
% 15.40/15.52 ! [V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self2__is__id,axiom,
% 15.40/15.52 ! [V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__mult1__if,axiom,
% 15.40/15.52 ! [V_b,V_a,V_c,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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) )
% 15.40/15.52 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__mult__div__cancel,axiom,
% 15.40/15.52 ! [V_b,V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__swap,axiom,
% 15.40/15.52 ! [V_a,V_b,V_c,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__div__mult__self,axiom,
% 15.40/15.52 ! [V_b,V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__div__mult,axiom,
% 15.40/15.52 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__div__if__dvd,axiom,
% 15.40/15.52 ! [V_w,V_z,V_x,V_y,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__neg__pos__less0,axiom,
% 15.40/15.52 ! [V_b,V_a] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 15.40/15.52 ! [V_aa_2,V_b_2] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 15.40/15.52 ! [V_aa_2,V_b_2] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_zdiv__zero,axiom,
% 15.40/15.52 ! [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) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__by__0,axiom,
% 15.40/15.52 ! [V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__0,axiom,
% 15.40/15.52 ! [V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_zdvd__mult__div__cancel,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 15.40/15.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__power,axiom,
% 15.40/15.52 ! [V_n,V_x,V_y,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.40/15.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__dvd__div,axiom,
% 15.40/15.52 ! [V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_c_2))
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2)),c_Divides_Odiv__class_Odiv(T_a,V_c_2,V_aa_2)))
% 15.40/15.52 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b_2),V_c_2)) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__by__1,axiom,
% 15.40/15.52 ! [V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__div__neg,axiom,
% 15.40/15.52 ! [V_x,V_y,T_a] :
% 15.40/15.52 ( class_Divides_Oring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__neg__div,axiom,
% 15.40/15.52 ! [V_x,V_y,T_a] :
% 15.40/15.52 ( class_Divides_Oring__div(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_zdiv__zminus__zminus,axiom,
% 15.40/15.52 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_zdiv__zminus2,axiom,
% 15.40/15.52 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_zdiv__self,axiom,
% 15.40/15.52 ! [V_a] :
% 15.40/15.52 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__self,axiom,
% 15.40/15.52 ! [V_a,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self2,axiom,
% 15.40/15.52 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self1,axiom,
% 15.40/15.52 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__add__self2,axiom,
% 15.40/15.52 ! [V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__add__self1,axiom,
% 15.40/15.52 ! [V_a,V_b,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__div__div__eq__mult,axiom,
% 15.40/15.52 ! [V_d_2,V_b_2,V_c_2,V_aa_2,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c_2),V_d_2))
% 15.40/15.52 => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = c_Divides_Odiv__class_Odiv(T_a,V_d_2,V_c_2)
% 15.40/15.52 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2) ) ) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_dvd__div__eq__mult,axiom,
% 15.40/15.52 ! [V_c_2,V_b_2,V_aa_2,T_a] :
% 15.40/15.52 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.52 => ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.52 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
% 15.40/15.52 => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = V_c_2
% 15.40/15.52 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_split__zdiv,axiom,
% 15.40/15.52 ! [V_k_2,V_nb_2,V_P_2] :
% 15.40/15.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)))
% 15.40/15.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 15.40/15.52 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 15.40/15.52 => ! [B_i] :
% 15.40/15.52 ( ? [B_j] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 15.40/15.52 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 15.40/15.52 & V_nb_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) )
% 15.40/15.52 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 15.40/15.52 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 => ! [B_i] :
% 15.40/15.52 ( ? [B_j] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 15.40/15.52 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.52 & V_nb_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) )
% 15.40/15.52 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_divmod__int__rel__div__eq,axiom,
% 15.40/15.52 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 15.40/15.52 ( 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)
% 15.40/15.52 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1)
% 15.40/15.52 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1) ) )
% 15.40/15.52 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1)
% 15.40/15.52 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 15.40/15.52 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_z3div__def,axiom,
% 15.40/15.52 ! [V_k,V_l] :
% 15.40/15.52 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 15.40/15.52 => c_SMT_Oz3div(V_k,V_l) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l) )
% 15.40/15.52 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 15.40/15.52 => c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_tsub__def,axiom,
% 15.40/15.52 ! [V_x,V_y] :
% 15.40/15.52 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 15.40/15.52 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 15.40/15.52 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 15.40/15.52 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__le__mono2,axiom,
% 15.40/15.52 ! [V_k,V_n,V_m] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self1__is__m,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.52 => 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 ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult__self__is__m,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.52 => 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 ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_nat__mult__div__cancel1,axiom,
% 15.40/15.52 ! [V_n,V_m,V_k] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 15.40/15.52 => 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) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__less__dividend,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 15.40/15.52 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__le__dividend,axiom,
% 15.40/15.52 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__le__mono,axiom,
% 15.40/15.52 ! [V_k,V_n,V_m] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => 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)) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__1,axiom,
% 15.40/15.52 ! [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 ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__less,axiom,
% 15.40/15.52 ! [V_n,V_m] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__mult2__eq,axiom,
% 15.40/15.52 ! [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) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_poly__div__minus__right,axiom,
% 15.40/15.52 ! [V_y,V_x,T_a] :
% 15.40/15.52 ( class_Fields_Ofield(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_poly__div__minus__left,axiom,
% 15.40/15.52 ! [V_y,V_x,T_a] :
% 15.40/15.52 ( class_Fields_Ofield(T_a)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_poly__div__mult__right,axiom,
% 15.40/15.52 ! [V_z,V_y,V_x,T_a] :
% 15.40/15.52 ( class_Fields_Ofield(T_a)
% 15.40/15.52 => 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) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_nat__mult__div__cancel__disj,axiom,
% 15.40/15.52 ! [V_n,V_m,V_k] :
% 15.40/15.52 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.52 => 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) )
% 15.40/15.52 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.52 => 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) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__poly__eq,axiom,
% 15.40/15.52 ! [V_r,V_q,V_y,V_x,T_a] :
% 15.40/15.52 ( class_Fields_Ofield(T_a)
% 15.40/15.52 => ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_q ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__poly__less,axiom,
% 15.40/15.52 ! [V_y,V_x,T_a] :
% 15.40/15.52 ( class_Fields_Ofield(T_a)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__if,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.52 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.40/15.52 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => 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)) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_div__geq,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.52 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_split__div,axiom,
% 15.40/15.52 ! [V_k_2,V_nb_2,V_P_2] :
% 15.40/15.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_nb_2,V_k_2)))
% 15.40/15.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 15.40/15.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.52 => ! [B_i,B_j] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
% 15.40/15.52 => ( V_nb_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)
% 15.40/15.52 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_split__div_H,axiom,
% 15.40/15.52 ! [V_nb_2,V_m_2,V_P_2] :
% 15.40/15.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2)))
% 15.40/15.52 <=> ( ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.40/15.52 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 15.40/15.52 | ? [B_q] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),B_q),V_m_2)
% 15.40/15.52 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(B_q)))
% 15.40/15.52 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_split__div__lemma,axiom,
% 15.40/15.52 ! [V_m_2,V_qb_2,V_nb_2] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
% 15.40/15.52 => ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_qb_2),V_m_2)
% 15.40/15.52 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(V_qb_2))) )
% 15.40/15.52 <=> V_qb_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_le__div__geq,axiom,
% 15.40/15.52 ! [V_m,V_n] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 15.40/15.52 ! [V_y,V_x] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 15.40/15.52 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 15.40/15.52 => 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)) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_tsub__eq,axiom,
% 15.40/15.52 ! [V_x,V_y] :
% 15.40/15.52 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 15.40/15.52 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_Deriv_Oadd__diff__add,axiom,
% 15.40/15.52 ! [V_d,V_b,V_c,V_a,T_a] :
% 15.40/15.52 ( class_Groups_Oab__group__add(T_a)
% 15.40/15.52 => 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)) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_sgn__poly__def,axiom,
% 15.40/15.52 ! [V_x,T_a] :
% 15.40/15.52 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.52 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.52 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.52 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 15.40/15.52 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 15.40/15.52 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 15.40/15.52 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 15.40/15.52 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) ) ) ) ) ) ).
% 15.40/15.52
% 15.40/15.52 fof(fact_sgn__minus,axiom,
% 15.40/15.53 ! [V_x,T_a] :
% 15.40/15.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__one,axiom,
% 15.40/15.53 ! [T_a] :
% 15.40/15.53 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__sgn,axiom,
% 15.40/15.53 ! [V_a,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__mult,axiom,
% 15.40/15.53 ! [V_y,V_x,T_a] :
% 15.40/15.53 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__times,axiom,
% 15.40/15.53 ! [V_b,V_a,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn0,axiom,
% 15.40/15.53 ! [T_a] :
% 15.40/15.53 ( class_Groups_Osgn__if(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__zero,axiom,
% 15.40/15.53 ! [T_a] :
% 15.40/15.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__zero__iff,axiom,
% 15.40/15.53 ! [V_x_2,T_a] :
% 15.40/15.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 15.40/15.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__0__0,axiom,
% 15.40/15.53 ! [V_aa_2,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.53 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__greater,axiom,
% 15.40/15.53 ! [V_aa_2,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
% 15.40/15.53 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__less,axiom,
% 15.40/15.53 ! [V_aa_2,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.53 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__1__pos,axiom,
% 15.40/15.53 ! [V_aa_2,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
% 15.40/15.53 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__pos,axiom,
% 15.40/15.53 ! [V_a,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__if,axiom,
% 15.40/15.53 ! [V_x,T_a] :
% 15.40/15.53 ( class_Groups_Osgn__if(T_a)
% 15.40/15.53 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 15.40/15.53 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 15.40/15.53 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 15.40/15.53 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__1__neg,axiom,
% 15.40/15.53 ! [V_aa_2,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 15.40/15.53 <=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_sgn__neg,axiom,
% 15.40/15.53 ! [V_a,T_a] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_a)
% 15.40/15.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 15.40/15.53 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_decr__mult__lemma,axiom,
% 15.40/15.53 ! [V_k_2,V_P_2,V_d_2] :
% 15.40/15.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
% 15.40/15.53 => ( ! [B_x] :
% 15.40/15.53 ( hBOOL(hAPP(V_P_2,B_x))
% 15.40/15.53 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2))) )
% 15.40/15.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 15.40/15.53 => ! [B_x] :
% 15.40/15.53 ( hBOOL(hAPP(V_P_2,B_x))
% 15.40/15.53 => 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)))) ) ) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_split__neg__lemma,axiom,
% 15.40/15.53 ! [V_nb_2,V_P_2,V_k_2] :
% 15.40/15.53 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.53 => ( hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2)))
% 15.40/15.53 <=> ! [B_i,B_j] :
% 15.40/15.53 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 15.40/15.53 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 15.40/15.53 & V_nb_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) )
% 15.40/15.53 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_div__mod__equality,axiom,
% 15.40/15.53 ! [V_c,V_b,V_a,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_div__mod__equality2,axiom,
% 15.40/15.53 ! [V_c,V_a,V_b,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_mod__div__equality,axiom,
% 15.40/15.53 ! [V_b,V_a,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_mod__div__equality2,axiom,
% 15.40/15.53 ! [V_a,V_b,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 15.40/15.53 ! [V_b,V_a,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_zdiv__zadd1__eq,axiom,
% 15.40/15.53 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_zmod__zdiv__trivial,axiom,
% 15.40/15.53 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_mod__div__trivial,axiom,
% 15.40/15.53 ! [V_b,V_a,T_a] :
% 15.40/15.53 ( class_Divides_Osemiring__div(T_a)
% 15.40/15.53 => c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_DIVISION__BY__ZERO,axiom,
% 15.40/15.53 ! [V_a] :
% 15.40/15.53 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 15.40/15.53 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_zmod__zdiv__equality,axiom,
% 15.40/15.53 ! [V_b,V_a] : V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 15.40/15.53
% 15.40/15.53 fof(fact_zdiv__zmult1__eq,axiom,
% 15.40/15.53 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) ).
% 15.40/15.53
% 15.40/15.53 %----Arity declarations (210)
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Lattices_Oboolean__algebra(T_1)
% 15.40/15.53 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Orderings_Opreorder,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Orderings_Opreorder(T_1)
% 15.40/15.53 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Orderings_Oorder,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Orderings_Oorder(T_1)
% 15.40/15.53 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Orderings_Oord,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Orderings_Oord(T_1)
% 15.40/15.53 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Groups_Ouminus,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Groups_Ouminus(T_1)
% 15.40/15.53 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_fun__Groups_Ominus,axiom,
% 15.40/15.53 ! [T_2,T_1] :
% 15.40/15.53 ( class_Groups_Ominus(T_1)
% 15.40/15.53 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.40/15.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.40/15.53 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 15.40/15.53 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 15.40/15.53 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 15.40/15.53 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 15.40/15.53 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 15.40/15.53 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 15.40/15.53 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 15.40/15.53 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 15.40/15.53 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 15.40/15.53 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 15.40/15.53 class_Orderings_Opreorder(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 15.40/15.53 class_Orderings_Olinorder(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 15.40/15.53 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 15.40/15.53 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 15.40/15.53 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 15.40/15.53 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 15.40/15.53 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 15.40/15.53 class_Divides_Oring__div(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 15.40/15.53 class_Rings_Omult__zero(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 15.40/15.53 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 15.40/15.53 class_Orderings_Oorder(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 15.40/15.53 class_Int_Oring__char__0(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 15.40/15.53 class_Rings_Osemiring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 15.40/15.53 class_Orderings_Oord(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 15.40/15.53 class_Groups_Ouminus(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 15.40/15.53 class_Groups_Osgn__if(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 15.40/15.53 class_Rings_Oring__1(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 15.40/15.53 class_Groups_Ominus(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Power_Opower,axiom,
% 15.40/15.53 class_Power_Opower(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 15.40/15.53 class_Groups_Ozero(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oring,axiom,
% 15.40/15.53 class_Rings_Oring(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 15.40/15.53 class_Rings_Oidom(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Groups_Oone,axiom,
% 15.40/15.53 class_Groups_Oone(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 15.40/15.53 class_Rings_Odvd(tc_Int_Oint) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.40/15.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.40/15.53 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 15.40/15.53 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 15.40/15.53 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 15.40/15.53 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 15.40/15.53 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 15.40/15.53 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 15.40/15.53 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 15.40/15.53 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 15.40/15.53 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 15.40/15.53 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 15.40/15.53 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 15.40/15.53 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 15.40/15.53 class_Orderings_Oorder(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 15.40/15.53 class_Rings_Osemiring(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 15.40/15.53 class_Orderings_Oord(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 15.40/15.53 class_Groups_Ominus(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Power_Opower,axiom,
% 15.40/15.53 class_Power_Opower(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 15.40/15.53 class_Groups_Ozero(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 15.40/15.53 class_Groups_Oone(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 15.40/15.53 class_Rings_Odvd(tc_Nat_Onat) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 15.40/15.53 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 15.40/15.53 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 15.40/15.53 class_Orderings_Oorder(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 15.40/15.53 class_Orderings_Oord(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 15.40/15.53 class_Groups_Ouminus(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 15.40/15.53 class_Groups_Ominus(tc_HOL_Obool) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.40/15.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 15.40/15.53 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 15.40/15.53 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 15.40/15.53 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 15.40/15.53 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 15.40/15.53 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 15.40/15.53 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 15.40/15.53 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 15.40/15.53 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 15.40/15.53 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 15.40/15.53 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 15.40/15.53 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 15.40/15.53 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 15.40/15.53 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 15.40/15.53 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 15.40/15.53 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 15.40/15.53 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 15.40/15.53 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 15.40/15.53 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 15.40/15.53 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 15.40/15.53 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 15.40/15.53 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 15.40/15.53 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 15.40/15.53 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 15.40/15.53 class_Power_Opower(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 15.40/15.53 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 15.40/15.53 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 15.40/15.53 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 15.40/15.53 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 15.40/15.53 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Oidom(T_1)
% 15.40/15.53 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Oidom(T_1)
% 15.40/15.53 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Oidom(T_1)
% 15.40/15.53 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Oidom(T_1)
% 15.40/15.53 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Fields_Ofield(T_1)
% 15.40/15.53 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Oab__group__add(T_1)
% 15.40/15.53 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__ring__1(T_1)
% 15.40/15.53 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 15.40/15.53 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Oab__group__add(T_1)
% 15.40/15.53 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Fields_Ofield(T_1)
% 15.40/15.53 => class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__ring(T_1)
% 15.40/15.53 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 15.40/15.53 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Oab__group__add(T_1)
% 15.40/15.53 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Olinordered__idom(T_1)
% 15.40/15.53 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__ring__1(T_1)
% 15.40/15.53 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Oab__group__add(T_1)
% 15.40/15.53 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Groups_Ozero(T_1)
% 15.40/15.53 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__ring(T_1)
% 15.40/15.53 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Oidom(T_1)
% 15.40/15.53 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 15.40/15.53 ! [T_1] :
% 15.40/15.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 15.40/15.53 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 15.40/15.53
% 15.40/15.53 %----Helper facts (2)
% 15.40/15.53 fof(help_c__fequal__1,axiom,
% 15.40/15.53 ! [V_y_2,V_x_2] :
% 15.40/15.53 ( ~ hBOOL(c_fequal(V_x_2,V_y_2))
% 15.40/15.53 | V_x_2 = V_y_2 ) ).
% 15.40/15.53
% 15.40/15.53 fof(help_c__fequal__2,axiom,
% 15.40/15.53 ! [V_y_2,V_x_2] :
% 15.40/15.53 ( V_x_2 != V_y_2
% 15.40/15.53 | hBOOL(c_fequal(V_x_2,V_y_2)) ) ).
% 15.40/15.53
% 15.40/15.53 %----Conjectures (2)
% 15.40/15.53 fof(conj_0,hypothesis,
% 15.40/15.53 ( ? [B_r] : v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r)
% 15.40/15.53 => v_thesis____ ) ).
% 15.40/15.53
% 15.40/15.53 fof(conj_1,conjecture,
% 15.40/15.53 v_thesis____ ).
% 15.40/15.53
% 15.40/15.53 %------------------------------------------------------------------------------
% 15.40/15.53 %-------------------------------------------
% 15.40/15.53 % Proof found
% 15.40/15.53 % SZS status Theorem for theBenchmark
% 15.40/15.53 % SZS output start Proof
% 15.40/15.54 %ClaNum:1860(EqnAxiom:240)
% 15.40/15.54 %VarNum:10197(SingletonVarNum:3463)
% 15.40/15.54 %MaxLitNum:8
% 15.40/15.54 %MaxfuncDepth:8
% 15.40/15.54 %SharedTerms:228
% 15.40/15.54 %goalClause: 486
% 15.40/15.54 %singleGoalClaCount:1
% 15.40/15.54 [241]P1(a1)
% 15.40/15.54 [242]P1(a58)
% 15.40/15.54 [243]P1(a59)
% 15.40/15.54 [244]P2(a1)
% 15.40/15.54 [245]P2(a58)
% 15.40/15.54 [246]P2(a59)
% 15.40/15.54 [247]P32(a1)
% 15.40/15.54 [248]P32(a59)
% 15.40/15.54 [249]P48(a1)
% 15.40/15.54 [250]P48(a59)
% 15.40/15.54 [251]P46(a1)
% 15.40/15.54 [252]P46(a58)
% 15.40/15.54 [253]P46(a59)
% 15.40/15.54 [254]P3(a1)
% 15.40/15.54 [255]P3(a59)
% 15.40/15.54 [256]P49(a1)
% 15.40/15.54 [257]P49(a59)
% 15.40/15.54 [258]P50(a1)
% 15.40/15.54 [259]P50(a58)
% 15.40/15.54 [260]P50(a59)
% 15.40/15.54 [261]P51(a1)
% 15.40/15.54 [262]P51(a59)
% 15.40/15.54 [263]P52(a1)
% 15.40/15.54 [264]P52(a58)
% 15.40/15.54 [265]P52(a59)
% 15.40/15.54 [266]P68(a1)
% 15.40/15.54 [267]P68(a59)
% 15.40/15.54 [268]P53(a1)
% 15.40/15.54 [269]P53(a58)
% 15.40/15.54 [270]P53(a59)
% 15.40/15.54 [271]P69(a1)
% 15.40/15.54 [272]P69(a58)
% 15.40/15.54 [273]P69(a59)
% 15.40/15.54 [274]P33(a1)
% 15.40/15.54 [275]P12(a1)
% 15.40/15.54 [276]P12(a58)
% 15.40/15.54 [277]P12(a59)
% 15.40/15.54 [278]P19(a1)
% 15.40/15.54 [279]P19(a58)
% 15.40/15.54 [280]P19(a59)
% 15.40/15.54 [281]P20(a59)
% 15.40/15.54 [282]P21(a1)
% 15.40/15.54 [283]P21(a59)
% 15.40/15.54 [284]P34(a1)
% 15.40/15.54 [285]P34(a59)
% 15.40/15.54 [286]P42(a1)
% 15.40/15.54 [287]P42(a59)
% 15.40/15.54 [288]P13(a1)
% 15.40/15.54 [289]P13(a58)
% 15.40/15.54 [290]P13(a59)
% 15.40/15.54 [291]P24(a1)
% 15.40/15.54 [292]P24(a58)
% 15.40/15.54 [293]P24(a59)
% 15.40/15.54 [294]P67(a1)
% 15.40/15.54 [295]P67(a59)
% 15.40/15.54 [296]P35(a1)
% 15.40/15.54 [297]P35(a58)
% 15.40/15.54 [298]P35(a59)
% 15.40/15.54 [299]P70(a1)
% 15.40/15.54 [300]P70(a58)
% 15.40/15.54 [301]P70(a59)
% 15.40/15.54 [302]P54(a58)
% 15.40/15.54 [303]P54(a59)
% 15.40/15.54 [304]P25(a59)
% 15.40/15.54 [305]P63(a58)
% 15.40/15.54 [306]P63(a59)
% 15.40/15.54 [307]P64(a59)
% 15.40/15.54 [308]P66(a58)
% 15.40/15.54 [309]P66(a59)
% 15.40/15.54 [310]P65(a58)
% 15.40/15.54 [311]P65(a59)
% 15.40/15.54 [312]P55(a59)
% 15.40/15.54 [313]P56(a59)
% 15.40/15.54 [314]P57(a59)
% 15.40/15.54 [315]P59(a58)
% 15.40/15.54 [316]P59(a59)
% 15.40/15.54 [317]P58(a58)
% 15.40/15.54 [318]P58(a59)
% 15.40/15.54 [319]P60(a58)
% 15.40/15.54 [320]P60(a59)
% 15.40/15.54 [321]P36(a58)
% 15.40/15.54 [322]P36(a59)
% 15.40/15.54 [323]P36(a60)
% 15.40/15.54 [324]P37(a58)
% 15.40/15.54 [325]P37(a59)
% 15.40/15.54 [326]P40(a58)
% 15.40/15.54 [327]P40(a59)
% 15.40/15.54 [328]P40(a60)
% 15.40/15.54 [329]P41(a58)
% 15.40/15.54 [330]P41(a59)
% 15.40/15.54 [331]P41(a60)
% 15.40/15.54 [332]P38(a60)
% 15.40/15.54 [333]P26(a1)
% 15.40/15.54 [334]P26(a59)
% 15.40/15.54 [335]P26(a60)
% 15.40/15.54 [336]P27(a58)
% 15.40/15.54 [337]P27(a59)
% 15.40/15.54 [338]P28(a58)
% 15.40/15.54 [339]P28(a59)
% 15.40/15.54 [340]P15(a1)
% 15.40/15.54 [341]P15(a58)
% 15.40/15.54 [342]P15(a59)
% 15.40/15.54 [343]P72(a1)
% 15.40/15.54 [344]P72(a58)
% 15.40/15.54 [345]P72(a59)
% 15.40/15.54 [346]P22(a1)
% 15.40/15.54 [347]P22(a58)
% 15.40/15.54 [348]P22(a59)
% 15.40/15.54 [349]P29(a58)
% 15.40/15.54 [350]P29(a59)
% 15.40/15.54 [351]P71(a1)
% 15.40/15.54 [352]P71(a58)
% 15.40/15.54 [353]P71(a59)
% 15.40/15.54 [354]P47(a1)
% 15.40/15.54 [355]P47(a58)
% 15.40/15.54 [356]P47(a59)
% 15.40/15.54 [357]P16(a1)
% 15.40/15.54 [358]P16(a58)
% 15.40/15.54 [359]P16(a59)
% 15.40/15.54 [360]P17(a1)
% 15.40/15.54 [361]P17(a58)
% 15.40/15.54 [362]P17(a59)
% 15.40/15.54 [363]P14(a1)
% 15.40/15.54 [364]P14(a58)
% 15.40/15.54 [365]P14(a59)
% 15.40/15.54 [366]P30(a58)
% 15.40/15.54 [367]P30(a59)
% 15.40/15.54 [368]P61(a59)
% 15.40/15.54 [369]P62(a59)
% 15.40/15.54 [370]P4(a1)
% 15.40/15.54 [371]P23(a1)
% 15.40/15.54 [372]P23(a58)
% 15.40/15.54 [373]P23(a59)
% 15.40/15.54 [374]P23(a60)
% 15.40/15.54 [375]P5(a58)
% 15.40/15.54 [376]P5(a59)
% 15.40/15.54 [377]P6(a59)
% 15.40/15.54 [378]P43(a1)
% 15.40/15.54 [379]P44(a1)
% 15.40/15.54 [380]P45(a1)
% 15.40/15.54 [381]P31(a59)
% 15.40/15.54 [382]P18(a1)
% 15.40/15.54 [383]P18(a58)
% 15.40/15.54 [384]P18(a59)
% 15.40/15.54 [486]~P75(a500)
% 15.40/15.54 [385]E(f2(a1,a61),a62)
% 15.40/15.54 [386]E(f2(a1,a67),a63)
% 15.40/15.54 [411]P7(a59,f3(a59),f6(a59))
% 15.40/15.54 [412]P8(a59,f3(a59),f6(a59))
% 15.40/15.54 [487]~E(f3(a58),a62)
% 15.40/15.54 [488]~E(f3(a58),a63)
% 15.40/15.54 [489]~E(f6(a59),f3(a59))
% 15.40/15.54 [492]~E(f17(a1,a64,a61),f3(a58))
% 15.40/15.54 [387]E(f4(a59,f3(a59)),f3(a59))
% 15.40/15.54 [388]E(f21(f16(a1,a61),a64),f3(a1))
% 15.40/15.54 [490]~E(f3(f65(a1)),a68)
% 15.40/15.54 [491]~E(f3(f65(a1)),a61)
% 15.40/15.54 [485]P73(f21(f21(f22(f65(a1)),f21(f21(f27(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),f17(a1,a64,a61))),a61))
% 15.40/15.54 [510]~P73(f21(f21(f22(f65(a1)),f21(f21(f27(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),f11(a58,f17(a1,a64,a61),f6(a58)))),a61))
% 15.40/15.54 [483]P73(f21(f21(f22(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),a68))
% 15.40/15.54 [393]P7(a58,x3931,x3931)
% 15.40/15.54 [394]P7(a59,x3941,x3941)
% 15.40/15.54 [494]~P8(a58,x4941,x4941)
% 15.40/15.54 [398]E(f7(a58,x3981,x3981),f3(a58))
% 15.40/15.54 [400]P7(a58,f3(a58),x4001)
% 15.40/15.54 [428]P7(a58,f17(a1,x4281,a61),a62)
% 15.40/15.54 [497]~P8(a58,x4971,f3(a58))
% 15.40/15.54 [389]E(f4(a59,f4(a59,x3891)),x3891)
% 15.40/15.54 [390]E(f21(f21(f5(a58),x3901),f6(a58)),x3901)
% 15.40/15.54 [391]E(f21(f21(f5(a59),x3911),f6(a59)),x3911)
% 15.40/15.54 [392]E(f21(f21(f5(a58),x3921),f3(a58)),f3(a58))
% 15.40/15.54 [401]E(f11(a58,x4011,f3(a58)),x4011)
% 15.40/15.54 [402]E(f11(a59,x4021,f3(a59)),x4021)
% 15.40/15.54 [403]E(f7(a58,x4031,f3(a58)),x4031)
% 15.40/15.54 [404]E(f8(a59,x4041,f3(a59)),x4041)
% 15.40/15.54 [405]E(f11(a58,f3(a58),x4051),x4051)
% 15.40/15.54 [406]E(f11(a59,f3(a59),x4061),x4061)
% 15.40/15.54 [407]E(f9(a59,x4071,f3(a59)),f3(a59))
% 15.40/15.54 [408]E(f7(a58,f3(a58),x4081),f3(a58))
% 15.40/15.54 [409]E(f9(a59,f3(a59),x4091),f3(a59))
% 15.40/15.54 [414]E(f11(a59,f4(a59,x4141),x4141),f3(a59))
% 15.40/15.54 [418]P73(f21(f21(f22(a58),x4181),f3(a58)))
% 15.40/15.54 [437]P8(a58,x4371,f11(a58,x4371,f6(a58)))
% 15.40/15.54 [438]P8(a58,f3(a58),f11(a58,x4381,f6(a58)))
% 15.40/15.54 [499]~E(f11(a58,x4991,f6(a58)),x4991)
% 15.40/15.54 [505]~E(f11(a58,x5051,f6(a58)),f3(a58))
% 15.40/15.54 [508]~P7(a58,f11(a58,x5081,f6(a58)),x5081)
% 15.40/15.54 [395]E(f21(f21(f5(a58),f6(a58)),x3951),x3951)
% 15.40/15.54 [396]E(f21(f21(f5(a59),f6(a59)),x3961),x3961)
% 15.40/15.54 [397]E(f21(f21(f5(a58),f3(a58)),x3971),f3(a58))
% 15.40/15.54 [417]P73(f21(f21(f22(a58),x4171),x4171))
% 15.40/15.54 [421]P73(f21(f21(f22(a58),f6(a58)),x4211))
% 15.40/15.54 [425]P7(a58,x4251,f21(f21(f5(a58),x4251),x4251))
% 15.40/15.54 [440]E(f9(a58,x4401,f11(a58,f3(a58),f6(a58))),x4401)
% 15.40/15.54 [509]~E(f11(a59,f11(a59,f6(a59),x5091),x5091),f3(a59))
% 15.40/15.54 [457]P7(a58,x4571,f21(f21(f5(a58),x4571),f21(f21(f5(a58),x4571),x4571)))
% 15.40/15.54 [461]E(f21(f21(f27(a58),f11(a58,f3(a58),f6(a58))),x4611),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [478]P73(f21(f21(f22(a58),f11(a58,f3(a58),f6(a58))),x4781))
% 15.40/15.54 [419]E(f11(a58,x4191,x4192),f11(a58,x4192,x4191))
% 15.40/15.54 [420]E(f11(a59,x4201,x4202),f11(a59,x4202,x4201))
% 15.40/15.54 [429]P7(a58,x4291,f11(a58,x4292,x4291))
% 15.40/15.54 [430]P7(a58,x4301,f11(a58,x4301,x4302))
% 15.40/15.54 [431]P7(a58,f7(a58,x4311,x4312),x4311)
% 15.40/15.54 [432]P7(a58,f9(a58,x4321,x4322),x4321)
% 15.40/15.54 [506]~P8(a58,f11(a58,x5061,x5062),x5062)
% 15.40/15.54 [507]~P8(a58,f11(a58,x5071,x5072),x5071)
% 15.40/15.54 [424]E(f11(a59,x4241,f4(a59,x4242)),f7(a59,x4241,x4242))
% 15.40/15.54 [426]E(f9(a59,f4(a59,x4261),x4262),f9(a59,x4261,f4(a59,x4262)))
% 15.40/15.54 [427]E(f9(a59,f4(a59,x4271),f4(a59,x4272)),f9(a59,x4271,x4272))
% 15.40/15.54 [433]E(f7(a58,f11(a58,x4331,x4332),x4332),x4331)
% 15.40/15.54 [434]E(f7(a58,f11(a58,x4341,x4342),x4341),x4342)
% 15.40/15.54 [435]E(f7(a58,x4351,f11(a58,x4351,x4352)),f3(a58))
% 15.40/15.54 [436]E(f9(a59,f8(a59,x4361,x4362),x4362),f3(a59))
% 15.40/15.54 [442]E(f11(a59,f4(a59,x4421),f4(a59,x4422)),f4(a59,f11(a59,x4421,x4422)))
% 15.40/15.54 [444]P8(a58,f7(a58,x4441,x4442),f11(a58,x4441,f6(a58)))
% 15.40/15.54 [465]P8(a58,x4651,f11(a58,f11(a58,x4652,x4651),f6(a58)))
% 15.40/15.54 [466]P8(a58,x4661,f11(a58,f11(a58,x4661,x4662),f6(a58)))
% 15.40/15.54 [472]E(f11(a59,f21(f21(f5(a59),x4721),f9(a59,x4722,x4721)),f8(a59,x4722,x4721)),x4722)
% 15.40/15.54 [415]E(f21(f21(f5(a58),x4151),x4152),f21(f21(f5(a58),x4152),x4151))
% 15.40/15.54 [416]E(f21(f21(f5(a59),x4161),x4162),f21(f21(f5(a59),x4162),x4161))
% 15.40/15.54 [456]E(f11(a58,f11(a58,x4561,f6(a58)),x4562),f11(a58,f11(a58,x4561,x4562),f6(a58)))
% 15.40/15.54 [458]E(f7(a58,f7(a58,x4581,f6(a58)),x4582),f7(a58,x4581,f11(a58,x4582,f6(a58))))
% 15.40/15.54 [459]E(f11(a58,f11(a58,x4591,f6(a58)),x4592),f11(a58,x4591,f11(a58,x4592,f6(a58))))
% 15.40/15.54 [441]E(f21(f21(f5(a59),f4(a59,x4411)),x4412),f4(a59,f21(f21(f5(a59),x4411),x4412)))
% 15.40/15.54 [445]E(f21(f21(f5(a58),x4451),f11(a58,x4452,f6(a58))),f11(a58,x4451,f21(f21(f5(a58),x4451),x4452)))
% 15.40/15.54 [471]E(f21(f21(f5(a58),f11(a58,x4711,f6(a58))),x4712),f11(a58,x4712,f21(f21(f5(a58),x4711),x4712)))
% 15.40/15.54 [447]E(f11(a58,x4471,f11(a58,x4472,x4473)),f11(a58,x4472,f11(a58,x4471,x4473)))
% 15.40/15.54 [448]E(f11(a59,x4481,f11(a59,x4482,x4483)),f11(a59,x4482,f11(a59,x4481,x4483)))
% 15.40/15.54 [449]E(f11(a58,f11(a58,x4491,x4492),x4493),f11(a58,x4491,f11(a58,x4492,x4493)))
% 15.40/15.54 [450]E(f11(a59,f11(a59,x4501,x4502),x4503),f11(a59,x4501,f11(a59,x4502,x4503)))
% 15.40/15.54 [451]E(f7(a58,f7(a58,x4511,x4512),x4513),f7(a58,x4511,f11(a58,x4512,x4513)))
% 15.40/15.54 [452]E(f7(a58,f7(a58,x4521,x4522),x4523),f7(a58,f7(a58,x4521,x4523),x4522))
% 15.40/15.54 [453]E(f7(a58,f11(a58,x4531,x4532),f11(a58,x4533,x4532)),f7(a58,x4531,x4533))
% 15.40/15.54 [454]E(f7(a58,f11(a58,x4541,x4542),f11(a58,x4541,x4543)),f7(a58,x4542,x4543))
% 15.40/15.54 [479]E(f7(a58,f7(a58,f11(a58,x4791,f6(a58)),x4792),f11(a58,x4793,f6(a58))),f7(a58,f7(a58,x4791,x4792),x4793))
% 15.40/15.54 [446]E(f9(a58,x4461,f21(f21(f5(a58),x4462),x4463)),f9(a58,f9(a58,x4461,x4462),x4463))
% 15.40/15.54 [467]E(f11(a58,f21(f21(f5(a58),x4671),x4672),f21(f21(f5(a58),x4671),x4673)),f21(f21(f5(a58),x4671),f11(a58,x4672,x4673)))
% 15.40/15.54 [468]E(f7(a58,f21(f21(f5(a58),x4681),x4682),f21(f21(f5(a58),x4681),x4683)),f21(f21(f5(a58),x4681),f7(a58,x4682,x4683)))
% 15.40/15.54 [469]E(f11(a59,f21(f21(f5(a59),x4691),x4692),f21(f21(f5(a59),x4691),x4693)),f21(f21(f5(a59),x4691),f11(a59,x4692,x4693)))
% 15.40/15.54 [470]E(f7(a59,f21(f21(f5(a59),x4701),x4702),f21(f21(f5(a59),x4701),x4703)),f21(f21(f5(a59),x4701),f7(a59,x4702,x4703)))
% 15.40/15.54 [473]E(f21(f21(f5(a59),f21(f21(f27(a59),x4731),x4732)),f21(f21(f27(a59),x4731),x4733)),f21(f21(f27(a59),x4731),f11(a58,x4732,x4733)))
% 15.40/15.54 [474]E(f11(a58,f21(f21(f5(a58),x4741),x4742),f21(f21(f5(a58),x4743),x4742)),f21(f21(f5(a58),f11(a58,x4741,x4743)),x4742))
% 15.40/15.54 [475]E(f7(a58,f21(f21(f5(a58),x4751),x4752),f21(f21(f5(a58),x4753),x4752)),f21(f21(f5(a58),f7(a58,x4751,x4753)),x4752))
% 15.40/15.54 [476]E(f11(a59,f21(f21(f5(a59),x4761),x4762),f21(f21(f5(a59),x4763),x4762)),f21(f21(f5(a59),f11(a59,x4761,x4763)),x4762))
% 15.40/15.54 [477]E(f7(a59,f21(f21(f5(a59),x4771),x4772),f21(f21(f5(a59),x4773),x4772)),f21(f21(f5(a59),f7(a59,x4771,x4773)),x4772))
% 15.40/15.54 [482]E(f11(a59,f21(f21(f5(a59),x4821),f9(a59,x4822,x4823)),f9(a59,f21(f21(f5(a59),x4821),f8(a59,x4822,x4823)),x4823)),f9(a59,f21(f21(f5(a59),x4821),x4822),x4823))
% 15.40/15.54 [484]E(f11(a59,f11(a59,f9(a59,x4841,x4842),f9(a59,x4843,x4842)),f9(a59,f11(a59,f8(a59,x4841,x4842),f8(a59,x4843,x4842)),x4842)),f9(a59,f11(a59,x4841,x4843),x4842))
% 15.40/15.54 [462]E(f21(f21(f5(a58),f21(f21(f5(a58),x4621),x4622)),x4623),f21(f21(f5(a58),x4621),f21(f21(f5(a58),x4622),x4623)))
% 15.40/15.54 [463]E(f21(f21(f5(a59),f21(f21(f5(a59),x4631),x4632)),x4633),f21(f21(f5(a59),x4631),f21(f21(f5(a59),x4632),x4633)))
% 15.40/15.54 [464]E(f21(f21(f27(a59),f21(f21(f27(a59),x4641),x4642)),x4643),f21(f21(f27(a59),x4641),f21(f21(f5(a58),x4642),x4643)))
% 15.40/15.54 [443]E(f21(f21(f23(x4431,x4432,x4433),x4434),f3(a58)),x4432)
% 15.40/15.54 [481]E(f11(a58,f21(f21(f5(a58),x4811),x4812),f11(a58,f21(f21(f5(a58),x4813),x4812),x4814)),f11(a58,f21(f21(f5(a58),f11(a58,x4811,x4813)),x4812),x4814))
% 15.40/15.54 [480]E(f21(f21(f23(x4801,x4802,x4803),x4804),f11(a58,x4805,f6(a58))),f21(f21(x4803,x4804),f21(f21(f23(x4801,x4802,x4803),x4804),x4805)))
% 15.40/15.54 [511]~P1(x5111)+P1(f65(x5111))
% 15.40/15.54 [512]~P2(x5121)+P2(f65(x5121))
% 15.40/15.54 [513]~P32(x5131)+P32(f65(x5131))
% 15.40/15.54 [514]~P51(x5141)+P48(f65(x5141))
% 15.40/15.54 [515]~P46(x5151)+P46(f65(x5151))
% 15.40/15.54 [516]~P3(x5161)+P3(f65(x5161))
% 15.40/15.54 [517]~P42(x5171)+P49(f65(x5171))
% 15.40/15.54 [518]~P1(x5181)+P50(f65(x5181))
% 15.40/15.54 [519]~P51(x5191)+P51(f65(x5191))
% 15.40/15.54 [520]~P51(x5201)+P52(f65(x5201))
% 15.40/15.54 [521]~P51(x5211)+P68(f65(x5211))
% 15.40/15.54 [522]~P46(x5221)+P53(f65(x5221))
% 15.40/15.54 [523]~P1(x5231)+P69(f65(x5231))
% 15.40/15.54 [524]~P1(x5241)+P12(f65(x5241))
% 15.40/15.54 [525]~P1(x5251)+P19(f65(x5251))
% 15.40/15.54 [526]~P57(x5261)+P20(f65(x5261))
% 15.40/15.54 [527]~P3(x5271)+P21(f65(x5271))
% 15.40/15.54 [528]~P57(x5281)+P34(f65(x5281))
% 15.40/15.54 [529]~P42(x5291)+P42(f65(x5291))
% 15.40/15.54 [530]~P46(x5301)+P13(f65(x5301))
% 15.40/15.54 [531]~P1(x5311)+P24(f65(x5311))
% 15.40/15.54 [532]~P32(x5321)+P67(f65(x5321))
% 15.40/15.54 [533]~P1(x5331)+P35(f65(x5331))
% 15.40/15.54 [534]~P46(x5341)+P70(f65(x5341))
% 15.40/15.54 [535]~P57(x5351)+P54(f65(x5351))
% 15.40/15.54 [536]~P57(x5361)+P25(f65(x5361))
% 15.40/15.54 [537]~P57(x5371)+P63(f65(x5371))
% 15.40/15.54 [538]~P57(x5381)+P64(f65(x5381))
% 15.40/15.54 [539]~P57(x5391)+P66(f65(x5391))
% 15.40/15.54 [540]~P57(x5401)+P65(f65(x5401))
% 15.40/15.54 [541]~P57(x5411)+P55(f65(x5411))
% 15.40/15.54 [542]~P57(x5421)+P56(f65(x5421))
% 15.40/15.54 [543]~P57(x5431)+P57(f65(x5431))
% 15.40/15.54 [544]~P57(x5441)+P59(f65(x5441))
% 15.40/15.54 [545]~P57(x5451)+P58(f65(x5451))
% 15.40/15.54 [546]~P57(x5461)+P60(f65(x5461))
% 15.40/15.54 [547]~P57(x5471)+P36(f65(x5471))
% 15.40/15.54 [548]~P57(x5481)+P37(f65(x5481))
% 15.40/15.54 [549]~P57(x5491)+P40(f65(x5491))
% 15.40/15.54 [550]~P57(x5501)+P41(f65(x5501))
% 15.40/15.54 [551]~P3(x5511)+P26(f65(x5511))
% 15.40/15.54 [552]~P57(x5521)+P27(f65(x5521))
% 15.40/15.54 [553]~P57(x5531)+P28(f65(x5531))
% 15.40/15.54 [554]~P15(x5541)+P15(f65(x5541))
% 15.40/15.54 [555]~P51(x5551)+P72(f65(x5551))
% 15.40/15.54 [556]~P15(x5561)+P22(f65(x5561))
% 15.40/15.54 [557]~P57(x5571)+P29(f65(x5571))
% 15.40/15.54 [558]~P46(x5581)+P71(f65(x5581))
% 15.40/15.54 [559]~P46(x5591)+P47(f65(x5591))
% 15.40/15.54 [560]~P18(x5601)+P16(f65(x5601))
% 15.40/15.54 [561]~P18(x5611)+P17(f65(x5611))
% 15.40/15.54 [562]~P15(x5621)+P14(f65(x5621))
% 15.40/15.54 [563]~P57(x5631)+P30(f65(x5631))
% 15.40/15.54 [564]~P57(x5641)+P61(f65(x5641))
% 15.40/15.54 [565]~P57(x5651)+P62(f65(x5651))
% 15.40/15.54 [566]~P3(x5661)+P23(f65(x5661))
% 15.40/15.54 [567]~P4(x5671)+P5(f65(x5671))
% 15.40/15.54 [568]~P4(x5681)+P6(f65(x5681))
% 15.40/15.54 [569]~P57(x5691)+P31(f65(x5691))
% 15.40/15.54 [570]~P18(x5701)+P18(f65(x5701))
% 15.40/15.54 [572]~P69(x5721)+~E(f6(x5721),f3(x5721))
% 15.40/15.54 [622]E(x6221,f3(a59))+E(f9(a59,x6221,x6221),f6(a59))
% 15.40/15.54 [625]E(x6251,f3(a58))+P8(a58,f3(a58),x6251)
% 15.40/15.54 [677]~P54(x6771)+P7(x6771,f3(x6771),f6(x6771))
% 15.40/15.54 [678]~P54(x6781)+P8(x6781,f3(x6781),f6(x6781))
% 15.40/15.54 [726]E(x7261,f3(a58))+~P7(a58,x7261,f3(a58))
% 15.40/15.54 [778]~P54(x7781)+~P7(x7781,f6(x7781),f3(x7781))
% 15.40/15.54 [779]~P54(x7791)+~P8(x7791,f6(x7791),f3(x7791))
% 15.40/15.54 [849]~P8(a59,f3(a59),x8491)+P7(a59,f6(a59),x8491)
% 15.40/15.54 [850]~P7(a59,f6(a59),x8501)+P8(a59,f3(a59),x8501)
% 15.40/15.54 [575]~P21(x5751)+E(f4(x5751,f3(x5751)),f3(x5751))
% 15.40/15.54 [576]~P43(x5761)+E(f12(x5761,f3(x5761)),f3(x5761))
% 15.40/15.54 [577]~P31(x5771)+E(f12(x5771,f3(x5771)),f3(x5771))
% 15.40/15.54 [578]~P44(x5781)+E(f12(x5781,f6(x5781)),f6(x5781))
% 15.40/15.54 [621]~P57(x6211)+~P9(x6211,f3(f65(x6211)))
% 15.40/15.54 [686]~P35(x6861)+E(f23(x6861,f6(x6861),f5(x6861)),f27(x6861))
% 15.40/15.54 [729]~E(f21(f16(a1,a61),x7291),f3(a1))+E(f21(f16(a1,a68),x7291),f3(a1))
% 15.40/15.54 [730]~E(f21(f16(a1,a67),x7301),f3(a1))+E(f21(f16(a1,a69),x7301),f3(a1))
% 15.40/15.54 [874]~P8(a58,f3(a58),x8741)+E(f11(a58,f41(x8741),f6(a58)),x8741)
% 15.40/15.54 [881]E(x8811,f6(a58))+~P73(f21(f21(f22(a58),x8811),f6(a58)))
% 15.40/15.54 [961]~P54(x9611)+P8(x9611,f3(x9611),f11(x9611,f6(x9611),f6(x9611)))
% 15.40/15.54 [1099]~P7(a59,f3(a59),x10991)+P8(a59,f3(a59),f11(a59,f6(a59),x10991))
% 15.40/15.54 [1101]~P8(a58,f3(a58),x11011)+E(f11(a58,f7(a58,x11011,f6(a58)),f6(a58)),x11011)
% 15.40/15.54 [1115]E(x11151,f3(a58))+~P8(a58,x11151,f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1474]~P8(a58,f3(a58),x14741)+E(f11(a58,f7(a58,x14741,f11(a58,f3(a58),f6(a58))),f6(a58)),x14741)
% 15.40/15.54 [599]~P2(x5991)+E(f2(x5991,f3(f65(x5991))),f3(a58))
% 15.40/15.54 [600]~P1(x6001)+E(f2(x6001,f6(f65(x6001))),f3(a58))
% 15.40/15.54 [617]~P3(x6171)+E(f4(f65(x6171),f3(f65(x6171))),f3(f65(x6171)))
% 15.40/15.54 [733]~P1(x7331)+E(f19(x7331,f6(x7331),f3(f65(x7331))),f6(f65(x7331)))
% 15.40/15.54 [734]~P2(x7341)+E(f19(x7341,f3(x7341),f3(f65(x7341))),f3(f65(x7341)))
% 15.40/15.54 [770]~P4(x7701)+E(f24(x7701,f3(f65(x7701)),f3(f65(x7701))),f3(f65(x7701)))
% 15.40/15.54 [1469]~P8(a59,x14691,f3(a59))+P8(a59,f11(a59,f11(a59,f6(a59),x14691),x14691),f3(a59))
% 15.40/15.54 [1579]E(x15791,f11(a58,f3(a58),f6(a58)))+~P73(f21(f21(f22(a58),x15791),f11(a58,f3(a58),f6(a58))))
% 15.40/15.54 [1632]P8(a59,x16321,f3(a59))+~P8(a59,f11(a59,f11(a59,f6(a59),x16321),x16321),f3(a59))
% 15.40/15.54 [1779]P75(a500)+~E(f21(f21(f5(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),x17791),a68)
% 15.40/15.54 [620]~E(x6201,x6202)+P7(a58,x6201,x6202)
% 15.40/15.54 [633]~P36(x6331)+P7(x6331,x6332,x6332)
% 15.40/15.54 [706]~E(x7061,x7062)+~P8(a58,x7061,x7062)
% 15.40/15.54 [707]~E(x7071,x7072)+~P8(a59,x7071,x7072)
% 15.40/15.54 [727]~P8(x7271,x7272,x7272)+~P36(x7271)
% 15.40/15.54 [766]P7(a58,x7662,x7661)+P7(a58,x7661,x7662)
% 15.40/15.54 [767]P7(a59,x7672,x7671)+P7(a59,x7671,x7672)
% 15.40/15.54 [828]~P8(a58,x8281,x8282)+P7(a58,x8281,x8282)
% 15.40/15.54 [829]~P8(a59,x8291,x8292)+P7(a59,x8291,x8292)
% 15.40/15.54 [584]~E(x5841,x5842)+P73(f28(x5841,x5842))
% 15.40/15.54 [587]~P36(x5872)+P36(f66(x5871,x5872))
% 15.40/15.54 [588]~P40(x5882)+P40(f66(x5881,x5882))
% 15.40/15.54 [589]~P41(x5892)+P41(f66(x5891,x5892))
% 15.40/15.54 [590]~P38(x5902)+P38(f66(x5901,x5902))
% 15.40/15.54 [591]~P26(x5912)+P26(f66(x5911,x5912))
% 15.40/15.54 [592]~P23(x5922)+P23(f66(x5921,x5922))
% 15.40/15.54 [608]E(x6081,x6082)+~P73(f28(x6081,x6082))
% 15.40/15.54 [623]E(f11(a58,x6231,x6232),x6232)+~E(x6231,f3(a58))
% 15.40/15.54 [632]~E(x6322,f3(a59))+E(f9(a59,x6321,x6322),f3(a59))
% 15.40/15.54 [641]~P21(x6411)+E(f7(x6411,x6412,x6412),f3(x6411))
% 15.40/15.54 [664]P7(a59,x6642,x6641)+E(f14(x6641,x6642),f3(a59))
% 15.40/15.54 [711]~E(f11(a58,x7112,x7111),x7112)+E(x7111,f3(a58))
% 15.40/15.54 [715]~P8(a58,x7152,x7151)+~E(x7151,f3(a58))
% 15.40/15.54 [720]E(x7201,f3(a58))+~E(f11(a58,x7202,x7201),f3(a58))
% 15.40/15.54 [721]E(x7211,f3(a58))+~E(f11(a58,x7211,x7212),f3(a58))
% 15.40/15.54 [838]~P7(a58,x8381,x8382)+E(f7(a58,x8381,x8382),f3(a58))
% 15.40/15.54 [839]~P8(a58,x8391,x8392)+E(f9(a58,x8391,x8392),f3(a58))
% 15.40/15.54 [844]P7(a58,x8441,x8442)+~E(f7(a58,x8441,x8442),f3(a58))
% 15.40/15.54 [869]~P7(a59,x8692,x8691)+E(f7(a59,x8691,x8692),f14(x8691,x8692))
% 15.40/15.54 [879]E(f9(a59,x8791,x8792),f29(x8791,x8792))+~P7(a59,f3(a59),x8792)
% 15.40/15.54 [1072]~P8(a58,x10722,x10721)+P8(a58,f3(a58),f7(a58,x10721,x10722))
% 15.40/15.54 [1073]~P8(a59,x10731,x10732)+P8(a59,f7(a59,x10731,x10732),f3(a59))
% 15.40/15.54 [1173]P8(a58,x11731,x11732)+~P8(a58,f3(a58),f7(a58,x11732,x11731))
% 15.40/15.54 [1174]P8(a59,x11741,x11742)+~P8(a59,f7(a59,x11741,x11742),f3(a59))
% 15.40/15.54 [606]~P21(x6061)+E(f4(x6061,f4(x6061,x6062)),x6062)
% 15.40/15.54 [607]~P38(x6071)+E(f4(x6071,f4(x6071,x6072)),x6072)
% 15.40/15.54 [631]~P57(x6311)+E(f12(x6311,f12(x6311,x6312)),f12(x6311,x6312))
% 15.40/15.54 [635]~P1(x6351)+E(f21(f21(f27(x6351),x6352),f6(a58)),x6352)
% 15.40/15.54 [636]~P19(x6361)+E(f21(f21(f27(x6361),x6362),f6(a58)),x6362)
% 15.40/15.54 [642]~P1(x6421)+E(f21(f21(f5(x6421),x6422),f6(x6421)),x6422)
% 15.40/15.54 [643]~P12(x6431)+E(f21(f21(f5(x6431),x6432),f6(x6431)),x6432)
% 15.40/15.54 [644]~P19(x6441)+E(f21(f21(f5(x6441),x6442),f6(x6441)),x6442)
% 15.40/15.54 [645]~P1(x6451)+E(f21(f21(f27(x6451),x6452),f3(a58)),f6(x6451))
% 15.40/15.54 [646]~P35(x6461)+E(f21(f21(f27(x6461),x6462),f3(a58)),f6(x6461))
% 15.40/15.54 [648]~P1(x6481)+E(f11(x6481,x6482,f3(x6481)),x6482)
% 15.40/15.54 [649]~P15(x6491)+E(f11(x6491,x6492,f3(x6491)),x6492)
% 15.40/15.54 [650]~P22(x6501)+E(f11(x6501,x6502,f3(x6501)),x6502)
% 15.40/15.54 [651]~P21(x6511)+E(f7(x6511,x6512,f3(x6511)),x6512)
% 15.40/15.54 [652]~P5(x6521)+E(f9(x6521,x6522,f6(x6521)),x6522)
% 15.40/15.54 [653]~P1(x6531)+E(f11(x6531,f3(x6531),x6532),x6532)
% 15.40/15.54 [654]~P15(x6541)+E(f11(x6541,f3(x6541),x6542),x6542)
% 15.40/15.54 [655]~P22(x6551)+E(f11(x6551,f3(x6551),x6552),x6552)
% 15.40/15.54 [660]~P1(x6601)+E(f21(f21(f5(x6601),x6602),f3(x6601)),f3(x6601))
% 15.40/15.54 [661]~P53(x6611)+E(f21(f21(f5(x6611),x6612),f3(x6611)),f3(x6611))
% 15.40/15.54 [663]~P33(x6631)+E(f21(f21(f5(x6631),x6632),f3(x6631)),f3(x6631))
% 15.40/15.54 [668]~P5(x6681)+E(f9(x6681,x6682,f3(x6681)),f3(x6681))
% 15.40/15.54 [669]~P5(x6691)+E(f9(x6691,f3(x6691),x6692),f3(x6691))
% 15.40/15.54 [687]~P2(x6871)+E(f18(x6871,f3(x6871),x6872),f3(f65(x6871)))
% 15.40/15.54 [693]~P21(x6931)+E(f7(x6931,f3(x6931),x6932),f4(x6931,x6932))
% 15.40/15.54 [701]~P43(x7011)+E(f12(x7011,f4(x7011,x7012)),f4(x7011,f12(x7011,x7012)))
% 15.40/15.54 [722]~P21(x7221)+E(f11(x7221,x7222,f4(x7221,x7222)),f3(x7221))
% 15.40/15.54 [723]~P3(x7231)+E(f11(x7231,f4(x7231,x7232),x7232),f3(x7231))
% 15.40/15.54 [724]~P21(x7241)+E(f11(x7241,f4(x7241,x7242),x7242),f3(x7241))
% 15.40/15.54 [814]~P1(x8141)+P73(f21(f21(f22(x8141),x8142),f3(x8141)))
% 15.40/15.54 [816]E(x8161,x8162)+~E(f21(x8161,f30(x8162,x8161)),f21(x8162,f30(x8162,x8161)))
% 15.40/15.54 [851]P8(a58,f3(a58),x8511)+~E(x8511,f11(a58,x8512,f6(a58)))
% 15.40/15.54 [883]~P7(a58,x8831,x8832)+E(f11(a58,x8831,f32(x8832,x8831)),x8832)
% 15.40/15.54 [884]~P7(a58,x8841,x8842)+E(f11(a58,x8841,f34(x8842,x8841)),x8842)
% 15.40/15.54 [885]~E(x8851,x8852)+P8(a58,x8851,f11(a58,x8852,f6(a58)))
% 15.40/15.54 [886]~E(x8861,x8862)+P8(a59,x8861,f11(a59,x8862,f6(a59)))
% 15.40/15.54 [890]~E(x8901,f3(a58))+P8(a58,x8901,f11(a58,x8902,f6(a58)))
% 15.40/15.54 [927]~P54(x9271)+P8(x9271,x9272,f11(x9271,x9272,f6(x9271)))
% 15.40/15.54 [983]P8(a58,x9832,x9831)+E(f11(a58,x9831,f7(a58,x9832,x9831)),x9832)
% 15.40/15.54 [1001]P8(a58,x10011,x10012)+P8(a58,x10012,f11(a58,x10011,f6(a58)))
% 15.40/15.54 [1002]P7(a58,x10021,x10022)+P7(a58,f11(a58,x10022,f6(a58)),x10021)
% 15.40/15.54 [1067]~P7(a58,x10671,x10672)+E(f11(a58,x10671,f7(a58,x10672,x10671)),x10672)
% 15.40/15.54 [1068]~P7(a58,x10682,x10681)+E(f7(a58,x10681,f7(a58,x10681,x10682)),x10682)
% 15.40/15.54 [1069]~P7(a58,x10692,x10691)+E(f11(a58,f7(a58,x10691,x10692),x10692),x10691)
% 15.40/15.54 [1079]~P8(a59,x10791,x10792)+P7(a59,x10791,f7(a59,x10792,f6(a59)))
% 15.40/15.54 [1081]~P7(a58,x10811,x10812)+P8(a58,x10811,f11(a58,x10812,f6(a58)))
% 15.40/15.54 [1084]~P7(a59,x10841,x10842)+P8(a59,x10841,f11(a59,x10842,f6(a59)))
% 15.40/15.54 [1085]~P8(a59,x10851,x10852)+P8(a59,x10851,f11(a59,x10852,f6(a59)))
% 15.40/15.54 [1088]~P8(a58,x10881,x10882)+P7(a58,f11(a58,x10881,f6(a58)),x10882)
% 15.40/15.54 [1090]~P8(a59,x10901,x10902)+P7(a59,f11(a59,x10901,f6(a59)),x10902)
% 15.40/15.54 [1149]~P8(a58,x11491,x11492)+E(f11(a58,f11(a58,x11491,f35(x11492,x11491)),f6(a58)),x11492)
% 15.40/15.54 [1176]P7(a58,x11761,x11762)+~P8(a58,x11761,f11(a58,x11762,f6(a58)))
% 15.40/15.54 [1177]P7(a59,x11771,x11772)+~P8(a59,x11771,f11(a59,x11772,f6(a59)))
% 15.40/15.54 [1178]P8(a59,x11781,x11782)+~P7(a59,x11781,f7(a59,x11782,f6(a59)))
% 15.40/15.54 [1182]P8(a58,x11821,x11822)+~P7(a58,f11(a58,x11821,f6(a58)),x11822)
% 15.40/15.54 [1184]P8(a59,x11841,x11842)+~P7(a59,f11(a59,x11841,f6(a59)),x11842)
% 15.40/15.54 [1260]~P8(a58,x12601,x12602)+~P8(a58,x12602,f11(a58,x12601,f6(a58)))
% 15.40/15.54 [1261]~P7(a58,x12611,x12612)+~P7(a58,f11(a58,x12612,f6(a58)),x12611)
% 15.40/15.54 [1415]E(x14151,f3(a58))+E(f11(a58,f11(a58,f7(a58,x14151,f6(a58)),x14152),f6(a58)),f11(a58,x14151,x14152))
% 15.40/15.54 [1475]P7(a58,x14751,x14752)+~P7(a58,f11(a58,x14751,f6(a58)),f11(a58,x14752,f6(a58)))
% 15.40/15.54 [1477]P8(a58,x14771,x14772)+~P8(a58,f11(a58,x14771,f6(a58)),f11(a58,x14772,f6(a58)))
% 15.40/15.54 [1762]~P4(x17621)+P11(x17621,x17622,f3(f65(x17621)),f3(f65(x17621)),x17622)
% 15.40/15.54 [1773]~P4(x17731)+P11(x17731,f3(f65(x17731)),x17732,f3(f65(x17731)),f3(f65(x17731)))
% 15.40/15.54 [612]~E(x6122,f3(a58))+E(f21(f21(f5(a58),x6121),x6122),f3(a58))
% 15.40/15.54 [614]~E(x6141,f3(a58))+E(f21(f21(f5(a58),x6141),x6142),f3(a58))
% 15.40/15.54 [615]~E(x6152,f3(a58))+E(f21(f21(f27(a58),x6151),x6152),f6(a58))
% 15.40/15.54 [627]~P39(x6271)+E(f21(f21(f5(x6271),x6272),x6272),x6272)
% 15.40/15.54 [673]~P1(x6731)+E(f21(f21(f5(x6731),f6(x6731)),x6732),x6732)
% 15.40/15.54 [674]~P12(x6741)+E(f21(f21(f5(x6741),f6(x6741)),x6742),x6742)
% 15.40/15.54 [675]~P19(x6751)+E(f21(f21(f5(x6751),f6(x6751)),x6752),x6752)
% 15.40/15.54 [676]~P3(x6761)+E(f2(x6761,f4(f65(x6761),x6762)),f2(x6761,x6762))
% 15.40/15.54 [681]~P1(x6811)+E(f21(f21(f5(x6811),f3(x6811)),x6812),f3(x6811))
% 15.40/15.54 [682]~P53(x6821)+E(f21(f21(f5(x6821),f3(x6821)),x6822),f3(x6821))
% 15.40/15.54 [684]~P33(x6841)+E(f21(f21(f5(x6841),f3(x6841)),x6842),f3(x6841))
% 15.40/15.54 [685]~P19(x6851)+E(f21(f21(f27(x6851),f6(x6851)),x6852),f6(x6851))
% 15.40/15.54 [691]E(x6911,f6(a58))+~E(f21(f21(f5(a58),x6912),x6911),f6(a58))
% 15.40/15.54 [692]E(x6921,f6(a58))+~E(f21(f21(f5(a58),x6921),x6922),f6(a58))
% 15.40/15.54 [698]~P15(x6981)+E(f11(f65(x6981),x6982,f3(f65(x6981))),x6982)
% 15.40/15.54 [699]~P3(x6991)+E(f7(f65(x6991),x6992,f3(f65(x6991))),x6992)
% 15.40/15.54 [700]~P15(x7001)+E(f11(f65(x7001),f3(f65(x7001)),x7002),x7002)
% 15.40/15.54 [716]~P4(x7161)+E(f24(x7161,x7162,f6(f65(x7161))),f6(f65(x7161)))
% 15.40/15.54 [717]~P46(x7171)+E(f20(x7171,f3(f65(x7171)),x7172),f3(f65(x7171)))
% 15.40/15.54 [718]~P46(x7181)+E(f25(x7181,f3(f65(x7181)),x7182),f3(f65(x7181)))
% 15.40/15.54 [719]~P4(x7191)+E(f24(x7191,f6(f65(x7191)),x7192),f6(f65(x7191)))
% 15.40/15.54 [748]~E(x7481,x7482)+P73(f21(f21(f22(a58),x7481),x7482))
% 15.40/15.54 [761]~P3(x7611)+E(f7(f65(x7611),f3(f65(x7611)),x7612),f4(f65(x7611),x7612))
% 15.40/15.54 [775]~E(x7752,f3(a58))+E(f21(f21(f27(a58),x7751),x7752),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [777]~P46(x7771)+E(f21(f21(f5(f65(x7771)),x7772),f3(f65(x7771))),f3(f65(x7771)))
% 15.40/15.54 [780]~P1(x7801)+P73(f21(f21(f22(x7801),x7802),x7802))
% 15.40/15.54 [832]~P2(x8321)+E(f19(x8321,x8322,f3(f65(x8321))),f18(x8321,x8322,f3(a58)))
% 15.40/15.54 [833]~P1(x8331)+P73(f21(f21(f22(x8331),f6(x8331)),x8332))
% 15.40/15.54 [876]~E(x8762,f3(a58))+P8(a58,f3(a58),f21(f21(f27(a58),x8761),x8762))
% 15.40/15.54 [897]~P56(x8971)+P7(x8971,f3(x8971),f21(f21(f5(x8971),x8972),x8972))
% 15.40/15.54 [962]~E(x9621,f11(a58,f3(a58),f6(a58)))+E(f21(f21(f27(a58),x9621),x9622),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1016]E(x10161,f11(a58,f3(a58),f6(a58)))+~E(f21(f21(f5(a58),x10162),x10161),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1017]E(x10171,f11(a58,f3(a58),f6(a58)))+~E(f21(f21(f5(a58),x10171),x10172),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1030]P7(a59,f3(a59),x10302)+E(f4(a59,f9(a59,x10301,f4(a59,x10302))),f29(x10301,x10302))
% 15.40/15.54 [1044]~P7(a59,f3(a59),x10441)+P7(a59,f3(a59),f21(f21(f27(a59),x10441),x10442))
% 15.40/15.54 [1046]~P8(a58,f3(a58),x10461)+P8(a58,f3(a58),f21(f21(f27(a58),x10461),x10462))
% 15.40/15.54 [1107]~P56(x11071)+~P8(x11071,f21(f21(f5(x11071),x11072),x11072),f3(x11071))
% 15.40/15.54 [1131]P8(a58,f3(a58),x11311)+~P8(a58,f3(a58),f21(f21(f5(a58),x11312),x11311))
% 15.40/15.54 [1132]P8(a58,f3(a58),x11321)+~P8(a58,f3(a58),f21(f21(f5(a58),x11321),x11322))
% 15.40/15.54 [1134]P73(f21(f21(f22(a59),x11341),f4(a59,x11342)))+~P73(f21(f21(f22(a59),x11341),x11342))
% 15.40/15.54 [1161]E(f21(f21(f5(a59),x11611),f9(a59,x11612,x11611)),x11612)+~P73(f21(f21(f22(a59),x11611),x11612))
% 15.40/15.54 [1190]~P73(f21(f21(f22(a59),x11901),f4(a59,x11902)))+P73(f21(f21(f22(a59),x11901),x11902))
% 15.40/15.54 [1245]~P73(f21(f21(f22(a59),x12451),x12452))+P73(f21(f21(f22(a59),f4(a59,x12451)),x12452))
% 15.40/15.54 [1344]P73(f21(f21(f22(a59),x13441),x13442))+~P73(f21(f21(f22(a59),f4(a59,x13441)),x13442))
% 15.40/15.54 [1452]P73(f21(f21(f22(a58),x14521),f11(a58,x14522,x14521)))+~P73(f21(f21(f22(a58),x14521),x14522))
% 15.40/15.54 [1468]~P8(a58,f3(a58),x14681)+P8(a58,f7(a58,x14681,f11(a58,x14682,f6(a58))),x14681)
% 15.40/15.54 [1523]~P7(a58,f11(a58,f3(a58),f6(a58)),x15231)+P7(a58,f11(a58,f3(a58),f6(a58)),f21(f21(f27(a58),x15231),x15232))
% 15.40/15.54 [1577]~P73(f21(f21(f22(a58),x15771),f11(a58,x15772,x15771)))+P73(f21(f21(f22(a58),x15771),x15772))
% 15.40/15.54 [1585]P7(a58,f11(a58,f3(a58),f6(a58)),x15851)+~P7(a58,f11(a58,f3(a58),f6(a58)),f21(f21(f5(a58),x15852),x15851))
% 15.40/15.54 [1586]P7(a58,f11(a58,f3(a58),f6(a58)),x15861)+~P7(a58,f11(a58,f3(a58),f6(a58)),f21(f21(f5(a58),x15861),x15862))
% 15.40/15.54 [1587]~P67(x15871)+E(f21(f21(f5(x15871),f11(x15871,x15872,f6(x15871))),f7(x15871,x15872,f6(x15871))),f7(x15871,f21(f21(f5(x15871),x15872),x15872),f6(x15871)))
% 15.40/15.54 [708]~P46(x7081)+E(f21(f16(x7081,f3(f65(x7081))),x7082),f3(x7081))
% 15.40/15.54 [709]~P1(x7091)+E(f21(f16(x7091,f6(f65(x7091))),x7092),f6(x7091))
% 15.40/15.54 [710]~P2(x7101)+E(f21(f13(x7101,f3(f65(x7101))),x7102),f3(x7101))
% 15.40/15.54 [820]~P46(x8201)+E(f21(f21(f5(f65(x8201)),f3(f65(x8201))),x8202),f3(f65(x8201)))
% 15.40/15.54 [858]~P32(x8581)+E(f21(f21(f5(x8581),f4(x8581,f6(x8581))),x8582),f4(x8581,x8582))
% 15.40/15.54 [887]~P2(x8871)+E(f2(x8871,f19(x8871,x8872,f3(f65(x8871)))),f3(a58))
% 15.40/15.54 [1031]~P8(a58,f3(a58),x10312)+E(f9(a58,f21(f21(f5(a58),x10311),x10312),x10312),x10311)
% 15.40/15.54 [1032]~P8(a58,f3(a58),x10321)+E(f9(a58,f21(f21(f5(a58),x10321),x10322),x10321),x10322)
% 15.40/15.54 [1327]~P1(x13271)+E(f11(x13271,x13272,x13272),f21(f21(f5(x13271),f11(x13271,f6(x13271),f6(x13271))),x13272))
% 15.40/15.54 [1366]E(x13661,f3(a58))+E(f21(f21(f5(a58),x13662),f21(f21(f27(a58),x13662),f7(a58,x13661,f6(a58)))),f21(f21(f27(a58),x13662),x13661))
% 15.40/15.54 [1625]E(x16251,f3(a58))+E(f11(a58,x16252,f21(f21(f5(a58),f7(a58,x16251,f6(a58))),x16252)),f21(f21(f5(a58),x16251),x16252))
% 15.40/15.54 [787]~P1(x7871)+E(f11(x7871,x7872,x7873),f11(x7871,x7873,x7872))
% 15.40/15.54 [788]~P4(x7881)+E(f24(x7881,x7882,x7883),f24(x7881,x7883,x7882))
% 15.40/15.54 [835]P7(a58,x8351,x8352)+~E(x8352,f11(a58,x8351,x8353))
% 15.40/15.54 [888]E(x8881,x8882)+~E(f11(a58,x8883,x8881),f11(a58,x8883,x8882))
% 15.40/15.54 [889]E(x8891,x8892)+~E(f11(a58,x8891,x8893),f11(a58,x8892,x8893))
% 15.40/15.54 [1055]~P7(a58,x10551,x10553)+P7(a58,x10551,f11(a58,x10552,x10553))
% 15.40/15.54 [1057]~P7(a58,x10571,x10572)+P7(a58,x10571,f11(a58,x10572,x10573))
% 15.40/15.54 [1059]~P8(a58,x10591,x10593)+P8(a58,x10591,f11(a58,x10592,x10593))
% 15.40/15.54 [1061]~P8(a58,x10611,x10612)+P8(a58,x10611,f11(a58,x10612,x10613))
% 15.40/15.54 [1062]~P8(a58,x10621,x10623)+P8(a58,f7(a58,x10621,x10622),x10623)
% 15.40/15.54 [1166]P7(a58,x11661,x11662)+~P7(a58,f11(a58,x11663,x11661),x11662)
% 15.40/15.54 [1167]P7(a58,x11671,x11672)+~P7(a58,f11(a58,x11671,x11673),x11672)
% 15.40/15.54 [1168]P8(a58,x11681,x11682)+~P8(a58,f11(a58,x11681,x11683),x11682)
% 15.40/15.54 [1266]~P7(a58,x12662,x12663)+P7(a58,f11(a58,x12661,x12662),f11(a58,x12661,x12663))
% 15.40/15.54 [1267]~P7(a58,x12671,x12673)+P7(a58,f11(a58,x12671,x12672),f11(a58,x12673,x12672))
% 15.40/15.54 [1268]~P7(a58,x12683,x12682)+P7(a58,f7(a58,x12681,x12682),f7(a58,x12681,x12683))
% 15.40/15.54 [1269]~P7(a58,x12691,x12693)+P7(a58,f7(a58,x12691,x12692),f7(a58,x12693,x12692))
% 15.40/15.54 [1270]~P7(a58,x12701,x12703)+P7(a58,f9(a58,x12701,x12702),f9(a58,x12703,x12702))
% 15.40/15.54 [1271]~P7(a59,x12712,x12713)+P7(a59,f11(a59,x12711,x12712),f11(a59,x12711,x12713))
% 15.40/15.54 [1272]~P8(a58,x12722,x12723)+P8(a58,f11(a58,x12721,x12722),f11(a58,x12721,x12723))
% 15.40/15.54 [1273]~P8(a58,x12731,x12733)+P8(a58,f11(a58,x12731,x12732),f11(a58,x12733,x12732))
% 15.40/15.54 [1274]~P8(a59,x12741,x12743)+P8(a59,f11(a59,x12741,x12742),f11(a59,x12743,x12742))
% 15.40/15.54 [1362]~P7(a58,f7(a58,x13621,x13623),x13622)+P7(a58,x13621,f11(a58,x13622,x13623))
% 15.40/15.54 [1363]~P8(a58,f11(a58,x13631,x13633),x13632)+P8(a58,x13631,f7(a58,x13632,x13633))
% 15.40/15.54 [1364]~P7(a58,x13641,f11(a58,x13643,x13642))+P7(a58,f7(a58,x13641,x13642),x13643)
% 15.40/15.54 [1365]~P8(a58,x13651,f7(a58,x13653,x13652))+P8(a58,f11(a58,x13651,x13652),x13653)
% 15.40/15.54 [1466]P7(a58,x14661,x14662)+~P7(a58,f11(a58,x14663,x14661),f11(a58,x14663,x14662))
% 15.40/15.54 [1467]P8(a58,x14671,x14672)+~P8(a58,f11(a58,x14673,x14671),f11(a58,x14673,x14672))
% 15.40/15.54 [845]~P32(x8451)+E(f11(x8451,x8452,f4(x8451,x8453)),f7(x8451,x8452,x8453))
% 15.40/15.54 [846]~P3(x8461)+E(f11(x8461,x8462,f4(x8461,x8463)),f7(x8461,x8462,x8463))
% 15.40/15.54 [847]~P21(x8471)+E(f11(x8471,x8472,f4(x8471,x8473)),f7(x8471,x8472,x8473))
% 15.40/15.54 [848]~P21(x8481)+E(f7(x8481,x8482,f4(x8481,x8483)),f11(x8481,x8482,x8483))
% 15.40/15.54 [893]~P21(x8931)+E(f11(x8931,f7(x8931,x8932,x8933),x8933),x8932)
% 15.40/15.54 [894]~P21(x8941)+E(f7(x8941,f11(x8941,x8942,x8943),x8943),x8942)
% 15.40/15.54 [901]~P5(x9011)+E(f9(x9011,f8(x9011,x9012,x9013),x9013),f3(x9011))
% 15.40/15.54 [932]~P3(x9321)+E(f4(x9321,f7(x9321,x9322,x9323)),f7(x9321,x9323,x9322))
% 15.40/15.54 [958]~P21(x9581)+E(f11(x9581,f4(x9581,x9582),f11(x9581,x9582,x9583)),x9583)
% 15.40/15.54 [982]~P46(x9821)+E(f2(x9821,f25(x9821,x9822,x9823)),f7(a58,f2(x9821,x9822),f6(a58)))
% 15.40/15.54 [989]~P3(x9891)+E(f4(f65(x9891),f18(x9891,x9892,x9893)),f18(x9891,f4(x9891,x9892),x9893))
% 15.40/15.54 [1033]~P21(x10331)+E(f11(x10331,f4(x10331,x10332),f4(x10331,x10333)),f4(x10331,f11(x10331,x10333,x10332)))
% 15.40/15.54 [1034]~P3(x10341)+E(f11(x10341,f4(x10341,x10342),f4(x10341,x10343)),f4(x10341,f11(x10341,x10342,x10343)))
% 15.40/15.54 [1035]~P3(x10351)+E(f7(x10351,f4(x10351,x10352),f4(x10351,x10353)),f4(x10351,f7(x10351,x10352,x10353)))
% 15.40/15.54 [1108]~P2(x11081)+E(f21(f13(x11081,f19(x11081,x11082,x11083)),f3(a58)),x11082)
% 15.40/15.54 [1162]~P2(x11621)+P7(a58,f2(x11621,f18(x11621,x11622,x11623)),x11623)
% 15.40/15.54 [1175]P8(a58,x11751,x11752)+~E(x11752,f11(a58,f11(a58,x11751,x11753),f6(a58)))
% 15.40/15.54 [1216]~P74(x12161,x12163,x12162)+P73(f21(x12161,f9(a59,x12162,x12163)))
% 15.40/15.54 [1355]~P7(a58,x13552,x13553)+E(f7(a58,f11(a58,x13551,x13552),x13553),f7(a58,x13551,f7(a58,x13553,x13552)))
% 15.40/15.54 [1356]~P7(a58,x13563,x13562)+E(f11(a58,x13561,f7(a58,x13562,x13563)),f7(a58,f11(a58,x13561,x13562),x13563))
% 15.40/15.54 [1358]~P7(a58,x13582,x13581)+E(f11(a58,f7(a58,x13581,x13582),x13583),f7(a58,f11(a58,x13581,x13583),x13582))
% 15.40/15.54 [1408]P74(x14081,x14082,x14083)+~P73(f21(x14081,f9(a59,x14083,x14082)))
% 15.40/15.54 [1431]~P7(a58,x14313,x14312)+P7(a58,x14311,f7(a58,f11(a58,x14312,x14311),x14313))
% 15.40/15.54 [1465]~P2(x14651)+P7(a58,f2(x14651,f19(x14651,x14652,x14653)),f11(a58,f2(x14651,x14653),f6(a58)))
% 15.40/15.54 [1486]~P5(x14861)+E(f11(x14861,f21(f21(f5(x14861),x14862),f9(x14861,x14863,x14862)),f8(x14861,x14863,x14862)),x14863)
% 15.40/15.54 [1550]~P46(x15501)+P7(a58,f2(x15501,f20(x15501,x15502,x15503)),f21(f21(f5(a58),f2(x15501,x15502)),f2(x15501,x15503)))
% 15.40/15.54 [1657]~P5(x16571)+E(f11(x16571,f21(f21(f5(x16571),f9(x16571,x16572,x16573)),x16573),f8(x16571,x16572,x16573)),x16572)
% 15.40/15.54 [749]~E(x7492,f3(a58))+E(f21(f21(f5(a58),x7491),x7492),f21(f21(f5(a58),x7493),x7492))
% 15.40/15.54 [751]~E(x7511,f3(a58))+E(f21(f21(f5(a58),x7511),x7512),f21(f21(f5(a58),x7511),x7513))
% 15.40/15.54 [776]~P1(x7761)+E(f21(f21(f5(x7761),x7762),x7763),f21(f21(f5(x7761),x7763),x7762))
% 15.40/15.54 [877]~P4(x8771)+E(f24(x8771,x8772,f4(f65(x8771),x8773)),f24(x8771,x8772,x8773))
% 15.40/15.54 [878]~P4(x8781)+E(f24(x8781,f4(f65(x8781),x8782),x8783),f24(x8781,x8782,x8783))
% 15.40/15.54 [944]~P49(x9441)+E(f21(f21(f5(x9441),f4(x9441,x9442)),x9443),f21(f21(f5(x9441),x9442),f4(x9441,x9443)))
% 15.40/15.54 [945]~P49(x9451)+E(f21(f21(f5(x9451),f4(x9451,x9452)),f4(x9451,x9453)),f21(f21(f5(x9451),x9452),x9453))
% 15.40/15.54 [1009]~P21(x10091)+E(f11(x10091,x10092,f11(x10091,f4(x10091,x10092),x10093)),x10093)
% 15.40/15.54 [1074]~P4(x10741)+E(f9(f65(x10741),x10742,f4(f65(x10741),x10743)),f4(f65(x10741),f9(f65(x10741),x10742,x10743)))
% 15.40/15.54 [1075]~P4(x10751)+E(f9(f65(x10751),f4(f65(x10751),x10752),x10753),f4(f65(x10751),f9(f65(x10751),x10752,x10753)))
% 15.40/15.54 [1095]~P3(x10951)+E(f19(x10951,f4(x10951,x10952),f4(f65(x10951),x10953)),f4(f65(x10951),f19(x10951,x10952,x10953)))
% 15.40/15.54 [1136]P8(a58,f3(a58),x11361)+P7(a58,f21(f21(f5(a58),x11362),x11361),f21(f21(f5(a58),x11363),x11361))
% 15.40/15.54 [1137]P8(a58,f3(a58),x11371)+P7(a58,f21(f21(f5(a58),x11371),x11372),f21(f21(f5(a58),x11371),x11373))
% 15.40/15.54 [1194]~P7(a58,x11942,x11943)+P7(a58,f21(f21(f5(a58),x11941),x11942),f21(f21(f5(a58),x11941),x11943))
% 15.40/15.54 [1196]~P7(a58,x11961,x11963)+P7(a58,f21(f21(f5(a58),x11961),x11962),f21(f21(f5(a58),x11963),x11962))
% 15.40/15.54 [1258]~P2(x12581)+E(f18(x12581,x12582,f11(a58,x12583,f6(a58))),f19(x12581,f3(x12581),f18(x12581,x12582,x12583)))
% 15.40/15.54 [1386]P8(a58,x13861,x13862)+~P8(a58,f21(f21(f5(a58),x13863),x13861),f21(f21(f5(a58),x13863),x13862))
% 15.40/15.54 [1387]P8(a58,x13871,x13872)+~P8(a58,f21(f21(f5(a58),x13871),x13873),f21(f21(f5(a58),x13872),x13873))
% 15.40/15.54 [1392]P8(a58,f3(a58),x13921)+~P8(a58,f21(f21(f5(a58),x13922),x13921),f21(f21(f5(a58),x13923),x13921))
% 15.40/15.54 [1393]P8(a58,f3(a58),x13931)+~P8(a58,f21(f21(f5(a58),x13931),x13932),f21(f21(f5(a58),x13931),x13933))
% 15.40/15.54 [1596]~P4(x15961)+P73(f21(f21(f22(f65(x15961)),f24(x15961,x15962,x15963)),x15963))
% 15.40/15.54 [1597]~P4(x15971)+P73(f21(f21(f22(f65(x15971)),f24(x15971,x15972,x15973)),x15972))
% 15.40/15.54 [1665]~P7(a58,x16652,x16653)+E(f7(a58,f11(a58,x16651,x16652),f11(a58,x16653,f6(a58))),f7(a58,x16651,f11(a58,f7(a58,x16653,x16652),f6(a58))))
% 15.40/15.54 [1666]~P7(a58,x16662,x16661)+E(f7(a58,f11(a58,f7(a58,x16661,x16662),f6(a58)),x16663),f7(a58,f11(a58,x16661,f6(a58)),f11(a58,x16662,x16663)))
% 15.40/15.54 [1728]~P46(x17281)+E(f21(f13(x17281,f21(f21(f5(f65(x17281)),x17282),x17283)),f11(a58,f2(x17281,x17282),f2(x17281,x17283))),f21(f21(f5(x17281),f21(f13(x17281,x17282),f2(x17281,x17282))),f21(f13(x17281,x17283),f2(x17281,x17283))))
% 15.40/15.54 [970]~P49(x9701)+E(f21(f21(f5(x9701),x9702),f4(x9701,x9703)),f4(x9701,f21(f21(f5(x9701),x9702),x9703)))
% 15.40/15.54 [972]~P33(x9721)+E(f21(f21(f5(x9721),x9722),f4(x9721,x9723)),f4(x9721,f21(f21(f5(x9721),x9722),x9723)))
% 15.40/15.54 [988]~P39(x9881)+E(f21(f21(f5(x9881),x9882),f21(f21(f5(x9881),x9882),x9883)),f21(f21(f5(x9881),x9882),x9883))
% 15.40/15.54 [999]~P42(x9991)+E(f21(f16(x9991,f4(f65(x9991),x9992)),x9993),f4(x9991,f21(f16(x9991,x9992),x9993)))
% 15.40/15.54 [1000]~P3(x10001)+E(f21(f13(x10001,f4(f65(x10001),x10002)),x10003),f4(x10001,f21(f13(x10001,x10002),x10003)))
% 15.40/15.54 [1018]~P49(x10181)+E(f21(f21(f5(x10181),f4(x10181,x10182)),x10183),f4(x10181,f21(f21(f5(x10181),x10182),x10183)))
% 15.40/15.54 [1020]~P33(x10201)+E(f21(f21(f5(x10201),f4(x10201,x10202)),x10203),f4(x10201,f21(f21(f5(x10201),x10202),x10203)))
% 15.40/15.54 [1066]~E(x10661,f3(a58))+E(f9(a58,f21(f21(f5(a58),x10661),x10662),f21(f21(f5(a58),x10661),x10663)),f3(a58))
% 15.40/15.54 [1097]~P57(x10971)+E(f21(f21(f5(x10971),f12(x10971,x10972)),f12(x10971,x10973)),f12(x10971,f21(f21(f5(x10971),x10972),x10973)))
% 15.40/15.54 [1098]~P45(x10981)+E(f21(f21(f5(x10981),f12(x10981,x10982)),f12(x10981,x10983)),f12(x10981,f21(f21(f5(x10981),x10982),x10983)))
% 15.40/15.54 [1135]E(x11351,f3(a58))+E(f9(a58,f21(f21(f5(a58),x11351),x11352),f21(f21(f5(a58),x11351),x11353)),f9(a58,x11352,x11353))
% 15.40/15.54 [1197]~P1(x11971)+P73(f21(f21(f22(x11971),x11972),f21(f21(f5(x11971),x11973),x11972)))
% 15.40/15.54 [1198]~P1(x11981)+P73(f21(f21(f22(x11981),x11982),f21(f21(f5(x11981),x11982),x11983)))
% 15.40/15.54 [1211]~P1(x12111)+E(f21(f21(f5(x12111),x12112),f21(f21(f27(x12111),x12112),x12113)),f21(f21(f27(x12111),x12112),f11(a58,x12113,f6(a58))))
% 15.40/15.54 [1212]~P35(x12121)+E(f21(f21(f5(x12121),x12122),f21(f21(f27(x12121),x12122),x12123)),f21(f21(f27(x12121),x12122),f11(a58,x12123,f6(a58))))
% 15.40/15.54 [1326]~P8(a58,f3(a58),x13261)+E(f9(a58,f21(f21(f5(a58),x13261),x13262),f21(f21(f5(a58),x13261),x13263)),f9(a58,x13262,x13263))
% 15.40/15.54 [1345]~P8(a59,f3(a59),x13453)+E(f9(a59,x13451,f21(f21(f5(a59),x13452),x13453)),f9(a59,f9(a59,x13451,x13452),x13453))
% 15.40/15.54 [1457]~P1(x14571)+E(f11(x14571,x14572,f21(f21(f5(x14571),x14573),x14572)),f21(f21(f5(x14571),f11(x14571,x14573,f6(x14571))),x14572))
% 15.40/15.54 [1458]~P1(x14581)+E(f11(x14581,f21(f21(f5(x14581),x14582),x14583),x14583),f21(f21(f5(x14581),f11(x14581,x14582,f6(x14581))),x14583))
% 15.40/15.54 [1593]~P56(x15931)+P7(x15931,f3(x15931),f11(x15931,f21(f21(f5(x15931),x15932),x15932),f21(f21(f5(x15931),x15933),x15933)))
% 15.40/15.54 [1631]~E(x16311,f3(a58))+P73(f21(f21(f22(a58),f21(f21(f5(a58),x16311),x16312)),f21(f21(f5(a58),x16311),x16313)))
% 15.40/15.54 [1656]~P5(x16561)+E(f11(x16561,f8(x16561,x16562,x16563),f21(f21(f5(x16561),f9(x16561,x16562,x16563)),x16563)),x16562)
% 15.40/15.54 [1685]~P67(x16851)+E(f21(f21(f5(x16851),f21(f21(f27(x16851),f4(x16851,f6(x16851))),x16852)),f21(f21(f27(x16851),x16853),x16852)),f21(f21(f27(x16851),f4(x16851,x16853)),x16852))
% 15.40/15.54 [1686]~P73(f21(f21(f22(a58),x16862),x16863))+P73(f21(f21(f22(a58),f21(f21(f5(a58),x16861),x16862)),f21(f21(f5(a58),x16861),x16863)))
% 15.40/15.54 [1702]E(x17021,x17022)+~E(f21(f21(f5(a58),f11(a58,x17023,f6(a58))),x17021),f21(f21(f5(a58),f11(a58,x17023,f6(a58))),x17022))
% 15.40/15.54 [1713]~P56(x17131)+~P8(x17131,f11(x17131,f21(f21(f5(x17131),x17132),x17132),f21(f21(f5(x17131),x17133),x17133)),f3(x17131))
% 15.40/15.54 [1758]~P8(a58,x17582,x17583)+P8(a58,f21(f21(f5(a58),f11(a58,x17581,f6(a58))),x17582),f21(f21(f5(a58),f11(a58,x17581,f6(a58))),x17583))
% 15.40/15.54 [1791]P7(a58,x17911,x17912)+~P7(a58,f21(f21(f5(a58),f11(a58,x17913,f6(a58))),x17911),f21(f21(f5(a58),f11(a58,x17913,f6(a58))),x17912))
% 15.40/15.54 [1806]~P32(x18061)+E(f7(x18061,f21(f21(f27(x18061),x18062),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58))),f21(f21(f27(x18061),x18063),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58)))),f21(f21(f5(x18061),f7(x18061,x18062,x18063)),f11(x18061,x18062,x18063)))
% 15.40/15.54 [1829]~P32(x18291)+E(f11(f65(x18291),f21(f21(f5(f65(x18291)),f19(x18291,f4(x18291,x18292),f19(x18291,f6(x18291),f3(f65(x18291))))),f25(x18291,x18293,x18292)),f19(x18291,f21(f16(x18291,x18293),x18292),f3(f65(x18291)))),x18293)
% 15.40/15.54 [1857]~P51(x18571)+P73(f21(f21(f22(f65(x18571)),f21(f21(f27(f65(x18571)),f19(x18571,f4(x18571,x18572),f19(x18571,f6(x18571),f3(f65(x18571))))),f17(x18571,x18572,x18573))),x18573))
% 15.40/15.54 [1385]~P19(x13851)+E(f21(f21(f5(x13851),f21(f21(f27(x13851),x13852),x13853)),x13852),f21(f21(f5(x13851),x13852),f21(f21(f27(x13851),x13852),x13853)))
% 15.40/15.54 [1399]~P19(x13991)+E(f21(f21(f5(x13991),f21(f21(f27(x13991),x13992),x13993)),x13992),f21(f21(f27(x13991),x13992),f11(a58,x13993,f6(a58))))
% 15.40/15.54 [1400]~P1(x14001)+E(f21(f21(f5(x14001),f21(f21(f27(x14001),x14002),x14003)),x14002),f21(f21(f27(x14001),x14002),f11(a58,x14003,f6(a58))))
% 15.40/15.54 [1592]~P1(x15921)+P7(a58,f2(x15921,f21(f21(f27(f65(x15921)),x15922),x15923)),f21(f21(f5(a58),f2(x15921,x15922)),x15923))
% 15.40/15.54 [1599]~P46(x15991)+P7(a58,f2(x15991,f21(f21(f5(f65(x15991)),x15992),x15993)),f11(a58,f2(x15991,x15992),f2(x15991,x15993)))
% 15.40/15.54 [1696]~P73(f21(f21(f22(a59),x16961),x16962))+P73(f21(f21(f22(a59),x16961),f11(a59,x16962,f21(f21(f5(a59),x16961),x16963))))
% 15.40/15.54 [1749]P73(f21(f21(f22(a59),x17491),x17492))+~P73(f21(f21(f22(a59),x17491),f11(a59,x17492,f21(f21(f5(a59),x17491),x17493))))
% 15.40/15.54 [1793]~P1(x17931)+E(f2(x17931,f21(f21(f27(f65(x17931)),f19(x17931,x17932,f19(x17931,f6(x17931),f3(f65(x17931))))),x17933)),x17933)
% 15.40/15.54 [1845]~P1(x18451)+E(f21(f13(x18451,f21(f21(f27(f65(x18451)),f19(x18451,x18452,f19(x18451,f6(x18451),f3(f65(x18451))))),x18453)),x18453),f6(x18451))
% 15.40/15.54 [1225]~P1(x12251)+E(f11(x12251,x12252,f11(x12251,x12253,x12254)),f11(x12251,x12253,f11(x12251,x12252,x12254)))
% 15.40/15.54 [1226]~P4(x12261)+E(f24(x12261,x12262,f24(x12261,x12263,x12264)),f24(x12261,x12263,f24(x12261,x12262,x12264)))
% 15.40/15.54 [1228]~P1(x12281)+E(f11(x12281,f11(x12281,x12282,x12283),x12284),f11(x12281,x12282,f11(x12281,x12283,x12284)))
% 15.40/15.54 [1229]~P14(x12291)+E(f11(x12291,f11(x12291,x12292,x12293),x12294),f11(x12291,x12292,f11(x12291,x12293,x12294)))
% 15.40/15.54 [1230]~P4(x12301)+E(f24(x12301,f24(x12301,x12302,x12303),x12304),f24(x12301,x12302,f24(x12301,x12303,x12304)))
% 15.40/15.54 [1231]~P1(x12311)+E(f11(x12311,f11(x12311,x12312,x12313),x12314),f11(x12311,f11(x12311,x12312,x12314),x12313))
% 15.40/15.54 [1378]~P46(x13781)+E(f25(x13781,f19(x13781,x13782,x13783),x13784),f19(x13781,f21(f16(x13781,x13783),x13784),f25(x13781,x13783,x13784)))
% 15.40/15.54 [1420]~P15(x14201)+E(f11(f65(x14201),f18(x14201,x14202,x14203),f18(x14201,x14204,x14203)),f18(x14201,f11(x14201,x14202,x14204),x14203))
% 15.40/15.54 [1421]~P3(x14211)+E(f7(f65(x14211),f18(x14211,x14212,x14213),f18(x14211,x14214,x14213)),f18(x14211,f7(x14211,x14212,x14214),x14213))
% 15.40/15.54 [836]~P26(x8362)+E(f21(f4(f66(x8361,x8362),x8363),x8364),f4(x8362,f21(x8363,x8364)))
% 15.40/15.54 [1330]~P46(x13301)+E(f21(f16(x13301,x13302),f21(f16(x13301,x13303),x13304)),f21(f16(x13301,f20(x13301,x13302,x13303)),x13304))
% 15.40/15.54 [1379]~P2(x13791)+E(f21(f13(x13791,f19(x13791,x13792,x13793)),f11(a58,x13794,f6(a58))),f21(f13(x13791,x13793),x13794))
% 15.40/15.54 [1673]~P46(x16731)+E(f11(f65(x16731),f19(x16731,x16732,f3(f65(x16731))),f21(f21(f5(f65(x16731)),x16733),f20(x16731,x16734,x16733))),f20(x16731,f19(x16731,x16732,x16734),x16733))
% 15.40/15.54 [1736]~P5(x17361)+E(f11(x17361,f11(x17361,f21(f21(f5(x17361),x17362),f9(x17361,x17363,x17362)),f8(x17361,x17363,x17362)),x17364),f11(x17361,x17363,x17364))
% 15.40/15.54 [1782]~P5(x17821)+E(f11(x17821,f11(x17821,f21(f21(f5(x17821),f9(x17821,x17822,x17823)),x17823),f8(x17821,x17822,x17823)),x17824),f11(x17821,x17822,x17824))
% 15.40/15.54 [1191]~P1(x11911)+E(f21(f21(f5(x11911),x11912),f21(f21(f5(x11911),x11913),x11914)),f21(f21(f5(x11911),x11913),f21(f21(f5(x11911),x11912),x11914)))
% 15.40/15.54 [1380]~P1(x13801)+E(f21(f21(f5(x13801),x13802),f21(f21(f27(x13801),x13803),x13804)),f21(f16(x13801,f18(x13801,x13802,x13804)),x13803))
% 15.40/15.54 [1394]~P1(x13941)+E(f11(x13941,f21(f21(f5(x13941),x13942),x13943),f21(f21(f5(x13941),x13942),x13944)),f21(f21(f5(x13941),x13942),f11(x13941,x13943,x13944)))
% 15.40/15.54 [1396]~P33(x13961)+E(f11(x13961,f21(f21(f5(x13961),x13962),x13963),f21(f21(f5(x13961),x13962),x13964)),f21(f21(f5(x13961),x13962),f11(x13961,x13963,x13964)))
% 15.40/15.54 [1398]~P33(x13981)+E(f7(x13981,f21(f21(f5(x13981),x13982),x13983),f21(f21(f5(x13981),x13982),x13984)),f21(f21(f5(x13981),x13982),f7(x13981,x13983,x13984)))
% 15.40/15.54 [1499]~P46(x14991)+E(f11(x14991,f21(f16(x14991,x14992),x14993),f21(f16(x14991,x14994),x14993)),f21(f16(x14991,f11(f65(x14991),x14992,x14994)),x14993))
% 15.40/15.54 [1500]~P42(x15001)+E(f7(x15001,f21(f16(x15001,x15002),x15003),f21(f16(x15001,x15004),x15003)),f21(f16(x15001,f7(f65(x15001),x15002,x15004)),x15003))
% 15.40/15.54 [1501]~P15(x15011)+E(f11(x15011,f21(f13(x15011,x15012),x15013),f21(f13(x15011,x15014),x15013)),f21(f13(x15011,f11(f65(x15011),x15012,x15014)),x15013))
% 15.40/15.54 [1502]~P3(x15021)+E(f7(x15021,f21(f13(x15021,x15022),x15023),f21(f13(x15021,x15024),x15023)),f21(f13(x15021,f7(f65(x15021),x15022,x15024)),x15023))
% 15.40/15.54 [1517]~P19(x15171)+E(f21(f21(f5(x15171),f21(f21(f27(x15171),x15172),x15173)),f21(f21(f27(x15171),x15172),x15174)),f21(f21(f27(x15171),x15172),f11(a58,x15173,x15174)))
% 15.40/15.54 [1518]~P1(x15181)+E(f21(f21(f5(x15181),f21(f21(f27(x15181),x15182),x15183)),f21(f21(f27(x15181),x15182),x15184)),f21(f21(f27(x15181),x15182),f11(a58,x15183,x15184)))
% 15.40/15.54 [1532]~P33(x15321)+E(f11(x15321,f21(f21(f5(x15321),x15322),x15323),f21(f21(f5(x15321),x15324),x15323)),f21(f21(f5(x15321),f11(x15321,x15322,x15324)),x15323))
% 15.40/15.54 [1533]~P47(x15331)+E(f11(x15331,f21(f21(f5(x15331),x15332),x15333),f21(f21(f5(x15331),x15334),x15333)),f21(f21(f5(x15331),f11(x15331,x15332,x15334)),x15333))
% 15.40/15.54 [1535]~P33(x15351)+E(f7(x15351,f21(f21(f5(x15351),x15352),x15353),f21(f21(f5(x15351),x15354),x15353)),f21(f21(f5(x15351),f7(x15351,x15352,x15354)),x15353))
% 15.40/15.54 [1536]~P1(x15361)+E(f11(x15361,f21(f21(f5(x15361),x15362),x15363),f21(f21(f5(x15361),x15364),x15363)),f21(f21(f5(x15361),f11(x15361,x15362,x15364)),x15363))
% 15.40/15.54 [1578]~P46(x15781)+E(f11(x15781,x15782,f21(f21(f5(x15781),x15783),f21(f16(x15781,x15784),x15783))),f21(f16(x15781,f19(x15781,x15782,x15784)),x15783))
% 15.40/15.54 [1359]~P4(x13591)+E(f9(f65(x13591),x13592,f21(f21(f5(f65(x13591)),x13593),x13594)),f9(f65(x13591),f9(f65(x13591),x13592,x13593),x13594))
% 15.40/15.54 [1374]~P1(x13741)+E(f21(f21(f27(x13741),f21(f21(f27(x13741),x13742),x13743)),x13744),f21(f21(f27(x13741),x13742),f21(f21(f5(a58),x13743),x13744)))
% 15.40/15.54 [1375]~P19(x13751)+E(f21(f21(f27(x13751),f21(f21(f27(x13751),x13752),x13753)),x13754),f21(f21(f27(x13751),x13752),f21(f21(f5(a58),x13753),x13754)))
% 15.40/15.54 [1383]~P1(x13831)+E(f21(f21(f5(x13831),f21(f21(f5(x13831),x13832),x13833)),x13834),f21(f21(f5(x13831),x13832),f21(f21(f5(x13831),x13833),x13834)))
% 15.40/15.54 [1384]~P13(x13841)+E(f21(f21(f5(x13841),f21(f21(f5(x13841),x13842),x13843)),x13844),f21(f21(f5(x13841),x13842),f21(f21(f5(x13841),x13843),x13844)))
% 15.40/15.54 [1516]~P1(x15161)+E(f21(f21(f5(x15161),f21(f21(f5(x15161),x15162),x15163)),x15164),f21(f21(f5(x15161),f21(f21(f5(x15161),x15162),x15164)),x15163))
% 15.40/15.54 [1610]~P1(x16101)+E(f21(f21(f5(x16101),f21(f21(f27(x16101),x16102),x16103)),f21(f21(f27(x16101),x16104),x16103)),f21(f21(f27(x16101),f21(f21(f5(x16101),x16102),x16104)),x16103))
% 15.40/15.54 [1611]~P12(x16111)+E(f21(f21(f5(x16111),f21(f21(f27(x16111),x16112),x16113)),f21(f21(f27(x16111),x16114),x16113)),f21(f21(f27(x16111),f21(f21(f5(x16111),x16112),x16114)),x16113))
% 15.40/15.54 [1652]~P46(x16521)+E(f11(f65(x16521),f21(f21(f5(f65(x16521)),x16522),x16523),f21(f21(f5(f65(x16521)),x16524),x16523)),f21(f21(f5(f65(x16521)),f11(f65(x16521),x16522,x16524)),x16523))
% 15.40/15.54 [1556]~P1(x15561)+E(f21(f16(x15561,f21(f21(f27(f65(x15561)),x15562),x15563)),x15564),f21(f21(f27(x15561),f21(f16(x15561,x15562),x15564)),x15563))
% 15.40/15.54 [1628]~P46(x16281)+E(f21(f21(f5(x16281),f21(f16(x16281,x16282),x16283)),f21(f16(x16281,x16284),x16283)),f21(f16(x16281,f21(f21(f5(f65(x16281)),x16282),x16284)),x16283))
% 15.40/15.54 [1787]~P32(x17871)+E(f21(f16(x17871,f21(f21(f5(f65(x17871)),f18(x17871,f6(x17871),x17872)),x17873)),x17874),f21(f21(f5(x17871),f21(f21(f27(x17871),x17874),x17872)),f21(f16(x17871,x17873),x17874)))
% 15.40/15.54 [1548]~P1(x15481)+E(f11(x15481,f11(x15481,x15482,x15483),f11(x15481,x15484,x15485)),f11(x15481,f11(x15481,x15482,x15484),f11(x15481,x15483,x15485)))
% 15.40/15.54 [1549]~P3(x15491)+E(f11(x15491,f7(x15491,x15492,x15493),f7(x15491,x15494,x15495)),f7(x15491,f11(x15491,x15492,x15494),f11(x15491,x15493,x15495)))
% 15.40/15.54 [1642]~P46(x16421)+E(f21(f21(f5(f65(x16421)),f18(x16421,x16422,x16423)),f18(x16421,x16424,x16425)),f18(x16421,f21(f21(f5(x16421),x16422),x16424),f11(a58,x16423,x16425)))
% 15.40/15.54 [1130]~P23(x11302)+E(f21(f7(f66(x11301,x11302),x11303,x11304),x11305),f7(x11302,f21(x11303,x11305),f21(x11304,x11305)))
% 15.40/15.54 [1557]~P15(x15571)+E(f19(x15571,f11(x15571,x15572,x15573),f11(f65(x15571),x15574,x15575)),f11(f65(x15571),f19(x15571,x15572,x15574),f19(x15571,x15573,x15575)))
% 15.40/15.54 [1558]~P3(x15581)+E(f19(x15581,f7(x15581,x15582,x15583),f7(f65(x15581),x15584,x15585)),f7(f65(x15581),f19(x15581,x15582,x15584),f19(x15581,x15583,x15585)))
% 15.40/15.54 [1669]~P1(x16691)+E(f21(f21(f5(x16691),f21(f21(f5(x16691),x16692),x16693)),f21(f21(f5(x16691),x16694),x16695)),f21(f21(f5(x16691),f21(f21(f5(x16691),x16692),x16694)),f21(f21(f5(x16691),x16693),x16695)))
% 15.40/15.54 [1753]~P49(x17531)+E(f11(x17531,f21(f21(f5(x17531),x17532),f7(x17531,x17533,x17534)),f21(f21(f5(x17531),f7(x17531,x17532,x17535)),x17534)),f7(x17531,f21(f21(f5(x17531),x17532),x17533),f21(f21(f5(x17531),x17535),x17534)))
% 15.40/15.54 [1843]~P33(x18431)+E(f11(x18431,f11(x18431,f21(f21(f5(x18431),f7(x18431,x18432,x18433)),f7(x18431,x18434,x18435)),f21(f21(f5(x18431),f7(x18431,x18432,x18433)),x18435)),f21(f21(f5(x18431),x18433),f7(x18431,x18434,x18435))),f7(x18431,f21(f21(f5(x18431),x18432),x18434),f21(f21(f5(x18431),x18433),x18435)))
% 15.40/15.54 [1732]~P71(x17321)+E(f11(x17321,f21(f21(f5(x17321),x17322),x17323),f11(x17321,f21(f21(f5(x17321),x17324),x17323),x17325)),f11(x17321,f21(f21(f5(x17321),f11(x17321,x17322,x17324)),x17323),x17325))
% 15.40/15.54 [1796]~P7(a58,x17961,x17964)+E(f7(a58,f11(a58,f21(f21(f5(a58),x17961),x17962),x17963),f11(a58,f21(f21(f5(a58),x17964),x17962),x17965)),f7(a58,x17963,f11(a58,f21(f21(f5(a58),f7(a58,x17964,x17961)),x17962),x17965)))
% 15.40/15.54 [1797]~P7(a58,x17974,x17971)+E(f7(a58,f11(a58,f21(f21(f5(a58),x17971),x17972),x17973),f11(a58,f21(f21(f5(a58),x17974),x17972),x17975)),f7(a58,f11(a58,f21(f21(f5(a58),f7(a58,x17971,x17974)),x17972),x17973),x17975))
% 15.40/15.54 [1856]~P2(x18565)+E(f21(f21(f21(x18561,x18562),x18563),f15(x18564,f28(x18563,f3(f65(x18565))),x18566,f26(x18564,x18565,x18566,x18561,x18563))),f26(x18564,x18565,x18566,x18561,f19(x18565,x18562,x18563)))
% 15.40/15.54 [1653]E(x16531,f3(a58))+E(x16531,f11(a58,f3(a58),f6(a58)))+~P8(a58,x16531,f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58)))
% 15.40/15.54 [773]E(x7731,x7732)+P8(a58,x7732,x7731)+P8(a58,x7731,x7732)
% 15.40/15.54 [774]E(x7741,x7742)+P8(a59,x7742,x7741)+P8(a59,x7741,x7742)
% 15.40/15.54 [842]E(x8421,x8422)+P8(a58,x8421,x8422)+~P7(a58,x8421,x8422)
% 15.40/15.54 [843]E(x8431,x8432)+P8(a59,x8431,x8432)+~P7(a59,x8431,x8432)
% 15.40/15.54 [895]E(x8951,x8952)+~P7(a58,x8952,x8951)+~P7(a58,x8951,x8952)
% 15.40/15.54 [896]E(x8961,x8962)+~P7(a59,x8962,x8961)+~P7(a59,x8961,x8962)
% 15.40/15.54 [574]~P20(x5741)+~E(x5742,f3(x5741))+E(f4(x5741,x5742),x5742)
% 15.40/15.54 [579]~P21(x5791)+~E(f3(x5791),x5792)+E(f4(x5791,x5792),f3(x5791))
% 15.40/15.54 [580]~P21(x5801)+~E(x5802,f3(x5801))+E(f4(x5801,x5802),f3(x5801))
% 15.40/15.54 [581]~P57(x5811)+~E(x5812,f3(x5811))+E(f12(x5811,x5812),f3(x5811))
% 15.40/15.54 [582]~P43(x5821)+~E(x5822,f3(x5821))+E(f12(x5821,x5822),f3(x5821))
% 15.40/15.54 [583]~P31(x5831)+~E(x5832,f3(x5831))+E(f12(x5831,x5832),f3(x5831))
% 15.40/15.54 [586]~P20(x5862)+~E(f4(x5862,x5861),x5861)+E(x5861,f3(x5862))
% 15.40/15.54 [593]~P21(x5932)+~E(f4(x5932,x5931),f3(x5932))+E(x5931,f3(x5932))
% 15.40/15.54 [594]~P57(x5942)+~E(f12(x5942,x5941),f3(x5942))+E(x5941,f3(x5942))
% 15.40/15.54 [595]~P43(x5952)+~E(f12(x5952,x5951),f3(x5952))+E(x5951,f3(x5952))
% 15.40/15.54 [596]~P21(x5961)+~E(f4(x5961,x5962),f3(x5961))+E(f3(x5961),x5962)
% 15.40/15.54 [647]~E(x6472,f3(a58))+~E(x6471,f3(a58))+E(f11(a58,x6471,x6472),f3(a58))
% 15.40/15.54 [665]~P5(x6652)+E(f9(x6652,x6651,x6651),f6(x6652))+E(x6651,f3(x6652))
% 15.40/15.54 [680]~P20(x6801)+~E(x6802,f3(x6801))+E(f11(x6801,x6802,x6802),f3(x6801))
% 15.40/15.54 [735]~P57(x7351)+P8(x7351,f3(x7351),x7352)+~E(f12(x7351,x7352),f6(x7351))
% 15.40/15.54 [760]~P20(x7602)+~E(f11(x7602,x7601,x7601),f3(x7602))+E(x7601,f3(x7602))
% 15.40/15.54 [808]~P57(x8081)+~P8(x8081,f3(x8081),x8082)+E(f12(x8081,x8082),f6(x8081))
% 15.40/15.54 [905]E(x9051,x9052)+~E(f7(a58,x9052,x9051),f3(a58))+~E(f7(a58,x9051,x9052),f3(a58))
% 15.40/15.54 [936]~P20(x9361)+~P7(x9361,x9362,f3(x9361))+P7(x9361,x9362,f4(x9361,x9362))
% 15.40/15.54 [937]~P57(x9371)+~P8(x9371,x9372,f3(x9371))+P8(x9371,x9372,f4(x9371,x9372))
% 15.40/15.54 [938]~P20(x9381)+~P7(x9381,f3(x9381),x9382)+P7(x9381,f4(x9381,x9382),x9382)
% 15.40/15.54 [939]~P20(x9391)+~P8(x9391,f3(x9391),x9392)+P8(x9391,f4(x9391,x9392),x9392)
% 15.40/15.54 [946]~P25(x9461)+~P7(x9461,x9462,f3(x9461))+P7(x9461,f3(x9461),f4(x9461,x9462))
% 15.40/15.54 [947]~P25(x9471)+~P8(x9471,x9472,f3(x9471))+P8(x9471,f3(x9471),f4(x9471,x9472))
% 15.40/15.54 [948]~P57(x9481)+~P8(x9481,f3(x9481),x9482)+P8(x9481,f3(x9481),f12(x9481,x9482))
% 15.40/15.54 [949]~P57(x9491)+~P8(x9491,x9492,f3(x9491))+P8(x9491,f12(x9491,x9492),f3(x9491))
% 15.40/15.54 [950]~P25(x9501)+~P7(x9501,f3(x9501),x9502)+P7(x9501,f4(x9501,x9502),f3(x9501))
% 15.40/15.54 [951]~P25(x9511)+~P8(x9511,f3(x9511),x9512)+P8(x9511,f4(x9511,x9512),f3(x9511))
% 15.40/15.54 [954]~P20(x9541)+~P7(x9541,x9542,f4(x9541,x9542))+P7(x9541,x9542,f3(x9541))
% 15.40/15.54 [955]~P57(x9551)+~P8(x9551,x9552,f4(x9551,x9552))+P8(x9551,x9552,f3(x9551))
% 15.40/15.54 [956]~P20(x9561)+~P7(x9561,f4(x9561,x9562),x9562)+P7(x9561,f3(x9561),x9562)
% 15.40/15.54 [957]~P20(x9571)+~P8(x9571,f4(x9571,x9572),x9572)+P8(x9571,f3(x9571),x9572)
% 15.40/15.54 [976]~P25(x9761)+~P7(x9761,f3(x9761),f4(x9761,x9762))+P7(x9761,x9762,f3(x9761))
% 15.40/15.54 [977]~P25(x9771)+~P8(x9771,f3(x9771),f4(x9771,x9772))+P8(x9771,x9772,f3(x9771))
% 15.40/15.54 [978]~P57(x9781)+~P8(x9781,f12(x9781,x9782),f3(x9781))+P8(x9781,x9782,f3(x9781))
% 15.40/15.54 [979]~P57(x9791)+~P8(x9791,f3(x9791),f12(x9791,x9792))+P8(x9791,f3(x9791),x9792)
% 15.40/15.54 [980]~P25(x9801)+~P7(x9801,f4(x9801,x9802),f3(x9801))+P7(x9801,f3(x9801),x9802)
% 15.40/15.54 [981]~P25(x9811)+~P8(x9811,f4(x9811,x9812),f3(x9811))+P8(x9811,f3(x9811),x9812)
% 15.40/15.54 [1022]~P8(a59,x10222,x10221)+~P7(a59,x10221,f3(a59))+E(f9(a59,x10221,x10222),f3(a59))
% 15.40/15.54 [1025]~P8(a59,x10251,x10252)+~P7(a59,f3(a59),x10251)+E(f9(a59,x10251,x10252),f3(a59))
% 15.40/15.54 [1103]~P7(a59,f3(a59),x11032)+~P7(a59,f3(a59),x11031)+P7(a59,f3(a59),f14(x11031,x11032))
% 15.40/15.54 [1116]~P20(x11161)+~P7(x11161,f3(x11161),x11162)+P7(x11161,f3(x11161),f11(x11161,x11162,x11162))
% 15.40/15.54 [1117]~P20(x11171)+~P8(x11171,f3(x11171),x11172)+P8(x11171,f3(x11171),f11(x11171,x11172,x11172))
% 15.40/15.54 [1118]~P20(x11181)+~P7(x11181,x11182,f3(x11181))+P7(x11181,f11(x11181,x11182,x11182),f3(x11181))
% 15.40/15.54 [1119]~P20(x11191)+~P8(x11191,x11192,f3(x11191))+P8(x11191,f11(x11191,x11192,x11192),f3(x11191))
% 15.40/15.54 [1120]~P57(x11201)+~P8(x11201,x11202,f3(x11201))+P8(x11201,f11(x11201,x11202,x11202),f3(x11201))
% 15.40/15.54 [1233]~P20(x12331)+~P7(x12331,f11(x12331,x12332,x12332),f3(x12331))+P7(x12331,x12332,f3(x12331))
% 15.40/15.54 [1234]~P20(x12341)+~P8(x12341,f11(x12341,x12342,x12342),f3(x12341))+P8(x12341,x12342,f3(x12341))
% 15.40/15.54 [1235]~P57(x12351)+~P8(x12351,f11(x12351,x12352,x12352),f3(x12351))+P8(x12351,x12352,f3(x12351))
% 15.40/15.54 [1236]~P20(x12361)+~P7(x12361,f3(x12361),f11(x12361,x12362,x12362))+P7(x12361,f3(x12361),x12362)
% 15.40/15.54 [1237]~P20(x12371)+~P8(x12371,f3(x12371),f11(x12371,x12372,x12372))+P8(x12371,f3(x12371),x12372)
% 15.40/15.54 [1240]~P7(a59,x12402,x12401)+~P8(a59,f3(a59),x12402)+P8(a59,f3(a59),f9(a59,x12401,x12402))
% 15.40/15.54 [1242]P8(a58,f7(a58,x12421,x12422),x12421)+~P8(a58,f3(a58),x12421)+~P8(a58,f3(a58),x12422)
% 15.40/15.54 [1243]P8(a58,f9(a58,x12431,x12432),x12431)+~P8(a58,f3(a58),x12431)+~P8(a58,f6(a58),x12432)
% 15.40/15.54 [1244]P8(a59,f9(a59,x12441,x12442),x12441)+~P8(a59,f3(a59),x12441)+~P8(a59,f6(a59),x12442)
% 15.40/15.54 [1249]~P7(a59,x12491,f3(a59))+~P8(a59,x12492,f3(a59))+P7(a59,f3(a59),f9(a59,x12491,x12492))
% 15.40/15.54 [1250]~P7(a59,f3(a59),x12502)+~P7(a59,f3(a59),x12501)+P7(a59,f3(a59),f11(a59,x12501,x12502))
% 15.40/15.54 [1251]~P7(a59,f3(a59),x12512)+~P7(a59,f3(a59),x12511)+P7(a59,f3(a59),f9(a59,x12511,x12512))
% 15.40/15.54 [1252]~P7(a59,f3(a59),x12521)+~P8(a59,f3(a59),x12522)+P7(a59,f3(a59),f9(a59,x12521,x12522))
% 15.40/15.54 [1253]~P7(a59,x12531,f3(a59))+~P8(a59,f3(a59),x12532)+P7(a59,f9(a59,x12531,x12532),f3(a59))
% 15.40/15.54 [1254]~P8(a59,x12542,f3(a59))+~P7(a59,f3(a59),x12541)+P7(a59,f9(a59,x12541,x12542),f3(a59))
% 15.40/15.54 [1255]~P8(a59,x12552,f3(a59))+~P8(a59,f3(a59),x12551)+P8(a59,f9(a59,x12551,x12552),f3(a59))
% 15.40/15.54 [1257]~P8(a59,x12571,f3(a59))+~P8(a59,f3(a59),x12572)+P8(a59,f9(a59,x12571,x12572),f3(a59))
% 15.40/15.54 [1312]P8(a58,f3(a58),x13121)+P8(a58,f3(a58),x13122)+~P8(a58,f3(a58),f11(a58,x13122,x13121))
% 15.40/15.54 [1347]P7(a59,x13471,x13472)+~P8(a59,f3(a59),x13471)+~P8(a59,f3(a59),f9(a59,x13472,x13471))
% 15.40/15.54 [1348]P7(a59,x13481,x13482)+~P7(a59,f3(a59),x13482)+~P8(a59,f3(a59),f9(a59,x13482,x13481))
% 15.40/15.54 [1349]P7(a59,x13491,f3(a59))+~P8(a59,x13492,f3(a59))+~P7(a59,f3(a59),f9(a59,x13491,x13492))
% 15.40/15.54 [1350]P8(a59,x13501,f3(a59))+~P8(a59,f3(a59),x13502)+~P8(a59,f9(a59,x13501,x13502),f3(a59))
% 15.40/15.54 [1351]P8(a59,f3(a59),x13511)+~P8(a59,x13512,f3(a59))+~P8(a59,f9(a59,x13511,x13512),f3(a59))
% 15.40/15.54 [1352]P7(a59,f3(a59),x13521)+~P8(a59,f3(a59),x13522)+~P7(a59,f3(a59),f9(a59,x13521,x13522))
% 15.40/15.54 [1353]P8(a59,f3(a59),x13531)+~P7(a59,f3(a59),x13532)+~P8(a59,f3(a59),f9(a59,x13532,x13531))
% 15.40/15.54 [598]~P2(x5981)+E(f10(x5981,x5982),f3(a58))+~E(x5982,f3(f65(x5981)))
% 15.40/15.54 [601]~P2(x6012)+~E(f10(x6012,x6011),f3(a58))+E(x6011,f3(f65(x6012)))
% 15.40/15.54 [616]~P57(x6161)+~E(x6162,f3(f65(x6161)))+E(f12(f65(x6161),x6162),f3(f65(x6161)))
% 15.40/15.54 [732]~P2(x7321)+~E(x7322,f3(f65(x7321)))+E(f21(f13(x7321,x7322),f2(x7321,x7322)),f3(x7321))
% 15.40/15.54 [783]~P2(x7832)+E(x7831,f3(f65(x7832)))+E(f11(a58,f2(x7832,x7831),f6(a58)),f10(x7832,x7831))
% 15.40/15.54 [809]~P57(x8091)+P8(x8091,x8092,f3(x8091))+~E(f12(x8091,x8092),f4(x8091,f6(x8091)))
% 15.40/15.54 [819]~P2(x8192)+~E(f21(f13(x8192,x8191),f2(x8192,x8191)),f3(x8192))+E(x8191,f3(f65(x8192)))
% 15.40/15.54 [831]~P57(x8311)+~P8(x8311,x8312,f3(x8311))+E(f12(x8311,x8312),f4(x8311,f6(x8311)))
% 15.40/15.54 [882]P8(a58,f31(x8822,x8821),x8822)+~P73(f21(x8821,x8822))+P73(f21(x8821,f3(a58)))
% 15.40/15.54 [934]E(x9341,f3(a58))+E(x9342,f3(a58))+~E(f11(a58,x9342,x9341),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [935]E(x9351,f3(a58))+E(x9352,f3(a58))+~E(f11(a58,f3(a58),f6(a58)),f11(a58,x9352,x9351))
% 15.40/15.54 [984]~E(x9842,f3(a58))+~E(x9841,f11(a58,f3(a58),f6(a58)))+E(f11(a58,x9841,x9842),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [985]~E(x9851,f3(a58))+~E(x9852,f11(a58,f3(a58),f6(a58)))+E(f11(a58,x9851,x9852),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [986]~E(x9862,f3(a58))+~E(x9861,f11(a58,f3(a58),f6(a58)))+E(f11(a58,f3(a58),f6(a58)),f11(a58,x9861,x9862))
% 15.40/15.54 [987]~E(x9871,f3(a58))+~E(x9872,f11(a58,f3(a58),f6(a58)))+E(f11(a58,f3(a58),f6(a58)),f11(a58,x9871,x9872))
% 15.40/15.54 [1006]~P57(x10061)+~P9(x10061,x10062)+P8(x10061,f3(x10061),f21(f13(x10061,x10062),f2(x10061,x10062)))
% 15.40/15.54 [1050]E(x10501,f3(a58))+E(x10501,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,x10502,x10501),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1051]E(x10511,f3(a58))+E(x10511,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,x10511,x10512),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1052]E(x10521,f3(a58))+E(x10521,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,f3(a58),f6(a58)),f11(a58,x10522,x10521))
% 15.40/15.54 [1053]E(x10531,f3(a58))+E(x10531,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,f3(a58),f6(a58)),f11(a58,x10531,x10532))
% 15.40/15.54 [1150]E(x11501,f11(a58,f3(a58),f6(a58)))+E(x11502,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,x11501,x11502),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1151]E(x11511,f11(a58,f3(a58),f6(a58)))+E(x11512,f11(a58,f3(a58),f6(a58)))+~E(f11(a58,f3(a58),f6(a58)),f11(a58,x11511,x11512))
% 15.40/15.54 [1172]~P8(a58,x11721,x11722)+P8(a58,f11(a58,x11721,f6(a58)),x11722)+E(f11(a58,x11721,f6(a58)),x11722)
% 15.40/15.54 [1188]E(x11881,x11882)+P8(a58,x11881,x11882)+~P8(a58,x11881,f11(a58,x11882,f6(a58)))
% 15.40/15.54 [1189]E(x11891,x11892)+P8(a59,x11891,x11892)+~P8(a59,x11891,f11(a59,x11892,f6(a59)))
% 15.40/15.54 [1209]~P57(x12091)+P9(x12091,x12092)+~P8(x12091,f3(x12091),f21(f13(x12091,x12092),f2(x12091,x12092)))
% 15.40/15.54 [1259]P8(a58,f51(x12592,x12591),x12592)+E(x12591,f3(a58))+~P8(a58,x12591,f11(a58,x12592,f6(a58)))
% 15.40/15.54 [1264]E(x12641,x12642)+~P7(a58,x12642,x12641)+~P8(a58,x12641,f11(a58,x12642,f6(a58)))
% 15.40/15.54 [1265]E(x12651,f3(a58))+~P8(a58,x12651,f11(a58,x12652,f6(a58)))+E(f11(a58,f51(x12652,x12651),f6(a58)),x12651)
% 15.40/15.54 [1322]P7(a58,x13221,x13222)+~P7(a58,x13221,f11(a58,x13222,f6(a58)))+E(x13221,f11(a58,x13222,f6(a58)))
% 15.40/15.54 [1560]P8(a58,x15601,x15602)+~P8(a58,f3(a58),x15602)+E(f11(a58,f9(a58,f7(a58,x15601,x15602),x15602),f6(a58)),f9(a58,x15601,x15602))
% 15.40/15.54 [1598]~P7(a58,x15982,x15981)+~P8(a58,f3(a58),x15982)+E(f11(a58,f9(a58,f7(a58,x15981,x15982),x15982),f6(a58)),f9(a58,x15981,x15982))
% 15.40/15.54 [629]~E(x6292,f6(a58))+~E(x6291,f6(a58))+E(f21(f21(f5(a58),x6291),x6292),f6(a58))
% 15.40/15.54 [672]~P48(x6721)+~E(x6722,f6(x6721))+E(f21(f21(f5(x6721),x6722),x6722),f6(x6721))
% 15.40/15.54 [694]E(x6941,f6(a58))+E(x6942,f3(a58))+~E(f21(f21(f5(a58),x6942),x6941),x6942)
% 15.40/15.54 [695]E(x6951,f3(a58))+E(x6952,f3(a58))+~E(f21(f21(f5(a58),x6952),x6951),f3(a58))
% 15.40/15.54 [743]~P48(x7431)+~E(x7432,f4(x7431,f6(x7431)))+E(f21(f21(f5(x7431),x7432),x7432),f6(x7431))
% 15.40/15.54 [891]E(x8911,f6(a59))+~P8(a59,f3(a59),x8912)+~E(f21(f21(f5(a59),x8912),x8911),f6(a59))
% 15.40/15.54 [892]E(x8921,f6(a59))+~P8(a59,f3(a59),x8921)+~E(f21(f21(f5(a59),x8921),x8922),f6(a59))
% 15.40/15.54 [953]~P35(x9531)+~P70(x9531)+E(f21(f21(f27(x9531),f3(x9531)),f11(a58,x9532,f6(a58))),f3(x9531))
% 15.40/15.54 [1004]~P1(x10042)+E(x10041,f3(x10042))+~P73(f21(f21(f22(x10042),f3(x10042)),x10041))
% 15.40/15.54 [1026]E(x10261,f3(a58))+E(x10262,f11(a58,f3(a58),f6(a58)))+~E(f21(f21(f27(a58),x10262),x10261),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1139]E(x11391,f3(a58))+P8(a58,f3(a58),x11392)+~P8(a58,f3(a58),f21(f21(f27(a58),x11392),x11391))
% 15.40/15.54 [1140]P7(a58,x11401,x11402)+~P8(a58,f3(a58),x11402)+~P73(f21(f21(f22(a58),x11401),x11402))
% 15.40/15.54 [1141]P7(a59,x11411,x11412)+~P8(a59,f3(a59),x11412)+~P73(f21(f21(f22(a59),x11411),x11412))
% 15.40/15.54 [1144]P8(a58,f3(a58),x11441)+~P8(a58,f3(a58),x11442)+~P73(f21(f21(f22(a58),x11441),x11442))
% 15.40/15.54 [1145]~E(x11452,f11(a58,f3(a58),f6(a58)))+~E(x11451,f11(a58,f3(a58),f6(a58)))+E(f21(f21(f5(a58),x11451),x11452),f11(a58,f3(a58),f6(a58)))
% 15.40/15.54 [1160]E(x11601,x11602)+~P73(f21(f21(f22(a58),x11602),x11601))+~P73(f21(f21(f22(a58),x11601),x11602))
% 15.40/15.54 [1207]~P8(a58,x12071,x12072)+~P8(a58,f3(a58),x12071)+~P73(f21(f21(f22(a58),x12072),x12071))
% 15.40/15.54 [1208]~P8(a59,x12081,x12082)+~P8(a59,f3(a59),x12081)+~P73(f21(f21(f22(a59),x12082),x12081))
% 15.40/15.54 [1214]~P7(a59,f3(a59),x12142)+~P7(a59,f3(a59),x12141)+P7(a59,f3(a59),f21(f21(f5(a59),x12141),x12142))
% 15.40/15.54 [1215]~P8(a58,f3(a58),x12152)+~P8(a58,f3(a58),x12151)+P8(a58,f3(a58),f21(f21(f5(a58),x12151),x12152))
% 15.40/15.54 [1417]~P73(f21(x14171,x14172))+P73(f21(x14171,f3(a58)))+P73(f21(x14171,f11(a58,f31(x14172,x14171),f6(a58))))
% 15.40/15.54 [1645]~P8(a58,f11(a58,f3(a58),f6(a58)),x16452)+~P8(a58,f11(a58,f3(a58),f6(a58)),x16451)+P8(a58,x16451,f21(f21(f5(a58),x16452),x16451))
% 15.40/15.54 [1646]~P8(a58,f11(a58,f3(a58),f6(a58)),x16462)+~P8(a58,f11(a58,f3(a58),f6(a58)),x16461)+P8(a58,x16461,f21(f21(f5(a58),x16461),x16462))
% 15.40/15.54 [1690]~P7(a58,f11(a58,f3(a58),f6(a58)),x16902)+~P7(a58,f11(a58,f3(a58),f6(a58)),x16901)+P7(a58,f11(a58,f3(a58),f6(a58)),f21(f21(f5(a58),x16901),x16902))
% 15.40/15.54 [1691]~P8(a58,f11(a58,f3(a58),f6(a58)),x16911)+~P8(a58,f11(a58,f3(a58),f6(a58)),x16912)+P8(a58,f11(a58,f3(a58),f6(a58)),f21(f21(f5(a58),x16911),x16912))
% 15.40/15.54 [725]~P1(x7252)+E(x7251,f3(a58))+E(f21(f13(x7252,f6(f65(x7252))),x7251),f3(x7252))
% 15.40/15.54 [728]~P1(x7281)+~E(x7282,f3(a58))+E(f21(f13(x7281,f6(f65(x7281))),x7282),f6(x7281))
% 15.40/15.54 [1659]~P8(a58,f3(a58),x16592)+~P8(a59,f3(a59),x16591)+E(f9(a59,f21(f21(f27(a59),x16591),x16592),x16591),f21(f21(f27(a59),x16591),f7(a58,x16592,f11(a58,f3(a58),f6(a58)))))
% 15.40/15.54 [1552]~E(x15522,f6(a58))+~P8(a58,f3(a58),x15521)+P73(f21(f21(f22(a58),f21(f21(f5(a58),x15521),x15522)),x15521))
% 15.40/15.54 [1553]~E(x15531,f6(a58))+~P8(a58,f3(a58),x15532)+P73(f21(f21(f22(a58),f21(f21(f5(a58),x15531),x15532)),x15532))
% 15.40/15.54 [1694]E(x16941,f6(a58))+~P8(a58,f3(a58),x16942)+~P73(f21(f21(f22(a58),f21(f21(f5(a58),x16942),x16941)),x16942))
% 15.40/15.54 [1695]E(x16951,f6(a58))+~P8(a58,f3(a58),x16952)+~P73(f21(f21(f22(a58),f21(f21(f5(a58),x16951),x16952)),x16952))
% 15.40/15.54 [638]~E(x6382,x6383)+~P36(x6381)+P7(x6381,x6382,x6383)
% 15.40/15.54 [640]~E(x6402,x6403)+~P41(x6401)+P7(x6401,x6402,x6403)
% 15.40/15.54 [741]~P8(x7413,x7411,x7412)+~E(x7411,x7412)+~P37(x7413)
% 15.40/15.54 [742]~P8(x7423,x7421,x7422)+~E(x7421,x7422)+~P41(x7423)
% 15.40/15.54 [790]P7(x7901,x7903,x7902)+~P37(x7901)+P7(x7901,x7902,x7903)
% 15.40/15.54 [795]P8(x7951,x7953,x7952)+~P37(x7951)+P7(x7951,x7952,x7953)
% 15.40/15.54 [853]~P36(x8531)+~P8(x8531,x8532,x8533)+P7(x8531,x8532,x8533)
% 15.40/15.54 [855]~P41(x8551)+~P8(x8551,x8552,x8553)+P7(x8551,x8552,x8553)
% 15.40/15.54 [909]~P8(x9091,x9093,x9092)+~P36(x9091)+~P7(x9091,x9092,x9093)
% 15.40/15.54 [913]~P8(x9131,x9133,x9132)+~P36(x9131)+~P8(x9131,x9132,x9133)
% 15.40/15.54 [916]~P8(x9161,x9163,x9162)+~P37(x9161)+~P7(x9161,x9162,x9163)
% 15.40/15.54 [917]~P8(x9171,x9173,x9172)+~P37(x9171)+~P8(x9171,x9172,x9173)
% 15.40/15.54 [918]~P8(x9181,x9183,x9182)+~P41(x9181)+~P8(x9181,x9182,x9183)
% 15.40/15.54 [1007]~P7(a58,x10071,x10073)+P7(a58,x10071,x10072)+~P7(a58,x10073,x10072)
% 15.40/15.54 [1008]~P7(a59,x10081,x10083)+P7(a59,x10081,x10082)+~P7(a59,x10083,x10082)
% 15.40/15.54 [603]~P21(x6032)+~E(x6033,f4(x6032,x6031))+E(x6031,f4(x6032,x6033))
% 15.40/15.54 [605]~P21(x6051)+~E(f4(x6051,x6053),x6052)+E(f4(x6051,x6052),x6053)
% 15.40/15.54 [609]~P21(x6093)+E(x6091,x6092)+~E(f4(x6093,x6091),f4(x6093,x6092))
% 15.40/15.54 [610]~P38(x6103)+E(x6101,x6102)+~E(f4(x6103,x6101),f4(x6103,x6102))
% 15.40/15.54 [611]~P2(x6113)+E(x6111,x6112)+~E(f13(x6113,x6111),f13(x6113,x6112))
% 15.40/15.54 [657]~E(x6572,x6573)+~P3(x6571)+E(f7(x6571,x6572,x6573),f3(x6571))
% 15.40/15.54 [658]~E(x6582,x6583)+~P21(x6581)+E(f7(x6581,x6582,x6583),f3(x6581))
% 15.40/15.54 [666]~P72(x6661)+~E(x6663,f3(x6661))+E(f11(x6661,x6662,x6663),x6662)
% 15.40/15.54 [667]~E(x6672,x6673)+~P57(x6671)+P7(f65(x6671),x6672,x6673)
% 15.40/15.54 [713]~P21(x7131)+~E(x7133,f4(x7131,x7132))+E(f11(x7131,x7132,x7133),f3(x7131))
% 15.40/15.54 [714]~P21(x7141)+~E(x7142,f4(x7141,x7143))+E(f11(x7141,x7142,x7143),f3(x7141))
% 15.40/15.54 [755]~P72(x7552)+~E(f11(x7552,x7553,x7551),x7553)+E(x7551,f3(x7552))
% 15.40/15.54 [757]~P3(x7573)+E(x7571,x7572)+~E(f7(x7573,x7571,x7572),f3(x7573))
% 15.40/15.54 [758]~P21(x7583)+E(x7581,x7582)+~E(f7(x7583,x7581,x7582),f3(x7583))
% 15.40/15.54 [784]~P21(x7842)+~E(f11(x7842,x7843,x7841),f3(x7842))+E(x7841,f4(x7842,x7843))
% 15.40/15.54 [785]~P21(x7852)+~E(f11(x7852,x7851,x7853),f3(x7852))+E(x7851,f4(x7852,x7853))
% 15.40/15.54 [786]~P21(x7861)+~E(f11(x7861,x7862,x7863),f3(x7861))+E(f4(x7861,x7862),x7863)
% 15.40/15.54 [873]~P57(x8731)+~P9(x8731,x8733)+P9(x8731,f19(x8731,x8732,x8733))
% 15.40/15.54 [964]~P25(x9641)+~P7(x9641,x9643,x9642)+P7(x9641,f4(x9641,x9642),f4(x9641,x9643))
% 15.40/15.54 [966]~P38(x9661)+~P7(x9661,x9663,x9662)+P7(x9661,f4(x9661,x9662),f4(x9661,x9663))
% 15.40/15.54 [967]~P25(x9671)+~P8(x9671,x9673,x9672)+P8(x9671,f4(x9671,x9672),f4(x9671,x9673))
% 15.40/15.54 [991]~P25(x9911)+~P7(x9911,x9913,f4(x9911,x9912))+P7(x9911,x9912,f4(x9911,x9913))
% 15.40/15.54 [993]~P25(x9931)+~P8(x9931,x9933,f4(x9931,x9932))+P8(x9931,x9932,f4(x9931,x9933))
% 15.40/15.54 [995]~P25(x9951)+~P7(x9951,f4(x9951,x9953),x9952)+P7(x9951,f4(x9951,x9952),x9953)
% 15.40/15.54 [997]~P25(x9971)+~P8(x9971,f4(x9971,x9973),x9972)+P8(x9971,f4(x9971,x9972),x9973)
% 15.40/15.54 [1012]~P7(a58,x10123,x10121)+~E(f7(a58,x10121,x10123),x10122)+E(x10121,f11(a58,x10122,x10123))
% 15.40/15.54 [1013]~P7(a58,x10132,x10131)+~E(x10131,f11(a58,x10133,x10132))+E(f7(a58,x10131,x10132),x10133)
% 15.40/15.54 [1027]~P25(x10271)+P7(x10271,x10272,x10273)+~P7(x10271,f4(x10271,x10273),f4(x10271,x10272))
% 15.40/15.54 [1028]~P38(x10281)+P7(x10281,x10282,x10283)+~P7(x10281,f4(x10281,x10283),f4(x10281,x10282))
% 15.40/15.54 [1029]~P25(x10291)+P8(x10291,x10292,x10293)+~P8(x10291,f4(x10291,x10293),f4(x10291,x10292))
% 15.40/15.54 [1076]~P2(x10761)+P8(a58,x10763,f53(x10762,x10763,x10761))+P7(a58,f2(x10761,x10762),x10763)
% 15.40/15.54 [1104]~P25(x11041)+~P7(x11041,x11042,x11043)+P7(x11041,f7(x11041,x11042,x11043),f3(x11041))
% 15.40/15.54 [1105]~P25(x11051)+~P8(x11051,x11052,x11053)+P8(x11051,f7(x11051,x11052,x11053),f3(x11051))
% 15.40/15.54 [1142]~P2(x11423)+~P8(a58,x11421,f2(x11423,x11422))+P8(a58,x11421,f33(x11422,x11421,x11423))
% 15.40/15.54 [1217]~P25(x12171)+P7(x12171,x12172,x12173)+~P7(x12171,f7(x12171,x12172,x12173),f3(x12171))
% 15.40/15.54 [1218]~P25(x12181)+P8(x12181,x12182,x12183)+~P8(x12181,f7(x12181,x12182,x12183),f3(x12181))
% 15.40/15.54 [1405]~P8(a58,x14053,x14051)+~P8(a58,x14053,x14052)+P8(a58,f7(a58,x14051,x14052),f7(a58,x14051,x14053))
% 15.40/15.54 [1406]~P7(a58,x14062,x14061)+~P8(a58,x14061,x14063)+P8(a58,f7(a58,x14061,x14062),f7(a58,x14063,x14062))
% 15.40/15.54 [1410]~P7(a59,x14103,x14101)+P7(a59,f9(a59,x14101,x14102),f9(a59,x14103,x14102))+~P8(a59,x14102,f3(a59))
% 15.40/15.54 [1411]~P7(a58,x14113,x14112)+P7(a58,f9(a58,x14111,x14112),f9(a58,x14111,x14113))+~P8(a58,f3(a58),x14113)
% 15.40/15.54 [1412]~P7(a59,x14121,x14123)+P7(a59,f9(a59,x14121,x14122),f9(a59,x14123,x14122))+~P8(a59,f3(a59),x14122)
% 15.40/15.54 [1492]~P7(a58,x14923,x14922)+~P7(a58,f11(a58,x14921,x14923),x14922)+P7(a58,x14921,f7(a58,x14922,x14923))
% 15.40/15.54 [1493]~P7(a58,x14932,x14933)+~P7(a58,x14931,f7(a58,x14933,x14932))+P7(a58,f11(a58,x14931,x14932),x14933)
% 15.40/15.54 [656]~P51(x6561)+~E(x6562,f3(f65(x6561)))+E(f21(f16(x6561,x6562),x6563),f3(x6561))
% 15.40/15.54 [688]~P2(x6881)+~E(x6882,f3(x6881))+E(f18(x6881,x6882,x6883),f3(f65(x6881)))
% 15.40/15.54 [752]~P46(x7521)+~E(f2(x7521,x7522),f3(a58))+E(f25(x7521,x7522,x7523),f3(f65(x7521)))
% 15.40/15.54 [771]~P51(x7711)+E(f17(x7711,x7712,x7713),f3(a58))+E(f21(f16(x7711,x7713),x7712),f3(x7711))
% 15.40/15.54 [781]~P2(x7812)+E(x7811,f3(x7812))+~E(f18(x7812,x7811,x7813),f3(f65(x7812)))
% 15.40/15.54 [782]~P2(x7822)+E(x7821,f3(x7822))+~E(f19(x7822,x7821,x7823),f3(f65(x7822)))
% 15.40/15.54 [803]~P2(x8032)+~E(f19(x8032,x8033,x8031),f3(f65(x8032)))+E(x8031,f3(f65(x8032)))
% 15.40/15.54 [804]~P4(x8042)+~E(f24(x8042,x8043,x8041),f3(f65(x8042)))+E(x8041,f3(f65(x8042)))
% 15.40/15.54 [805]~P4(x8052)+~E(f24(x8052,x8051,x8053),f3(f65(x8052)))+E(x8051,f3(f65(x8052)))
% 15.40/15.54 [813]~P46(x8131)+E(f2(x8131,x8132),f3(a58))+~E(f25(x8131,x8132,x8133),f3(f65(x8131)))
% 15.40/15.54 [817]~P74(x8171,x8172,x8173)+~E(x8172,f3(a59))+P73(f21(x8171,f3(a59)))
% 15.40/15.54 [821]~P2(x8211)+P7(a58,x8213,f2(x8211,x8212))+E(f21(f13(x8211,x8212),x8213),f3(x8211))
% 15.40/15.54 [822]~P2(x8222)+E(x8221,f3(x8222))+E(f2(x8222,f18(x8222,x8221,x8223)),x8223)
% 15.40/15.54 [856]~P2(x8561)+~E(x8563,f3(f65(x8561)))+E(f2(x8561,f19(x8561,x8562,x8563)),f3(a58))
% 15.40/15.54 [904]~P2(x9041)+~P8(a58,f2(x9041,x9042),x9043)+E(f21(f13(x9041,x9042),x9043),f3(x9041))
% 15.40/15.54 [975]~P51(x9752)+P7(a58,f17(x9752,x9753,x9751),f2(x9752,x9751))+E(x9751,f3(f65(x9752)))
% 15.40/15.54 [1011]~P2(x10112)+E(x10111,f3(f65(x10112)))+E(f2(x10112,f19(x10112,x10113,x10111)),f11(a58,f2(x10112,x10111),f6(a58)))
% 15.40/15.54 [1048]~P57(x10481)+~P8(f65(x10481),x10483,x10482)+P9(x10481,f7(f65(x10481),x10482,x10483))
% 15.40/15.54 [1071]~P4(x10711)+~P8(a58,f2(x10711,x10712),f2(x10711,x10713))+E(f9(f65(x10711),x10712,x10713),f3(f65(x10711)))
% 15.40/15.54 [1125]~P57(x11251)+P7(f65(x11251),x11252,x11253)+~P9(x11251,f7(f65(x11251),x11253,x11252))
% 15.40/15.54 [1126]~P57(x11261)+P8(f65(x11261),x11262,x11263)+~P9(x11261,f7(f65(x11261),x11263,x11262))
% 15.40/15.54 [1170]~E(x11703,f3(a58))+P73(f21(x11701,f9(a58,x11702,x11703)))+~P73(f21(x11701,f3(a58)))
% 15.40/15.54 [1213]~P2(x12131)+P7(a58,f2(x12131,x12132),x12133)+~E(f21(f13(x12131,x12132),f53(x12132,x12133,x12131)),f3(x12131))
% 15.40/15.54 [1232]~P8(a58,x12321,x12323)+~P8(a58,x12323,x12322)+P8(a58,f11(a58,x12321,f6(a58)),x12322)
% 15.40/15.54 [1248]~P8(a58,x12483,x12482)+P8(a58,x12481,f11(a58,x12482,f6(a58)))+~E(x12481,f11(a58,x12483,f6(a58)))
% 15.40/15.54 [1262]~P5(x12622)+E(x12621,f3(x12622))+E(f9(x12622,f11(x12622,x12623,x12621),x12621),f11(x12622,f9(x12622,x12623,x12621),f6(x12622)))
% 15.40/15.54 [1263]~P5(x12632)+E(x12631,f3(x12632))+E(f9(x12632,f11(x12632,x12631,x12633),x12631),f11(x12632,f9(x12632,x12633,x12631),f6(x12632)))
% 15.40/15.54 [1324]~P2(x13241)+~P8(a58,x13243,f2(x13241,x13242))+~E(f21(f13(x13241,x13242),f33(x13242,x13243,x13241)),f3(x13241))
% 15.40/15.54 [1361]P8(a58,f43(x13611,x13612,x13613),x13611)+E(x13611,f3(a58))+P73(f21(x13613,f9(a58,x13612,x13611)))
% 15.40/15.54 [1381]~E(x13812,f3(a58))+~P73(f21(x13811,f9(a58,x13813,x13812)))+P73(f21(x13811,f3(a58)))
% 15.40/15.54 [1455]P8(a58,x14552,x14551)+E(f11(a58,x14551,f38(x14551,x14552,x14553)),x14552)+P73(f21(x14553,f7(a58,x14552,x14551)))
% 15.40/15.54 [1456]P8(a58,x14562,x14561)+E(f11(a58,x14561,f39(x14561,x14562,x14563)),x14562)+P73(f21(x14563,f7(a58,x14562,x14561)))
% 15.40/15.54 [1461]P8(a58,f43(x14611,x14612,x14613),x14611)+P73(f21(x14613,f9(a58,x14612,x14611)))+~P73(f21(x14613,f3(a58)))
% 15.40/15.54 [1462]E(f11(a58,x14621,f38(x14621,x14622,x14623)),x14622)+P73(f21(x14623,f7(a58,x14622,x14621)))+~P73(f21(x14623,f3(a58)))
% 15.40/15.54 [1463]E(f11(a58,x14631,f39(x14631,x14632,x14633)),x14632)+P73(f21(x14633,f7(a58,x14632,x14631)))+~P73(f21(x14633,f3(a58)))
% 15.40/15.54 [1471]~P2(x14713)+E(x14711,x14712)+~E(f21(f13(x14713,x14711),f54(x14712,x14711,x14713)),f21(f13(x14713,x14712),f54(x14712,x14711,x14713)))
% 15.40/15.54 [1473]~P7(a58,x14732,x14733)+~P7(a58,x14732,x14731)+E(f7(a58,f7(a58,x14731,x14732),f7(a58,x14733,x14732)),f7(a58,x14731,x14733))
% 15.40/15.54 [1498]~P8(a58,x14982,x14983)+~P73(f21(x14981,f7(a58,x14982,x14983)))+P73(f21(x14981,f3(a58)))
% 15.40/15.54 [1609]E(x16091,f3(a58))+P73(f21(x16092,f45(x16091,x16093,x16092)))+~P73(f21(x16092,f9(a58,x16093,x16091)))
% 15.40/15.54 [1612]E(x16121,f3(a58))+~P73(f21(x16122,f40(x16121,x16123,x16122)))+P73(f21(x16122,f9(a58,x16123,x16121)))
% 15.40/15.54 [1634]P73(f21(x16341,f45(x16342,x16343,x16341)))+~P73(f21(x16341,f9(a58,x16343,x16342)))+P73(f21(x16341,f3(a58)))
% 15.40/15.54 [1643]P8(a58,x16431,x16432)+~P73(f21(x16433,f38(x16432,x16431,x16433)))+P73(f21(x16433,f7(a58,x16431,x16432)))
% 15.40/15.54 [1644]P8(a58,x16441,x16442)+~P73(f21(x16443,f39(x16442,x16441,x16443)))+P73(f21(x16443,f7(a58,x16441,x16442)))
% 15.40/15.54 [1647]~P73(f21(x16471,f38(x16473,x16472,x16471)))+P73(f21(x16471,f7(a58,x16472,x16473)))+~P73(f21(x16471,f3(a58)))
% 15.40/15.54 [1648]~P73(f21(x16481,f39(x16483,x16482,x16481)))+P73(f21(x16481,f7(a58,x16482,x16483)))+~P73(f21(x16481,f3(a58)))
% 15.40/15.54 [1649]~P73(f21(x16491,f40(x16493,x16492,x16491)))+P73(f21(x16491,f9(a58,x16492,x16493)))+~P73(f21(x16491,f3(a58)))
% 15.40/15.54 [1661]E(x16611,f3(a58))+E(f11(a58,f21(f21(f5(a58),x16611),f40(x16611,x16612,x16613)),f43(x16611,x16612,x16613)),x16612)+P73(f21(x16613,f9(a58,x16612,x16611)))
% 15.40/15.54 [1670]E(x16701,f3(a58))+P7(a58,f21(f21(f5(a58),x16701),f45(x16701,x16702,x16703)),x16702)+~P73(f21(x16703,f9(a58,x16702,x16701)))
% 15.40/15.54 [1680]E(f11(a58,f21(f21(f5(a58),x16801),f40(x16801,x16802,x16803)),f43(x16801,x16802,x16803)),x16802)+P73(f21(x16803,f9(a58,x16802,x16801)))+~P73(f21(x16803,f3(a58)))
% 15.40/15.54 [1682]P7(a58,f21(f21(f5(a58),x16822),f45(x16822,x16823,x16821)),x16823)+~P73(f21(x16821,f9(a58,x16823,x16822)))+P73(f21(x16821,f3(a58)))
% 15.40/15.54 [1721]P8(a59,x17211,f46(x17212,x17213,x17211))+~P8(a59,x17211,f3(a59))+P73(f21(f21(x17213,f9(a59,x17212,x17211)),f8(a59,x17212,x17211)))
% 15.40/15.54 [1722]~P8(a59,x17223,f3(a59))+P7(a59,f46(x17221,x17222,x17223),f3(a59))+P73(f21(f21(x17222,f9(a59,x17221,x17223)),f8(a59,x17221,x17223)))
% 15.40/15.54 [1769]~P8(a59,x17691,f3(a59))+E(f11(a59,f21(f21(f5(a59),x17691),f48(x17692,x17693,x17691)),f46(x17692,x17693,x17691)),x17692)+P73(f21(f21(x17693,f9(a59,x17692,x17691)),f8(a59,x17692,x17691)))
% 15.40/15.54 [1800]~P8(a59,x18003,f3(a59))+~P73(f21(f21(x18001,f48(x18002,x18001,x18003)),f46(x18002,x18001,x18003)))+P73(f21(f21(x18001,f9(a59,x18002,x18003)),f8(a59,x18002,x18003)))
% 15.40/15.54 [659]~P35(x6591)+~E(x6593,f3(a58))+E(f21(f21(f27(x6591),x6592),x6593),f6(x6591))
% 15.40/15.54 [670]~P68(x6701)+~E(x6703,f3(x6701))+E(f21(f21(f5(x6701),x6702),x6703),f3(x6701))
% 15.40/15.54 [671]~P68(x6711)+~E(x6712,f3(x6711))+E(f21(f21(f5(x6711),x6712),x6713),f3(x6711))
% 15.40/15.54 [756]~P48(x7562)+E(x7561,f3(x7562))+~E(f21(f21(f27(x7562),x7561),x7563),f3(x7562))
% 15.40/15.54 [823]~P51(x8231)+~E(x8232,f4(x8231,x8233))+E(f21(f21(f5(x8231),x8232),x8232),f21(f21(f5(x8231),x8233),x8233))
% 15.40/15.54 [871]E(x8711,x8712)+E(x8713,f3(a58))+~E(f21(f21(f5(a58),x8713),x8711),f21(f21(f5(a58),x8713),x8712))
% 15.40/15.54 [872]E(x8721,x8722)+E(x8723,f3(a58))+~E(f21(f21(f5(a58),x8721),x8723),f21(f21(f5(a58),x8722),x8723))
% 15.40/15.54 [1047]E(x10471,x10472)+~P8(a58,f3(a58),x10473)+~E(f21(f21(f5(a58),x10473),x10471),f21(f21(f5(a58),x10473),x10472))
% 15.40/15.54 [1110]~P54(x11101)+~P7(x11101,f3(x11101),x11102)+P7(x11101,f3(x11101),f21(f21(f27(x11101),x11102),x11103))
% 15.40/15.54 [1111]~P54(x11111)+~P7(x11111,f6(x11111),x11112)+P7(x11111,f6(x11111),f21(f21(f27(x11111),x11112),x11113))
% 15.40/15.54 [1112]~P54(x11121)+~P8(x11121,f3(x11121),x11122)+P8(x11121,f3(x11121),f21(f21(f27(x11121),x11122),x11123))
% 15.40/15.54 [1192]~E(x11922,f9(a58,x11923,x11921))+~P8(a58,f3(a58),x11921)+P7(a58,f21(f21(f5(a58),x11921),x11922),x11923)
% 15.40/15.54 [1199]~P15(x11991)+~P8(a58,f2(x11991,x11993),f2(x11991,x11992))+E(f2(x11991,f11(f65(x11991),x11992,x11993)),f2(x11991,x11992))
% 15.40/15.54 [1200]~P15(x12001)+~P8(a58,f2(x12001,x12002),f2(x12001,x12003))+E(f2(x12001,f11(f65(x12001),x12002,x12003)),f2(x12001,x12003))
% 15.40/15.54 [1241]~P32(x12411)+P73(f21(f21(f22(x12411),x12412),f4(x12411,x12413)))+~P73(f21(f21(f22(x12411),x12412),x12413))
% 15.40/15.54 [1246]~P5(x12461)+E(f21(f21(f5(x12461),x12462),f9(x12461,x12463,x12462)),x12463)+~P73(f21(f21(f22(x12461),x12462),x12463))
% 15.40/15.54 [1311]~P32(x13111)+~P73(f21(f21(f22(x13111),x13112),f4(x13111,x13113)))+P73(f21(f21(f22(x13111),x13112),x13113))
% 15.40/15.54 [1328]~P6(x13281)+E(f9(x13281,x13282,f4(x13281,x13283)),f4(x13281,f9(x13281,x13282,x13283)))+~P73(f21(f21(f22(x13281),x13283),x13282))
% 15.40/15.54 [1329]~P6(x13291)+E(f9(x13291,f4(x13291,x13292),x13293),f4(x13291,f9(x13291,x13292,x13293)))+~P73(f21(f21(f22(x13291),x13293),x13292))
% 15.40/15.54 [1335]~P32(x13351)+~P73(f21(f21(f22(x13351),x13352),x13353))+P73(f21(f21(f22(x13351),f4(x13351,x13352)),x13353))
% 15.40/15.54 [1346]~P73(f21(f21(f22(a58),x13461),x13463))+P73(f21(f21(f22(a58),x13461),x13462))+~P73(f21(f21(f22(a58),x13463),x13462))
% 15.40/15.54 [1371]~P8(a58,x13711,x13713)+~P8(a58,f3(a58),x13712)+P8(a58,f21(f21(f5(a58),x13711),x13712),f21(f21(f5(a58),x13713),x13712))
% 15.40/15.54 [1372]~P8(a58,x13722,x13723)+~P8(a58,f3(a58),x13721)+P8(a58,f21(f21(f5(a58),x13721),x13722),f21(f21(f5(a58),x13721),x13723))
% 15.40/15.54 [1373]~P8(a59,x13732,x13733)+~P8(a59,f3(a59),x13731)+P8(a59,f21(f21(f5(a59),x13731),x13732),f21(f21(f5(a59),x13731),x13733))
% 15.40/15.54 [1419]~P5(x14191)+E(f21(f21(f5(x14191),f9(x14191,x14192,x14193)),x14193),x14192)+~P73(f21(f21(f22(x14191),x14193),x14192))
% 15.40/15.54 [1422]~P32(x14221)+~P73(f21(f21(f22(x14221),f4(x14221,x14222)),x14223))+P73(f21(f21(f22(x14221),x14222),x14223))
% 15.40/15.54 [1487]~P54(x14871)+~P8(x14871,f6(x14871),x14872)+P8(x14871,f6(x14871),f21(f21(f27(x14871),x14872),f11(a58,x14873,f6(a58))))
% 15.40/15.54 [1506]P7(a58,x15061,x15062)+~P8(a58,f3(a58),x15063)+~P7(a58,f21(f21(f5(a58),x15063),x15061),f21(f21(f5(a58),x15063),x15062))
% 15.40/15.54 [1507]P7(a58,x15071,x15072)+~P8(a58,f3(a58),x15073)+~P7(a58,f21(f21(f5(a58),x15071),x15073),f21(f21(f5(a58),x15072),x15073))
% 15.40/15.54 [1509]P8(a58,x15091,x15092)+~P8(a58,f3(a58),x15093)+~P8(a58,f21(f21(f27(a58),x15093),x15091),f21(f21(f27(a58),x15093),x15092))
% 15.40/15.54 [1514]~P4(x15142)+E(x15141,f3(f65(x15142)))+E(f21(f13(x15142,f24(x15142,x15143,x15141)),f2(x15142,f24(x15142,x15143,x15141))),f6(x15142))
% 15.40/15.54 [1515]~P4(x15152)+E(x15151,f3(f65(x15152)))+E(f21(f13(x15152,f24(x15152,x15151,x15153)),f2(x15152,f24(x15152,x15151,x15153))),f6(x15152))
% 15.40/15.54 [1539]~E(x15393,f9(a58,x15391,x15392))+~P8(a58,f3(a58),x15392)+P8(a58,x15391,f21(f21(f5(a58),x15392),f11(a58,x15393,f6(a58))))
% 15.40/15.54 [1601]P73(f21(f21(f22(a58),x16011),f7(a58,x16012,x16013)))+~P73(f21(f21(f22(a58),x16011),x16012))+~P73(f21(f21(f22(a58),x16011),x16013))
% 15.40/15.54 [1663]~P73(f21(f21(f22(a59),x16631),f7(a59,x16632,x16633)))+~P73(f21(f21(f22(a59),x16631),x16633))+P73(f21(f21(f22(a59),x16631),x16632))
% 15.40/15.54 [1698]~P51(x16981)+~E(x16982,f4(x16981,x16983))+E(f21(f21(f27(x16981),x16982),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58))),f21(f21(f27(x16981),x16983),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58))))
% 15.40/15.54 [1754]E(x17541,f3(a58))+P8(a58,x17542,f21(f21(f5(a58),x17541),f11(a58,f45(x17541,x17542,x17543),f6(a58))))+~P73(f21(x17543,f9(a58,x17542,x17541)))
% 15.40/15.54 [1759]P8(a58,x17592,f21(f21(f5(a58),x17593),f11(a58,f45(x17593,x17592,x17591),f6(a58))))+~P73(f21(x17591,f9(a58,x17592,x17593)))+P73(f21(x17591,f3(a58)))
% 15.40/15.54 [898]~P5(x8982)+E(x8981,f3(x8982))+E(f9(x8982,f21(f21(f5(x8982),x8983),x8981),x8981),x8983)
% 15.40/15.54 [899]~P5(x8992)+E(x8991,f3(x8992))+E(f9(x8992,f21(f21(f5(x8992),x8991),x8993),x8991),x8993)
% 15.40/15.54 [1222]~P1(x12221)+~E(x12222,f6(x12221))+P73(f21(f21(f22(x12221),x12222),f21(f21(f27(x12221),x12222),x12223)))
% 15.40/15.54 [1377]~P1(x13771)+~P8(a58,f3(a58),x13773)+P73(f21(f21(f22(x13771),x13772),f21(f21(f27(x13771),x13772),x13773)))
% 15.40/15.54 [1401]~P55(x14012)+E(x14011,f3(x14012))+~E(f11(x14012,f21(f21(f5(x14012),x14013),x14013),f21(f21(f5(x14012),x14011),x14011)),f3(x14012))
% 15.40/15.54 [1402]~P55(x14022)+E(x14021,f3(x14022))+~E(f11(x14022,f21(f21(f5(x14022),x14021),x14021),f21(f21(f5(x14022),x14023),x14023)),f3(x14022))
% 15.40/15.54 [1416]~P35(x14162)+E(x14161,f3(a58))+E(f21(f21(f5(x14162),x14163),f21(f21(f27(x14162),x14163),f7(a58,x14161,f6(a58)))),f21(f21(f27(x14162),x14163),x14161))
% 15.40/15.54 [1470]~P54(x14701)+~P8(x14701,f6(x14701),x14702)+P8(x14701,f6(x14701),f21(f21(f5(x14701),x14702),f21(f21(f27(x14701),x14702),x14703)))
% 15.40/15.54 [1576]~P54(x15761)+~P8(x15761,f6(x15761),x15762)+P8(x15761,f21(f21(f27(x15761),x15762),x15763),f21(f21(f5(x15761),x15762),f21(f21(f27(x15761),x15762),x15763)))
% 15.40/15.54 [1594]~P55(x15942)+E(x15941,f3(x15942))+P8(x15942,f3(x15942),f11(x15942,f21(f21(f5(x15942),x15943),x15943),f21(f21(f5(x15942),x15941),x15941)))
% 15.40/15.54 [1595]~P55(x15952)+E(x15951,f3(x15952))+P8(x15952,f3(x15952),f11(x15952,f21(f21(f5(x15952),x15951),x15951),f21(f21(f5(x15952),x15953),x15953)))
% 15.40/15.54 [1687]E(x16871,f3(a58))+~P73(f21(f21(f22(a58),x16872),x16873))+P73(f21(f21(f22(a58),f21(f21(f27(a58),x16872),x16871)),f21(f21(f27(a58),x16873),x16871)))
% 15.40/15.54 [1688]E(x16881,f3(a58))+~P73(f21(f21(f22(a59),x16882),x16883))+P73(f21(f21(f22(a59),f21(f21(f27(a59),x16882),x16881)),f21(f21(f27(a59),x16883),x16881)))
% 15.40/15.54 [1689]E(x16891,f3(a59))+~P73(f21(f21(f22(a59),x16892),x16893))+P73(f21(f21(f22(a59),f21(f21(f5(a59),x16891),x16892)),f21(f21(f5(a59),x16891),x16893)))
% 15.40/15.54 [1714]~P55(x17142)+E(x17141,f3(x17142))+~P7(x17142,f11(x17142,f21(f21(f5(x17142),x17143),x17143),f21(f21(f5(x17142),x17141),x17141)),f3(x17142))
% 15.40/15.54 [1715]~P55(x17152)+E(x17151,f3(x17152))+~P7(x17152,f11(x17152,f21(f21(f5(x17152),x17151),x17151),f21(f21(f5(x17152),x17153),x17153)),f3(x17152))
% 15.40/15.54 [1743]E(x17431,f3(a58))+P73(f21(f21(f22(a58),x17432),x17433))+~P73(f21(f21(f22(a58),f21(f21(f27(a58),x17432),x17431)),f21(f21(f27(a58),x17433),x17431)))
% 15.40/15.54 [1745]E(x17451,f3(a58))+P73(f21(f21(f22(a59),x17452),x17453))+~P73(f21(f21(f22(a59),f21(f21(f27(a59),x17452),x17451)),f21(f21(f27(a59),x17453),x17451)))
% 15.40/15.54 [1746]E(x17461,f3(a58))+P73(f21(f21(f22(a58),x17462),x17463))+~P73(f21(f21(f22(a58),f21(f21(f5(a58),x17461),x17462)),f21(f21(f5(a58),x17461),x17463)))
% 15.40/15.54 [1748]E(x17481,f3(a59))+P73(f21(f21(f22(a59),x17482),x17483))+~P73(f21(f21(f22(a59),f21(f21(f5(a59),x17481),x17482)),f21(f21(f5(a59),x17481),x17483)))
% 15.40/15.54 [1751]P7(a58,x17511,x17512)+~P8(a58,f6(a58),x17513)+~P73(f21(f21(f22(a58),f21(f21(f27(a58),x17513),x17511)),f21(f21(f27(a58),x17513),x17512)))
% 15.40/15.54 [1756]~P8(a58,f3(a58),x17563)+P73(f21(f21(f22(a58),x17561),x17562))+~P73(f21(f21(f22(a58),f21(f21(f5(a58),x17563),x17561)),f21(f21(f5(a58),x17563),x17562)))
% 15.40/15.54 [1703]~P19(x17031)+~P8(a58,f3(a58),x17033)+E(f21(f21(f5(x17031),f21(f21(f27(x17031),x17032),f7(a58,x17033,f6(a58)))),x17032),f21(f21(f27(x17031),x17032),x17033))
% 15.40/15.54 [1860]~P51(x18602)+E(x18601,f3(f65(x18602)))+~P73(f21(f21(f22(f65(x18602)),f21(f21(f27(f65(x18602)),f19(x18602,f4(x18602,x18603),f19(x18602,f6(x18602),f3(f65(x18602))))),f11(a58,f17(x18602,x18603,x18601),f6(a58)))),x18601))
% 15.40/15.54 [1804]~P51(x18041)+~E(f21(f16(x18041,x18043),f4(x18041,x18042)),f3(x18041))+P73(f21(f21(f22(f65(x18041)),f19(x18041,x18042,f19(x18041,f6(x18041),f3(f65(x18041))))),x18043))
% 15.40/15.54 [1810]~P51(x18101)+~E(f21(f16(x18101,x18103),x18102),f3(x18101))+P73(f21(f21(f22(f65(x18101)),f19(x18101,f4(x18101,x18102),f19(x18101,f6(x18101),f3(f65(x18101))))),x18103))
% 15.40/15.54 [1839]~P51(x18391)+E(f21(f16(x18391,x18392),f4(x18391,x18393)),f3(x18391))+~P73(f21(f21(f22(f65(x18391)),f19(x18391,x18393,f19(x18391,f6(x18391),f3(f65(x18391))))),x18392))
% 15.40/15.54 [1842]~P51(x18421)+E(f21(f16(x18421,x18422),x18423),f3(x18421))+~P73(f21(f21(f22(f65(x18421)),f19(x18421,f4(x18421,x18423),f19(x18421,f6(x18421),f3(f65(x18421))))),x18422))
% 15.40/15.54 [920]~P16(x9203)+E(x9201,x9202)+~E(f11(x9203,x9204,x9201),f11(x9203,x9204,x9202))
% 15.40/15.54 [921]~P17(x9213)+E(x9211,x9212)+~E(f11(x9213,x9214,x9211),f11(x9213,x9214,x9212))
% 15.40/15.54 [922]~P2(x9223)+E(x9221,x9222)+~E(f18(x9223,x9221,x9224),f18(x9223,x9222,x9224))
% 15.40/15.54 [924]~P16(x9243)+E(x9241,x9242)+~E(f11(x9243,x9241,x9244),f11(x9243,x9242,x9244))
% 15.40/15.54 [998]~P40(x9982)+~P8(f66(x9981,x9982),x9983,x9984)+P7(f66(x9981,x9982),x9983,x9984)
% 15.40/15.54 [1106]~P40(x11061)+~P8(f66(x11062,x11061),x11064,x11063)+~P7(f66(x11062,x11061),x11063,x11064)
% 15.40/15.54 [1171]~P8(a58,x11713,x11714)+P8(a58,x11711,x11712)+~E(f11(a58,x11713,x11712),f11(a58,x11711,x11714))
% 15.40/15.54 [1284]~P27(x12841)+~P7(x12841,x12843,x12844)+P7(x12841,f11(x12841,x12842,x12843),f11(x12841,x12842,x12844))
% 15.40/15.54 [1285]~P28(x12851)+~P7(x12851,x12853,x12854)+P7(x12851,f11(x12851,x12852,x12853),f11(x12851,x12852,x12854))
% 15.40/15.54 [1286]~P27(x12861)+~P7(x12861,x12862,x12864)+P7(x12861,f11(x12861,x12862,x12863),f11(x12861,x12864,x12863))
% 15.40/15.54 [1287]~P28(x12871)+~P7(x12871,x12872,x12874)+P7(x12871,f11(x12871,x12872,x12873),f11(x12871,x12874,x12873))
% 15.40/15.54 [1288]~P27(x12881)+~P8(x12881,x12883,x12884)+P8(x12881,f11(x12881,x12882,x12883),f11(x12881,x12882,x12884))
% 15.40/15.54 [1289]~P29(x12891)+~P8(x12891,x12893,x12894)+P8(x12891,f11(x12891,x12892,x12893),f11(x12891,x12892,x12894))
% 15.40/15.54 [1290]~P27(x12901)+~P8(x12901,x12902,x12904)+P8(x12901,f11(x12901,x12902,x12903),f11(x12901,x12904,x12903))
% 15.40/15.54 [1291]~P29(x12911)+~P8(x12911,x12912,x12914)+P8(x12911,f11(x12911,x12912,x12913),f11(x12911,x12914,x12913))
% 15.40/15.54 [1403]~P7(a58,x14032,x14034)+~P7(a58,x14031,x14033)+P7(a58,f11(a58,x14031,x14032),f11(a58,x14033,x14034))
% 15.40/15.54 [1404]~P8(a58,x14042,x14044)+~P8(a58,x14041,x14043)+P8(a58,f11(a58,x14041,x14042),f11(a58,x14043,x14044))
% 15.40/15.54 [1407]~P7(a59,x14072,x14074)+~P8(a59,x14071,x14073)+P8(a59,f11(a59,x14071,x14072),f11(a59,x14073,x14074))
% 15.40/15.54 [1479]~P27(x14791)+P7(x14791,x14792,x14793)+~P7(x14791,f11(x14791,x14794,x14792),f11(x14791,x14794,x14793))
% 15.40/15.54 [1481]~P27(x14811)+P7(x14811,x14812,x14813)+~P7(x14811,f11(x14811,x14812,x14814),f11(x14811,x14813,x14814))
% 15.40/15.54 [1483]~P27(x14831)+P8(x14831,x14832,x14833)+~P8(x14831,f11(x14831,x14834,x14832),f11(x14831,x14834,x14833))
% 15.40/15.54 [1485]~P27(x14851)+P8(x14851,x14852,x14853)+~P8(x14851,f11(x14851,x14852,x14854),f11(x14851,x14853,x14854))
% 15.40/15.54 [1495]~E(x14953,f11(a58,x14954,x14952))+P73(f21(x14951,x14952))+~P73(f21(x14951,f7(a58,x14953,x14954)))
% 15.40/15.54 [1799]E(x17991,x17992)+~P4(x17993)+~P11(x17993,x17992,f3(f65(x17993)),x17994,x17991)
% 15.40/15.54 [1801]~P4(x18012)+~P11(x18012,x18013,f3(f65(x18012)),x18011,x18014)+E(x18011,f3(f65(x18012)))
% 15.40/15.54 [1802]~P4(x18022)+~P11(x18022,f3(f65(x18022)),x18023,x18024,x18021)+E(x18021,f3(f65(x18022)))
% 15.40/15.54 [1803]~P4(x18032)+~P11(x18032,f3(f65(x18032)),x18033,x18031,x18034)+E(x18031,f3(f65(x18032)))
% 15.40/15.54 [1844]~P40(x18442)+P7(f66(x18441,x18442),x18443,x18444)+~P7(x18442,f21(x18443,f55(x18444,x18443,x18441,x18442)),f21(x18444,f55(x18444,x18443,x18441,x18442)))
% 15.40/15.54 [959]~P50(x9591)+~E(x9593,f21(f21(f5(x9591),x9592),x9594))+P73(f21(f21(f22(x9591),x9592),x9593))
% 15.40/15.54 [1109]~E(x11093,x11094)+~P2(x11091)+E(f21(f13(x11091,f18(x11091,x11092,x11093)),x11094),x11092)
% 15.40/15.54 [1113]~P2(x11133)+E(x11131,x11132)+E(f21(f13(x11133,f18(x11133,x11134,x11131)),x11132),f3(x11133))
% 15.40/15.54 [1360]~P7(a58,x13602,x13604)+~P7(a58,x13601,x13603)+P7(a58,f21(f21(f5(a58),x13601),x13602),f21(f21(f5(a58),x13603),x13604))
% 15.40/15.54 [1129]~P5(x11291)+~E(x11292,f3(x11291))+E(f9(x11291,f21(f21(f5(x11291),x11292),x11293),f21(f21(f5(x11291),x11292),x11294)),f3(x11291))
% 15.40/15.54 [1219]~P5(x12192)+E(x12191,f3(x12192))+E(f9(x12192,f21(f21(f5(x12192),x12193),x12191),f21(f21(f5(x12192),x12194),x12191)),f9(x12192,x12193,x12194))
% 15.40/15.54 [1221]~P5(x12212)+E(x12211,f3(x12212))+E(f9(x12212,f21(f21(f5(x12212),x12211),x12213),f21(f21(f5(x12212),x12211),x12214)),f9(x12212,x12213,x12214))
% 15.40/15.54 [1488]~P1(x14881)+~P73(f21(f21(f22(x14881),x14882),x14884))+P73(f21(f21(f22(x14881),x14882),f21(f21(f5(x14881),x14883),x14884)))
% 15.40/15.54 [1489]~P1(x14891)+~P73(f21(f21(f22(x14891),x14892),x14893))+P73(f21(f21(f22(x14891),x14892),f21(f21(f5(x14891),x14893),x14894)))
% 15.40/15.54 [1496]~P5(x14961)+E(f9(x14961,f21(f21(f5(x14961),x14962),x14963),x14964),f21(f21(f5(x14961),x14962),f9(x14961,x14963,x14964)))+~P73(f21(f21(f22(x14961),x14964),x14963))
% 15.40/15.54 [1600]~P5(x16001)+E(f9(x16001,f21(f21(f5(x16001),x16002),x16003),x16004),f21(f21(f5(x16001),f9(x16001,x16002,x16004)),x16003))+~P73(f21(f21(f22(x16001),x16004),x16002))
% 15.40/15.54 [1658]~P5(x16581)+E(f9(x16581,f21(f21(f27(x16581),x16582),x16583),f21(f21(f27(x16581),x16584),x16583)),f21(f21(f27(x16581),f9(x16581,x16582,x16584)),x16583))+~P73(f21(f21(f22(x16581),x16584),x16582))
% 15.40/15.54 [1671]~P51(x16711)+~E(x16713,f3(x16711))+P73(f21(f21(f22(x16711),f21(f21(f5(x16711),x16712),x16713)),f21(f21(f5(x16711),x16714),x16713)))
% 15.40/15.54 [1672]~P51(x16721)+~E(x16722,f3(x16721))+P73(f21(f21(f22(x16721),f21(f21(f5(x16721),x16722),x16723)),f21(f21(f5(x16721),x16722),x16724)))
% 15.40/15.54 [1678]~P4(x16781)+~P73(f21(f21(f22(f65(x16781)),x16782),f24(x16781,x16784,x16783)))+P73(f21(f21(f22(f65(x16781)),x16782),x16783))
% 15.40/15.54 [1679]~P4(x16791)+~P73(f21(f21(f22(f65(x16791)),x16792),f24(x16791,x16793,x16794)))+P73(f21(f21(f22(f65(x16791)),x16792),x16793))
% 15.40/15.54 [1697]~P1(x16971)+~P7(a58,x16973,x16974)+P73(f21(f21(f22(x16971),f21(f21(f27(x16971),x16972),x16973)),f21(f21(f27(x16971),x16972),x16974)))
% 15.40/15.54 [1708]~P51(x17081)+~P73(f21(f21(f22(x17081),x17083),x17084))+P73(f21(f21(f22(x17081),f21(f21(f5(x17081),x17082),x17083)),f21(f21(f5(x17081),x17082),x17084)))
% 15.40/15.54 [1709]~P51(x17091)+~P73(f21(f21(f22(x17091),x17092),x17094))+P73(f21(f21(f22(x17091),f21(f21(f5(x17091),x17092),x17093)),f21(f21(f5(x17091),x17094),x17093)))
% 15.40/15.54 [1710]~P1(x17101)+~P73(f21(f21(f22(x17101),x17102),x17104))+P73(f21(f21(f22(x17101),f21(f21(f27(x17101),x17102),x17103)),f21(f21(f27(x17101),x17104),x17103)))
% 15.40/15.54 [1750]~P19(x17501)+~P7(a58,x17504,x17503)+E(f21(f21(f5(x17501),f21(f21(f27(x17501),x17502),f7(a58,x17503,x17504))),x17502),f21(f21(f27(x17501),x17502),f7(a58,f11(a58,x17503,f6(a58)),x17504)))
% 15.40/15.54 [1781]~P2(x17812)+E(f26(x17811,x17812,x17813,x17814,f3(f65(x17812))),x17813)+~E(f21(f21(f21(x17814,f3(x17812)),f3(f65(x17812))),x17813),x17813)
% 15.40/15.54 [1541]~P5(x15412)+E(x15411,f3(x15412))+E(f9(x15412,f11(x15412,x15413,f21(f21(f5(x15412),x15414),x15411)),x15411),f11(x15412,x15414,f9(x15412,x15413,x15411)))
% 15.40/15.54 [1542]~P5(x15422)+E(x15421,f3(x15422))+E(f9(x15422,f11(x15422,x15423,f21(f21(f5(x15422),x15421),x15424)),x15421),f11(x15422,x15424,f9(x15422,x15423,x15421)))
% 15.40/15.54 [1716]~P1(x17161)+P73(f21(f21(f22(x17161),x17162),x17163))+~P73(f21(f21(f22(x17161),f21(f21(f5(x17161),x17164),x17162)),x17163))
% 15.40/15.54 [1717]~P1(x17171)+P73(f21(f21(f22(x17171),x17172),x17173))+~P73(f21(f21(f22(x17171),f21(f21(f5(x17171),x17172),x17174)),x17173))
% 15.40/15.54 [925]~P2(x9253)+E(x9251,x9252)+~E(f19(x9253,x9254,x9251),f19(x9253,x9255,x9252))
% 15.40/15.54 [926]~P2(x9263)+E(x9261,x9262)+~E(f19(x9263,x9261,x9264),f19(x9263,x9262,x9265))
% 15.40/15.54 [1065]~P40(x10651)+P7(x10651,f21(x10652,x10653),f21(x10654,x10653))+~P7(f66(x10655,x10651),x10652,x10654)
% 15.40/15.54 [1805]~P4(x18051)+~P11(x18051,x18052,x18053,x18054,x18055)+E(f9(f65(x18051),x18052,x18053),x18054)
% 15.40/15.54 [1525]~E(x15252,x15254)+~P72(x15251)+E(f11(x15251,f21(f21(f5(x15251),x15252),x15253),f21(f21(f5(x15251),x15254),x15255)),f11(x15251,f21(f21(f5(x15251),x15252),x15255),f21(f21(f5(x15251),x15254),x15253)))
% 15.40/15.54 [1740]~P7(a58,x17403,x17402)+E(x17401,f11(a58,f21(f21(f5(a58),f7(a58,x17402,x17403)),x17404),x17405))+~E(f11(a58,f21(f21(f5(a58),x17403),x17404),x17401),f11(a58,f21(f21(f5(a58),x17402),x17404),x17405))
% 15.40/15.54 [1741]~P7(a58,x17412,x17411)+E(f11(a58,f21(f21(f5(a58),f7(a58,x17411,x17412)),x17413),x17414),x17415)+~E(f11(a58,f21(f21(f5(a58),x17411),x17413),x17414),f11(a58,f21(f21(f5(a58),x17412),x17413),x17415))
% 15.40/15.54 [1763]~P7(a58,x17634,x17631)+~E(x17635,f11(a58,f21(f21(f5(a58),f7(a58,x17631,x17634)),x17632),x17633))+E(f11(a58,f21(f21(f5(a58),x17631),x17632),x17633),f11(a58,f21(f21(f5(a58),x17634),x17632),x17635))
% 15.40/15.54 [1764]~P7(a58,x17644,x17641)+~E(f11(a58,f21(f21(f5(a58),f7(a58,x17641,x17644)),x17642),x17643),x17645)+E(f11(a58,f21(f21(f5(a58),x17641),x17642),x17643),f11(a58,f21(f21(f5(a58),x17644),x17642),x17645))
% 15.40/15.54 [1811]~P7(a58,x18113,x18112)+P7(a58,x18111,f11(a58,f21(f21(f5(a58),f7(a58,x18112,x18113)),x18114),x18115))+~P7(a58,f11(a58,f21(f21(f5(a58),x18113),x18114),x18111),f11(a58,f21(f21(f5(a58),x18112),x18114),x18115))
% 15.40/15.54 [1812]~P7(a58,x18123,x18122)+P8(a58,x18121,f11(a58,f21(f21(f5(a58),f7(a58,x18122,x18123)),x18124),x18125))+~P8(a58,f11(a58,f21(f21(f5(a58),x18123),x18124),x18121),f11(a58,f21(f21(f5(a58),x18122),x18124),x18125))
% 15.40/15.54 [1813]~P7(a58,x18132,x18131)+P7(a58,f11(a58,f21(f21(f5(a58),f7(a58,x18131,x18132)),x18133),x18134),x18135)+~P7(a58,f11(a58,f21(f21(f5(a58),x18131),x18133),x18134),f11(a58,f21(f21(f5(a58),x18132),x18133),x18135))
% 15.40/15.54 [1814]~P7(a58,x18142,x18141)+P8(a58,f11(a58,f21(f21(f5(a58),f7(a58,x18141,x18142)),x18143),x18144),x18145)+~P8(a58,f11(a58,f21(f21(f5(a58),x18141),x18143),x18144),f11(a58,f21(f21(f5(a58),x18142),x18143),x18145))
% 15.40/15.54 [1821]~P7(a58,x18211,x18214)+~P7(a58,x18213,f11(a58,f21(f21(f5(a58),f7(a58,x18214,x18211)),x18212),x18215))+P7(a58,f11(a58,f21(f21(f5(a58),x18211),x18212),x18213),f11(a58,f21(f21(f5(a58),x18214),x18212),x18215))
% 15.40/15.54 [1822]~P7(a58,x18221,x18224)+~P8(a58,x18223,f11(a58,f21(f21(f5(a58),f7(a58,x18224,x18221)),x18222),x18225))+P8(a58,f11(a58,f21(f21(f5(a58),x18221),x18222),x18223),f11(a58,f21(f21(f5(a58),x18224),x18222),x18225))
% 15.40/15.54 [1823]~P7(a58,x18234,x18231)+~P7(a58,f11(a58,f21(f21(f5(a58),f7(a58,x18231,x18234)),x18232),x18233),x18235)+P7(a58,f11(a58,f21(f21(f5(a58),x18231),x18232),x18233),f11(a58,f21(f21(f5(a58),x18234),x18232),x18235))
% 15.40/15.54 [1824]~P7(a58,x18244,x18241)+~P8(a58,f11(a58,f21(f21(f5(a58),f7(a58,x18241,x18244)),x18242),x18243),x18245)+P8(a58,f11(a58,f21(f21(f5(a58),x18241),x18242),x18243),f11(a58,f21(f21(f5(a58),x18244),x18242),x18245))
% 15.40/15.54 [1809]~P4(x18092)+~P11(x18092,x18091,x18094,x18093,x18095)+E(x18091,f11(f65(x18092),f21(f21(f5(f65(x18092)),x18093),x18094),x18095))
% 15.40/15.54 [1808]~P73(f21(f21(f22(a59),x18081),f11(a59,x18082,x18085)))+~P73(f21(f21(f22(a59),x18081),x18084))+P73(f21(f21(f22(a59),x18081),f11(a59,f11(a59,x18082,f21(f21(f5(a59),x18083),x18084)),x18085)))
% 15.40/15.54 [1830]P73(f21(f21(f22(a59),x18301),f11(a59,x18302,x18303)))+~P73(f21(f21(f22(a59),x18301),x18304))+~P73(f21(f21(f22(a59),x18301),f11(a59,f11(a59,x18302,f21(f21(f5(a59),x18305),x18304)),x18303)))
% 15.40/15.54 [1738]~P49(x17382)+~E(f11(x17382,f21(f21(f5(x17382),x17384),x17385),x17381),f11(x17382,f21(f21(f5(x17382),x17383),x17385),x17386))+E(x17381,f11(x17382,f21(f21(f5(x17382),f7(x17382,x17383,x17384)),x17385),x17386))
% 15.40/15.54 [1739]~P49(x17391)+~E(f11(x17391,f21(f21(f5(x17391),x17392),x17394),x17395),f11(x17391,f21(f21(f5(x17391),x17393),x17394),x17396))+E(f11(x17391,f21(f21(f5(x17391),f7(x17391,x17392,x17393)),x17394),x17395),x17396)
% 15.40/15.54 [1760]~P49(x17601)+~E(x17606,f11(x17601,f21(f21(f5(x17601),f7(x17601,x17602,x17605)),x17603),x17604))+E(f11(x17601,f21(f21(f5(x17601),x17602),x17603),x17604),f11(x17601,f21(f21(f5(x17601),x17605),x17603),x17606))
% 15.40/15.54 [1761]~P49(x17611)+~E(f11(x17611,f21(f21(f5(x17611),f7(x17611,x17612,x17615)),x17613),x17614),x17616)+E(f11(x17611,f21(f21(f5(x17611),x17612),x17613),x17614),f11(x17611,f21(f21(f5(x17611),x17615),x17613),x17616))
% 15.40/15.54 [1817]~P64(x18171)+~P7(x18171,f11(x18171,f21(f21(f5(x18171),x18174),x18175),x18172),f11(x18171,f21(f21(f5(x18171),x18173),x18175),x18176))+P7(x18171,x18172,f11(x18171,f21(f21(f5(x18171),f7(x18171,x18173,x18174)),x18175),x18176))
% 15.40/15.54 [1818]~P64(x18181)+~P8(x18181,f11(x18181,f21(f21(f5(x18181),x18184),x18185),x18182),f11(x18181,f21(f21(f5(x18181),x18183),x18185),x18186))+P8(x18181,x18182,f11(x18181,f21(f21(f5(x18181),f7(x18181,x18183,x18184)),x18185),x18186))
% 15.40/15.54 [1819]~P64(x18191)+~P7(x18191,f11(x18191,f21(f21(f5(x18191),x18192),x18194),x18195),f11(x18191,f21(f21(f5(x18191),x18193),x18194),x18196))+P7(x18191,f11(x18191,f21(f21(f5(x18191),f7(x18191,x18192,x18193)),x18194),x18195),x18196)
% 15.40/15.54 [1820]~P64(x18201)+~P8(x18201,f11(x18201,f21(f21(f5(x18201),x18202),x18204),x18205),f11(x18201,f21(f21(f5(x18201),x18203),x18204),x18206))+P8(x18201,f11(x18201,f21(f21(f5(x18201),f7(x18201,x18202,x18203)),x18204),x18205),x18206)
% 15.40/15.54 [1825]~P64(x18251)+~P7(x18251,x18254,f11(x18251,f21(f21(f5(x18251),f7(x18251,x18255,x18252)),x18253),x18256))+P7(x18251,f11(x18251,f21(f21(f5(x18251),x18252),x18253),x18254),f11(x18251,f21(f21(f5(x18251),x18255),x18253),x18256))
% 15.40/15.54 [1826]~P64(x18261)+~P8(x18261,x18264,f11(x18261,f21(f21(f5(x18261),f7(x18261,x18265,x18262)),x18263),x18266))+P8(x18261,f11(x18261,f21(f21(f5(x18261),x18262),x18263),x18264),f11(x18261,f21(f21(f5(x18261),x18265),x18263),x18266))
% 15.40/15.54 [1827]~P64(x18271)+~P7(x18271,f11(x18271,f21(f21(f5(x18271),f7(x18271,x18272,x18275)),x18273),x18274),x18276)+P7(x18271,f11(x18271,f21(f21(f5(x18271),x18272),x18273),x18274),f11(x18271,f21(f21(f5(x18271),x18275),x18273),x18276))
% 15.40/15.54 [1828]~P64(x18281)+~P8(x18281,f11(x18281,f21(f21(f5(x18281),f7(x18281,x18282,x18285)),x18283),x18284),x18286)+P8(x18281,f11(x18281,f21(f21(f5(x18281),x18282),x18283),x18284),f11(x18281,f21(f21(f5(x18281),x18285),x18283),x18286))
% 15.40/15.54 [1853]~P2(x18532)+E(f26(x18531,x18532,x18533,x18534,f19(x18532,x18535,x18536)),f21(f21(f21(x18534,x18535),x18536),f26(x18531,x18532,x18533,x18534,x18536)))+~E(f21(f21(f21(x18534,f3(x18532)),f3(f65(x18532))),x18533),x18533)
% 15.40/15.54 [815]~P31(x8152)+~P8(x8152,f3(x8152),x8151)+E(f12(x8152,x8151),f6(x8152))+E(x8151,f3(x8152))
% 15.40/15.54 [960]P8(a59,x9601,x9602)+P8(a59,x9602,x9601)+E(x9601,f3(a59))+~E(f9(a59,x9602,x9601),f3(a59))
% 15.40/15.54 [968]P8(a59,x9682,x9681)+E(x9681,f3(a59))+P7(a59,x9682,f3(a59))+~E(f9(a59,x9682,x9681),f3(a59))
% 15.40/15.54 [969]P8(a59,x9691,x9692)+E(x9691,f3(a59))+P7(a59,f3(a59),x9692)+~E(f9(a59,x9692,x9691),f3(a59))
% 15.40/15.54 [696]P9(x6962,x6961)+~P57(x6962)+P9(x6962,f4(f65(x6962),x6961))+E(x6961,f3(f65(x6962)))
% 15.40/15.54 [768]~P31(x7682)+P8(x7682,f3(x7682),x7681)+E(x7681,f3(x7682))+E(f12(x7682,x7681),f4(x7682,f6(x7682)))
% 15.40/15.54 [902]~P57(x9022)+~P8(f65(x9022),f3(f65(x9022)),x9021)+E(f12(f65(x9022),x9021),f6(f65(x9022)))+E(x9021,f3(f65(x9022)))
% 15.40/15.54 [697]~P35(x6972)+~P70(x6972)+E(x6971,f3(a58))+E(f21(f21(f27(x6972),f3(x6972)),x6971),f3(x6972))
% 15.40/15.54 [810]~P48(x8102)+E(x8101,f6(x8102))+E(x8101,f4(x8102,f6(x8102)))+~E(f21(f21(f5(x8102),x8101),x8101),f6(x8102))
% 15.40/15.54 [857]~E(x8572,f6(a59))+~E(x8571,f6(a59))+~P8(a59,f3(a59),x8571)+E(f21(f21(f5(a59),x8571),x8572),f6(a59))
% 15.40/15.54 [880]~P57(x8802)+P8(f65(x8802),f3(f65(x8802)),x8801)+E(x8801,f3(f65(x8802)))+E(f12(f65(x8802),x8801),f4(f65(x8802),f6(f65(x8802))))
% 15.40/15.54 [796]P8(x7963,x7961,x7962)+~P57(x7963)+E(x7961,x7962)+P8(x7963,x7962,x7961)
% 15.40/15.54 [802]P8(x8023,x8021,x8022)+~P37(x8023)+E(x8021,x8022)+P8(x8023,x8022,x8021)
% 15.40/15.54 [806]P8(x8061,x8062,x8063)+~E(x8062,x8063)+~P37(x8061)+P7(x8061,x8062,x8063)
% 15.40/15.54 [859]~P41(x8593)+~P7(x8593,x8592,x8591)+E(x8591,x8592)+P8(x8593,x8592,x8591)
% 15.40/15.54 [861]~P37(x8613)+~P7(x8613,x8611,x8612)+E(x8611,x8612)+P8(x8613,x8611,x8612)
% 15.40/15.54 [867]~P41(x8673)+~P7(x8673,x8671,x8672)+E(x8671,x8672)+P8(x8673,x8671,x8672)
% 15.40/15.54 [931]~P7(x9313,x9312,x9311)+~P7(x9313,x9311,x9312)+E(x9311,x9312)+~P41(x9313)
% 15.40/15.54 [973]P8(x9731,x9733,x9732)+~P36(x9731)+~P7(x9731,x9733,x9732)+P7(x9731,x9732,x9733)
% 15.40/15.54 [630]~P51(x6303)+~P34(x6303)+E(x6301,x6302)+~E(f16(x6303,x6301),f16(x6303,x6302))
% 15.40/15.54 [1121]~P57(x11211)+P9(x11211,x11212)+P8(x11211,f3(x11211),x11213)+~P9(x11211,f19(x11211,x11213,x11212))
% 15.40/15.54 [1123]P74(x11232,x11231,x11233)+P8(a59,f42(x11233,x11231,x11232),x11231)+E(x11231,f3(a59))+P8(a59,x11231,f3(a59))
% 15.40/15.54 [1124]P74(x11242,x11241,x11243)+P8(a59,x11241,f49(x11243,x11241,x11242))+E(x11241,f3(a59))+P8(a59,f3(a59),x11241)
% 15.40/15.54 [1127]P74(x11272,x11271,x11273)+E(x11271,f3(a59))+P8(a59,x11271,f3(a59))+P7(a59,f3(a59),f42(x11273,x11271,x11272))
% 15.40/15.54 [1128]P74(x11282,x11281,x11283)+E(x11281,f3(a59))+P8(a59,f3(a59),x11281)+P7(a59,f49(x11283,x11281,x11282),f3(a59))
% 15.40/15.54 [1247]E(x12471,x12472)+~P7(a58,x12473,x12472)+~P7(a58,x12473,x12471)+~E(f7(a58,x12471,x12473),f7(a58,x12472,x12473))
% 15.40/15.54 [1316]~P30(x13161)+~P8(x13161,f3(x13161),x13163)+~P8(x13161,f3(x13161),x13162)+P8(x13161,f3(x13161),f11(x13161,x13162,x13163))
% 15.40/15.54 [1317]~P30(x13171)+~P7(x13171,x13173,f3(x13171))+~P7(x13171,x13172,f3(x13171))+P7(x13171,f11(x13171,x13172,x13173),f3(x13171))
% 15.40/15.54 [1318]~P30(x13181)+~P7(x13181,x13183,f3(x13181))+~P8(x13181,x13182,f3(x13181))+P8(x13181,f11(x13181,x13182,x13183),f3(x13181))
% 15.40/15.54 [1319]~P30(x13191)+~P7(x13191,x13192,f3(x13191))+~P8(x13191,x13193,f3(x13191))+P8(x13191,f11(x13191,x13192,x13193),f3(x13191))
% 15.40/15.54 [1320]~P30(x13201)+~P8(x13201,x13203,f3(x13201))+~P8(x13201,x13202,f3(x13201))+P8(x13201,f11(x13201,x13202,x13203),f3(x13201))
% 15.40/15.54 [1331]P74(x13312,x13311,x13313)+P8(a59,x13311,f49(x13313,x13311,x13312))+P8(a59,f42(x13313,x13311,x13312),x13311)+E(x13311,f3(a59))
% 15.40/15.54 [1332]P74(x13322,x13321,x13323)+P8(a59,x13321,f49(x13323,x13321,x13322))+E(x13321,f3(a59))+P7(a59,f3(a59),f42(x13323,x13321,x13322))
% 15.40/15.54 [1333]P74(x13332,x13331,x13333)+P8(a59,f42(x13333,x13331,x13332),x13331)+E(x13331,f3(a59))+P7(a59,f49(x13333,x13331,x13332),f3(a59))
% 15.40/15.54 [1334]P74(x13342,x13341,x13343)+E(x13341,f3(a59))+P7(a59,f3(a59),f42(x13343,x13341,x13342))+P7(a59,f49(x13343,x13341,x13342),f3(a59))
% 15.40/15.54 [1519]~P7(a59,x15192,x15193)+P7(a59,f9(a59,x15191,x15192),f9(a59,x15191,x15193))+~P8(a59,x15191,f3(a59))+~P8(a59,f3(a59),x15192)
% 15.40/15.54 [1520]~P7(a59,x15203,x15202)+P7(a59,f9(a59,x15201,x15202),f9(a59,x15201,x15203))+~P7(a59,f3(a59),x15201)+~P8(a59,f3(a59),x15203)
% 15.40/15.54 [1623]~P7(a58,x16233,x16231)+P7(a58,x16231,x16232)+~P7(a58,x16233,x16232)+~P7(a58,f7(a58,x16231,x16233),f7(a58,x16232,x16233))
% 15.40/15.54 [1624]~P7(a58,x16243,x16241)+P8(a58,x16241,x16242)+~P7(a58,x16243,x16242)+~P8(a58,f7(a58,x16241,x16243),f7(a58,x16242,x16243))
% 15.40/15.54 [753]~P2(x7531)+~E(x7532,f3(x7531))+~E(x7533,f3(f65(x7531)))+E(f19(x7531,x7532,x7533),f3(f65(x7531)))
% 15.40/15.54 [769]~P4(x7691)+~E(x7693,f3(f65(x7691)))+~E(x7692,f3(f65(x7691)))+E(f24(x7691,x7692,x7693),f3(f65(x7691)))
% 15.40/15.54 [906]~P51(x9062)+~E(f17(x9062,x9063,x9061),f3(a58))+~E(f21(f16(x9062,x9061),x9063),f3(x9062))+E(x9061,f3(f65(x9062)))
% 15.40/15.54 [942]~P57(x9421)+~P9(x9421,x9423)+~P9(x9421,x9422)+P9(x9421,f11(f65(x9421),x9422,x9423))
% 15.40/15.54 [1014]P9(x10142,x10141)+~P57(x10142)+~P9(x10142,f19(x10142,x10143,x10141))+E(x10141,f3(f65(x10142)))
% 15.40/15.54 [1015]P74(x10151,x10152,x10153)+P8(a59,x10152,f3(a59))+P8(a59,f3(a59),x10152)+~P73(f21(x10151,f3(a59)))
% 15.40/15.54 [1049]~P57(x10493)+E(x10491,x10492)+~P7(f65(x10493),x10491,x10492)+P9(x10493,f7(f65(x10493),x10492,x10491))
% 15.40/15.54 [1070]~P57(x10701)+~P8(x10701,f3(x10701),x10702)+P9(x10701,f19(x10701,x10702,x10703))+~E(x10703,f3(f65(x10701)))
% 15.40/15.54 [1102]~P7(a58,x11023,f31(x11022,x11021))+~P73(f21(x11021,x11022))+~P73(f21(x11021,x11023))+P73(f21(x11021,f3(a58)))
% 15.40/15.54 [1223]P74(x12231,x12232,x12233)+P8(a59,f42(x12233,x12232,x12231),x12232)+P8(a59,x12232,f3(a59))+~P73(f21(x12231,f3(a59)))
% 15.40/15.54 [1224]P74(x12241,x12242,x12243)+P8(a59,x12242,f49(x12243,x12242,x12241))+P8(a59,f3(a59),x12242)+~P73(f21(x12241,f3(a59)))
% 15.40/15.54 [1238]P74(x12381,x12382,x12383)+P8(a59,x12382,f3(a59))+P7(a59,f3(a59),f42(x12383,x12382,x12381))+~P73(f21(x12381,f3(a59)))
% 15.40/15.54 [1239]P74(x12391,x12392,x12393)+P8(a59,f3(a59),x12392)+P7(a59,f49(x12393,x12392,x12391),f3(a59))+~P73(f21(x12391,f3(a59)))
% 15.40/15.54 [1409]P74(x14091,x14092,x14093)+P8(a59,x14092,f49(x14093,x14092,x14091))+P8(a59,f42(x14093,x14092,x14091),x14092)+~P73(f21(x14091,f3(a59)))
% 15.40/15.54 [1413]P74(x14131,x14132,x14133)+P8(a59,x14132,f49(x14133,x14132,x14131))+P7(a59,f3(a59),f42(x14133,x14132,x14131))+~P73(f21(x14131,f3(a59)))
% 15.40/15.54 [1414]P74(x14141,x14142,x14143)+P8(a59,f42(x14143,x14142,x14141),x14142)+P7(a59,f49(x14143,x14142,x14141),f3(a59))+~P73(f21(x14141,f3(a59)))
% 15.40/15.54 [1418]P74(x14181,x14182,x14183)+P7(a59,f3(a59),f42(x14183,x14182,x14181))+P7(a59,f49(x14183,x14182,x14181),f3(a59))+~P73(f21(x14181,f3(a59)))
% 15.40/15.54 [1503]P74(x15032,x15031,x15033)+E(x15031,f3(a59))+P8(a59,x15031,f3(a59))+~P73(f21(x15032,f44(x15033,x15031,x15032)))
% 15.40/15.54 [1504]P74(x15042,x15041,x15043)+E(x15041,f3(a59))+P8(a59,f3(a59),x15041)+~P73(f21(x15042,f50(x15043,x15041,x15042)))
% 15.40/15.54 [1554]P74(x15541,x15542,x15543)+P8(a59,x15542,f3(a59))+~P73(f21(x15541,f44(x15543,x15542,x15541)))+~P73(f21(x15541,f3(a59)))
% 15.40/15.54 [1555]P74(x15551,x15552,x15553)+P8(a59,f3(a59),x15552)+~P73(f21(x15551,f50(x15553,x15552,x15551)))+~P73(f21(x15551,f3(a59)))
% 15.40/15.54 [1588]P74(x15883,x15881,x15882)+E(x15881,f3(a59))+P8(a59,x15881,f3(a59))+E(f11(a59,f21(f21(f5(a59),x15881),f44(x15882,x15881,x15883)),f42(x15882,x15881,x15883)),x15882)
% 15.40/15.54 [1589]P74(x15893,x15891,x15892)+E(x15891,f3(a59))+P8(a59,f3(a59),x15891)+E(f11(a59,f21(f21(f5(a59),x15891),f50(x15892,x15891,x15893)),f49(x15892,x15891,x15893)),x15892)
% 15.40/15.54 [1603]P74(x16032,x16031,x16033)+P8(a59,x16031,f49(x16033,x16031,x16032))+E(x16031,f3(a59))+~P73(f21(x16032,f44(x16033,x16031,x16032)))
% 15.40/15.54 [1604]P74(x16042,x16041,x16043)+P8(a59,f42(x16043,x16041,x16042),x16041)+E(x16041,f3(a59))+~P73(f21(x16042,f50(x16043,x16041,x16042)))
% 15.40/15.54 [1607]P74(x16072,x16071,x16073)+E(x16071,f3(a59))+P7(a59,f3(a59),f42(x16073,x16071,x16072))+~P73(f21(x16072,f50(x16073,x16071,x16072)))
% 15.40/15.54 [1608]P74(x16082,x16081,x16083)+E(x16081,f3(a59))+P7(a59,f49(x16083,x16081,x16082),f3(a59))+~P73(f21(x16082,f44(x16083,x16081,x16082)))
% 15.40/15.54 [1626]P74(x16263,x16261,x16262)+P8(a59,x16261,f3(a59))+E(f11(a59,f21(f21(f5(a59),x16261),f44(x16262,x16261,x16263)),f42(x16262,x16261,x16263)),x16262)+~P73(f21(x16263,f3(a59)))
% 15.40/15.54 [1627]P74(x16273,x16271,x16272)+P8(a59,f3(a59),x16271)+E(f11(a59,f21(f21(f5(a59),x16271),f50(x16272,x16271,x16273)),f49(x16272,x16271,x16273)),x16272)+~P73(f21(x16273,f3(a59)))
% 15.40/15.54 [1635]P74(x16351,x16352,x16353)+P8(a59,x16352,f49(x16353,x16352,x16351))+~P73(f21(x16351,f44(x16353,x16352,x16351)))+~P73(f21(x16351,f3(a59)))
% 15.40/15.54 [1636]P74(x16361,x16362,x16363)+P8(a59,f42(x16363,x16362,x16361),x16362)+~P73(f21(x16361,f50(x16363,x16362,x16361)))+~P73(f21(x16361,f3(a59)))
% 15.40/15.54 [1637]P74(x16371,x16372,x16373)+P7(a59,f3(a59),f42(x16373,x16372,x16371))+~P73(f21(x16371,f50(x16373,x16372,x16371)))+~P73(f21(x16371,f3(a59)))
% 15.40/15.54 [1638]P74(x16381,x16382,x16383)+P7(a59,f49(x16383,x16382,x16381),f3(a59))+~P73(f21(x16381,f44(x16383,x16382,x16381)))+~P73(f21(x16381,f3(a59)))
% 15.40/15.54 [1650]P74(x16503,x16501,x16502)+P8(a59,x16501,f49(x16502,x16501,x16503))+E(x16501,f3(a59))+E(f11(a59,f21(f21(f5(a59),x16501),f44(x16502,x16501,x16503)),f42(x16502,x16501,x16503)),x16502)
% 15.40/15.54 [1651]P74(x16513,x16511,x16512)+P8(a59,f42(x16512,x16511,x16513),x16511)+E(x16511,f3(a59))+E(f11(a59,f21(f21(f5(a59),x16511),f50(x16512,x16511,x16513)),f49(x16512,x16511,x16513)),x16512)
% 15.40/15.54 [1654]P74(x16543,x16541,x16542)+E(x16541,f3(a59))+P7(a59,f3(a59),f42(x16542,x16541,x16543))+E(f11(a59,f21(f21(f5(a59),x16541),f50(x16542,x16541,x16543)),f49(x16542,x16541,x16543)),x16542)
% 15.40/15.54 [1655]P74(x16553,x16551,x16552)+E(x16551,f3(a59))+P7(a59,f49(x16552,x16551,x16553),f3(a59))+E(f11(a59,f21(f21(f5(a59),x16551),f44(x16552,x16551,x16553)),f42(x16552,x16551,x16553)),x16552)
% 15.40/15.54 [1674]P74(x16743,x16741,x16742)+P8(a59,x16741,f49(x16742,x16741,x16743))+E(f11(a59,f21(f21(f5(a59),x16741),f44(x16742,x16741,x16743)),f42(x16742,x16741,x16743)),x16742)+~P73(f21(x16743,f3(a59)))
% 15.40/15.54 [1675]P74(x16753,x16751,x16752)+P8(a59,f42(x16752,x16751,x16753),x16751)+E(f11(a59,f21(f21(f5(a59),x16751),f50(x16752,x16751,x16753)),f49(x16752,x16751,x16753)),x16752)+~P73(f21(x16753,f3(a59)))
% 15.40/15.54 [1676]P74(x16763,x16761,x16762)+P7(a59,f3(a59),f42(x16762,x16761,x16763))+E(f11(a59,f21(f21(f5(a59),x16761),f50(x16762,x16761,x16763)),f49(x16762,x16761,x16763)),x16762)+~P73(f21(x16763,f3(a59)))
% 15.40/15.54 [1677]P74(x16773,x16771,x16772)+P7(a59,f49(x16772,x16771,x16773),f3(a59))+E(f11(a59,f21(f21(f5(a59),x16771),f44(x16772,x16771,x16773)),f42(x16772,x16771,x16773)),x16772)+~P73(f21(x16773,f3(a59)))
% 15.40/15.54 [1701]P74(x17012,x17011,x17013)+E(x17011,f3(a59))+~P73(f21(x17012,f44(x17013,x17011,x17012)))+~P73(f21(x17012,f50(x17013,x17011,x17012)))
% 15.40/15.54 [1707]P74(x17071,x17072,x17073)+~P73(f21(x17071,f44(x17073,x17072,x17071)))+~P73(f21(x17071,f50(x17073,x17072,x17071)))+~P73(f21(x17071,f3(a59)))
% 15.40/15.54 [1711]P74(x17113,x17111,x17112)+E(x17111,f3(a59))+E(f11(a59,f21(f21(f5(a59),x17111),f44(x17112,x17111,x17113)),f42(x17112,x17111,x17113)),x17112)+~P73(f21(x17113,f50(x17112,x17111,x17113)))
% 15.40/15.54 [1712]P74(x17123,x17121,x17122)+E(x17121,f3(a59))+E(f11(a59,f21(f21(f5(a59),x17121),f50(x17122,x17121,x17123)),f49(x17122,x17121,x17123)),x17122)+~P73(f21(x17123,f44(x17122,x17121,x17123)))
% 15.40/15.54 [1723]P74(x17233,x17231,x17232)+E(f11(a59,f21(f21(f5(a59),x17231),f44(x17232,x17231,x17233)),f42(x17232,x17231,x17233)),x17232)+~P73(f21(x17233,f50(x17232,x17231,x17233)))+~P73(f21(x17233,f3(a59)))
% 15.40/15.54 [1724]P74(x17243,x17241,x17242)+E(f11(a59,f21(f21(f5(a59),x17241),f50(x17242,x17241,x17243)),f49(x17242,x17241,x17243)),x17242)+~P73(f21(x17243,f44(x17242,x17241,x17243)))+~P73(f21(x17243,f3(a59)))
% 15.40/15.54 [1727]P74(x17273,x17271,x17272)+E(x17271,f3(a59))+E(f11(a59,f21(f21(f5(a59),x17271),f50(x17272,x17271,x17273)),f49(x17272,x17271,x17273)),x17272)+E(f11(a59,f21(f21(f5(a59),x17271),f44(x17272,x17271,x17273)),f42(x17272,x17271,x17273)),x17272)
% 15.40/15.54 [1731]P74(x17313,x17311,x17312)+E(f11(a59,f21(f21(f5(a59),x17311),f50(x17312,x17311,x17313)),f49(x17312,x17311,x17313)),x17312)+E(f11(a59,f21(f21(f5(a59),x17311),f44(x17312,x17311,x17313)),f42(x17312,x17311,x17313)),x17312)+~P73(f21(x17313,f3(a59)))
% 15.40/15.54 [763]~P52(x7632)+E(x7631,f3(x7632))+E(x7633,f3(x7632))+~E(f21(f21(f5(x7632),x7633),x7631),f3(x7632))
% 15.40/15.54 [764]~P68(x7642)+E(x7641,f3(x7642))+E(x7643,f3(x7642))+~E(f21(f21(f5(x7642),x7643),x7641),f3(x7642))
% 15.40/15.54 [943]~P51(x9433)+E(x9431,x9432)+E(x9431,f4(x9433,x9432))+~E(f21(f21(f5(x9433),x9431),x9431),f21(f21(f5(x9433),x9432),x9432))
% 15.40/15.54 [1280]~P54(x12801)+~P8(x12801,f6(x12801),x12802)+~P8(a58,f3(a58),x12803)+P8(x12801,f6(x12801),f21(f21(f27(x12801),x12802),x12803))
% 15.40/15.54 [1293]~P64(x12931)+~P7(x12931,x12933,f3(x12931))+~P7(x12931,x12932,f3(x12931))+P7(x12931,f3(x12931),f21(f21(f5(x12931),x12932),x12933))
% 15.40/15.54 [1294]~P55(x12941)+~P7(x12941,x12943,f3(x12941))+~P7(x12941,x12942,f3(x12941))+P7(x12941,f3(x12941),f21(f21(f5(x12941),x12942),x12943))
% 15.40/15.54 [1295]~P55(x12951)+~P8(x12951,x12953,f3(x12951))+~P8(x12951,x12952,f3(x12951))+P8(x12951,f3(x12951),f21(f21(f5(x12951),x12952),x12953))
% 15.40/15.54 [1296]~P63(x12961)+~P7(x12961,f3(x12961),x12963)+~P7(x12961,f3(x12961),x12962)+P7(x12961,f3(x12961),f21(f21(f5(x12961),x12962),x12963))
% 15.40/15.54 [1297]~P64(x12971)+~P7(x12971,f3(x12971),x12973)+~P7(x12971,f3(x12971),x12972)+P7(x12971,f3(x12971),f21(f21(f5(x12971),x12972),x12973))
% 15.40/15.54 [1298]~P55(x12981)+~P7(x12981,f3(x12981),x12983)+~P7(x12981,f3(x12981),x12982)+P7(x12981,f3(x12981),f21(f21(f5(x12981),x12982),x12983))
% 15.40/15.54 [1299]~P59(x12991)+~P8(x12991,f3(x12991),x12993)+~P8(x12991,f3(x12991),x12992)+P8(x12991,f3(x12991),f21(f21(f5(x12991),x12992),x12993))
% 15.40/15.54 [1300]~P54(x13001)+~P8(x13001,f6(x13001),x13003)+~P8(x13001,f6(x13001),x13002)+P8(x13001,f6(x13001),f21(f21(f5(x13001),x13002),x13003))
% 15.40/15.54 [1303]~P63(x13031)+~P7(x13031,x13033,f3(x13031))+~P7(x13031,f3(x13031),x13032)+P7(x13031,f21(f21(f5(x13031),x13032),x13033),f3(x13031))
% 15.40/15.54 [1305]~P63(x13051)+~P7(x13051,x13052,f3(x13051))+~P7(x13051,f3(x13051),x13053)+P7(x13051,f21(f21(f5(x13051),x13052),x13053),f3(x13051))
% 15.40/15.54 [1306]~P55(x13061)+~P7(x13061,x13063,f3(x13061))+~P7(x13061,f3(x13061),x13062)+P7(x13061,f21(f21(f5(x13061),x13062),x13063),f3(x13061))
% 15.40/15.54 [1307]~P55(x13071)+~P7(x13071,x13072,f3(x13071))+~P7(x13071,f3(x13071),x13073)+P7(x13071,f21(f21(f5(x13071),x13072),x13073),f3(x13071))
% 15.40/15.54 [1309]~P59(x13091)+~P8(x13091,x13093,f3(x13091))+~P8(x13091,f3(x13091),x13092)+P8(x13091,f21(f21(f5(x13091),x13092),x13093),f3(x13091))
% 15.40/15.54 [1310]~P59(x13101)+~P8(x13101,x13102,f3(x13101))+~P8(x13101,f3(x13101),x13103)+P8(x13101,f21(f21(f5(x13101),x13102),x13103),f3(x13101))
% 15.40/15.54 [1336]~P55(x13361)+P7(x13361,x13362,f3(x13361))+P7(x13361,x13363,f3(x13361))+~P7(x13361,f21(f21(f5(x13361),x13363),x13362),f3(x13361))
% 15.40/15.54 [1337]~P55(x13371)+P7(x13371,x13372,f3(x13371))+P7(x13371,f3(x13371),x13373)+~P7(x13371,f3(x13371),f21(f21(f5(x13371),x13373),x13372))
% 15.40/15.54 [1338]~P55(x13381)+P7(x13381,x13382,f3(x13381))+P7(x13381,f3(x13381),x13383)+~P7(x13381,f3(x13381),f21(f21(f5(x13381),x13382),x13383))
% 15.40/15.54 [1339]~P55(x13391)+P7(x13391,f3(x13391),x13392)+P7(x13391,x13392,f3(x13391))+~P7(x13391,f3(x13391),f21(f21(f5(x13391),x13393),x13392))
% 15.40/15.54 [1340]~P55(x13401)+P7(x13401,f3(x13401),x13402)+P7(x13401,x13402,f3(x13401))+~P7(x13401,f3(x13401),f21(f21(f5(x13401),x13402),x13403))
% 15.40/15.54 [1341]~P55(x13411)+P7(x13411,f3(x13411),x13412)+P7(x13411,x13412,f3(x13411))+~P7(x13411,f21(f21(f5(x13411),x13413),x13412),f3(x13411))
% 15.40/15.54 [1342]~P55(x13421)+P7(x13421,f3(x13421),x13422)+P7(x13421,x13422,f3(x13421))+~P7(x13421,f21(f21(f5(x13421),x13422),x13423),f3(x13421))
% 15.40/15.54 [1343]~P55(x13431)+P7(x13431,f3(x13431),x13432)+P7(x13431,f3(x13431),x13433)+~P7(x13431,f21(f21(f5(x13431),x13432),x13433),f3(x13431))
% 15.40/15.54 [1388]~P59(x13881)+P8(x13881,f3(x13881),x13882)+~P8(x13881,f3(x13881),x13883)+~P8(x13881,f3(x13881),f21(f21(f5(x13881),x13883),x13882))
% 15.40/15.54 [1389]~P59(x13891)+P8(x13891,f3(x13891),x13892)+~P8(x13891,f3(x13891),x13893)+~P8(x13891,f3(x13891),f21(f21(f5(x13891),x13892),x13893))
% 15.40/15.54 [1543]~P4(x15431)+~E(x15433,f3(f65(x15431)))+~E(x15432,f3(f65(x15431)))+E(f21(f13(x15431,f24(x15431,x15432,x15433)),f2(x15431,f24(x15431,x15432,x15433))),f3(x15431))
% 15.40/15.54 [1584]~P54(x15841)+~P7(x15841,x15842,f6(x15841))+~P7(x15841,f3(x15841),x15842)+P7(x15841,f21(f21(f27(x15841),x15842),f11(a58,x15843,f6(a58))),x15842)
% 15.40/15.54 [1591]~P54(x15911)+~P8(x15911,x15912,f6(x15911))+~P8(x15911,f3(x15911),x15912)+P8(x15911,f21(f21(f27(x15911),x15912),f11(a58,x15913,f6(a58))),f6(x15911))
% 15.40/15.54 [1692]~P7(a58,x16922,x16923)+~P73(f21(f21(f22(a58),x16921),f7(a58,x16923,x16922)))+~P73(f21(f21(f22(a58),x16921),x16923))+P73(f21(f21(f22(a58),x16921),x16922))
% 15.40/15.54 [1693]~P7(a58,x16933,x16932)+~P73(f21(f21(f22(a58),x16931),f7(a58,x16932,x16933)))+~P73(f21(f21(f22(a58),x16931),x16933))+P73(f21(f21(f22(a58),x16931),x16932))
% 15.40/15.54 [1720]E(x17201,f9(a58,x17202,x17203))+~P8(a58,f3(a58),x17203)+~P7(a58,f21(f21(f5(a58),x17203),x17201),x17202)+~P8(a58,x17202,f21(f21(f5(a58),x17203),f11(a58,x17201,f6(a58))))
% 15.40/15.55 [1771]~P51(x17713)+E(x17711,x17712)+E(x17711,f4(x17713,x17712))+~E(f21(f21(f27(x17713),x17711),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58))),f21(f21(f27(x17713),x17712),f11(a58,f11(a58,f3(a58),f6(a58)),f6(a58))))
% 15.40/15.55 [1003]~P57(x10031)+~P9(x10031,x10033)+~P9(x10031,x10032)+P9(x10031,f21(f21(f5(f65(x10031)),x10032),x10033))
% 15.40/15.55 [1133]~P55(x11331)+~E(x11333,f3(x11331))+~E(x11332,f3(x11331))+E(f11(x11331,f21(f21(f5(x11331),x11332),x11332),f21(f21(f5(x11331),x11333),x11333)),f3(x11331))
% 15.40/15.55 [1323]~P51(x13232)+P7(a58,f2(x13232,x13233),f2(x13232,x13231))+E(x13231,f3(f65(x13232)))+~P73(f21(f21(f22(f65(x13232)),x13233),x13231))
% 15.40/15.55 [1460]~P8(a59,x14602,x14603)+~P8(a59,f3(a59),x14603)+P7(a59,f6(a59),x14601)+~E(f11(a59,x14602,f21(f21(f5(a59),x14603),x14601)),x14603)
% 15.40/15.55 [1464]~P7(a59,f3(a59),x14642)+~P8(a59,f3(a59),x14643)+P7(a59,x14641,f6(a59))+~E(f11(a59,x14642,f21(f21(f5(a59),x14643),x14641)),x14643)
% 15.40/15.55 [1602]~P55(x16021)+~E(x16023,f3(x16021))+~E(x16022,f3(x16021))+P7(x16021,f11(x16021,f21(f21(f5(x16021),x16022),x16022),f21(f21(f5(x16021),x16023),x16023)),f3(x16021))
% 15.40/15.55 [1639]~P54(x16391)+~P8(x16391,x16392,f6(x16391))+~P8(x16391,f3(x16391),x16392)+P8(x16391,f21(f21(f5(x16391),x16392),f21(f21(f27(x16391),x16392),x16393)),f21(f21(f27(x16391),x16392),x16393))
% 15.40/15.55 [1681]~P8(a59,x16812,x16813)+~P8(a59,f3(a59),x16813)+P7(a59,f3(a59),x16811)+~P7(a59,f3(a59),f11(a59,f21(f21(f5(a59),x16813),x16811),x16812))
% 15.40/15.55 [1683]P7(a59,x16831,f3(a59))+~P7(a59,f3(a59),x16832)+~P8(a59,f3(a59),x16833)+~P8(a59,f11(a59,f21(f21(f5(a59),x16833),x16831),x16832),f3(a59))
% 15.40/15.55 [1719]~P55(x17192)+~E(x17191,f3(x17192))+~E(x17193,f3(x17192))+~P8(x17192,f3(x17192),f11(x17192,f21(f21(f5(x17192),x17193),x17193),f21(f21(f5(x17192),x17191),x17191)))
% 15.40/15.55 [1163]~P51(x11632)+E(x11631,f3(f65(x11632)))+E(x11633,f3(f65(x11632)))+E(f2(x11632,f21(f21(f5(f65(x11632)),x11633),x11631)),f11(a58,f2(x11632,x11633),f2(x11632,x11631)))
% 15.40/15.55 [1036]~P41(x10361)+~P7(x10361,x10364,x10363)+P7(x10361,x10362,x10363)+~P7(x10361,x10362,x10364)
% 15.40/15.55 [1037]~P36(x10371)+~P7(x10371,x10372,x10374)+P7(x10371,x10372,x10373)+~P7(x10371,x10374,x10373)
% 15.40/15.55 [1038]~P41(x10381)+~P8(x10381,x10384,x10383)+P8(x10381,x10382,x10383)+~P7(x10381,x10382,x10384)
% 15.40/15.55 [1039]~P41(x10391)+~P8(x10391,x10392,x10394)+P8(x10391,x10392,x10393)+~P7(x10391,x10394,x10393)
% 15.40/15.55 [1040]~P41(x10401)+~P8(x10401,x10404,x10403)+P8(x10401,x10402,x10403)+~P8(x10401,x10402,x10404)
% 15.40/15.55 [1041]~P36(x10411)+~P8(x10411,x10412,x10414)+P8(x10411,x10412,x10413)+~P7(x10411,x10414,x10413)
% 15.40/15.55 [1042]~P36(x10421)+~P8(x10421,x10424,x10423)+P8(x10421,x10422,x10423)+~P7(x10421,x10422,x10424)
% 15.40/15.55 [1043]~P36(x10431)+~P8(x10431,x10432,x10434)+P8(x10431,x10432,x10433)+~P8(x10431,x10434,x10433)
% 15.40/15.55 [1146]~P40(x11462)+P8(f66(x11461,x11462),x11464,x11463)+~P7(f66(x11461,x11462),x11464,x11463)+P7(f66(x11461,x11462),x11463,x11464)
% 15.40/15.55 [1275]~P30(x12751)+~P7(x12751,x12752,x12753)+~P7(x12751,f3(x12751),x12754)+P7(x12751,x12752,f11(x12751,x12753,x12754))
% 15.40/15.55 [1276]~P30(x12761)+~P7(x12761,x12762,x12764)+~P7(x12761,f3(x12761),x12763)+P7(x12761,x12762,f11(x12761,x12763,x12764))
% 15.40/15.55 [1277]~P54(x12771)+~P8(x12771,x12772,x12774)+~P8(x12771,f3(x12771),x12773)+P8(x12771,x12772,f11(x12771,x12773,x12774))
% 15.40/15.55 [1278]~P30(x12781)+~P7(x12781,x12782,x12784)+~P8(x12781,f3(x12781),x12783)+P8(x12781,x12782,f11(x12781,x12783,x12784))
% 15.40/15.55 [1279]~P30(x12791)+~P8(x12791,x12792,x12794)+~P7(x12791,f3(x12791),x12793)+P8(x12791,x12792,f11(x12791,x12793,x12794))
% 15.40/15.55 [1765]~E(x17654,x17652)+~P4(x17651)+P11(x17651,x17652,f3(f65(x17651)),x17653,x17654)+~E(x17653,f3(f65(x17651)))
% 15.40/15.55 [1772]~P4(x17721)+P11(x17721,f3(f65(x17721)),x17722,x17723,x17724)+~E(x17724,f3(f65(x17721)))+~E(x17723,f3(f65(x17721)))
% 15.40/15.55 [1114]~P54(x11143)+E(x11141,x11142)+~P8(x11143,f6(x11143),x11144)+~E(f21(f21(f27(x11143),x11144),x11141),f21(f21(f27(x11143),x11144),x11142))
% 15.40/15.55 [1423]~P54(x14231)+~P7(a58,x14233,x14234)+~P8(x14231,f6(x14231),x14232)+P7(x14231,f21(f21(f27(x14231),x14232),x14233),f21(f21(f27(x14231),x14232),x14234))
% 15.40/15.55 [1424]~P54(x14241)+~P7(a58,x14243,x14244)+~P7(x14241,f6(x14241),x14242)+P7(x14241,f21(f21(f27(x14241),x14242),x14243),f21(f21(f27(x14241),x14242),x14244))
% 15.40/15.55 [1426]~P54(x14261)+~P8(a58,x14263,x14264)+~P8(x14261,f6(x14261),x14262)+P8(x14261,f21(f21(f27(x14261),x14262),x14263),f21(f21(f27(x14261),x14262),x14264))
% 15.40/15.55 [1432]~P64(x14321)+~P7(x14321,x14324,x14323)+~P7(x14321,x14322,f3(x14321))+P7(x14321,f21(f21(f5(x14321),x14322),x14323),f21(f21(f5(x14321),x14322),x14324))
% 15.40/15.55 [1433]~P55(x14331)+~P7(x14331,x14334,x14333)+~P8(x14331,x14332,f3(x14331))+P7(x14331,f21(f21(f5(x14331),x14332),x14333),f21(f21(f5(x14331),x14332),x14334))
% 15.40/15.55 [1434]~P64(x14341)+~P7(x14341,x14344,x14342)+~P7(x14341,x14343,f3(x14341))+P7(x14341,f21(f21(f5(x14341),x14342),x14343),f21(f21(f5(x14341),x14344),x14343))
% 15.40/15.55 [1438]~P55(x14381)+~P8(x14381,x14384,x14382)+~P8(x14381,x14383,f3(x14381))+P8(x14381,f21(f21(f5(x14381),x14382),x14383),f21(f21(f5(x14381),x14384),x14383))
% 15.40/15.55 [1439]~P55(x14391)+~P8(x14391,x14394,x14393)+~P8(x14391,x14392,f3(x14391))+P8(x14391,f21(f21(f5(x14391),x14392),x14393),f21(f21(f5(x14391),x14392),x14394))
% 15.40/15.55 [1440]~P66(x14401)+~P7(x14401,x14403,x14404)+~P7(x14401,f3(x14401),x14402)+P7(x14401,f21(f21(f5(x14401),x14402),x14403),f21(f21(f5(x14401),x14402),x14404))
% 15.40/15.55 [1441]~P65(x14411)+~P7(x14411,x14413,x14414)+~P7(x14411,f3(x14411),x14412)+P7(x14411,f21(f21(f5(x14411),x14412),x14413),f21(f21(f5(x14411),x14412),x14414))
% 15.40/15.55 [1442]~P55(x14421)+~P7(x14421,x14423,x14424)+~P8(x14421,f3(x14421),x14422)+P7(x14421,f21(f21(f5(x14421),x14422),x14423),f21(f21(f5(x14421),x14422),x14424))
% 15.40/15.55 [1443]~P66(x14431)+~P7(x14431,x14432,x14434)+~P7(x14431,f3(x14431),x14433)+P7(x14431,f21(f21(f5(x14431),x14432),x14433),f21(f21(f5(x14431),x14434),x14433))
% 15.40/15.55 [1444]~P54(x14441)+~P7(x14441,x14442,x14444)+~P7(x14441,f3(x14441),x14442)+P7(x14441,f21(f21(f27(x14441),x14442),x14443),f21(f21(f27(x14441),x14444),x14443))
% 15.40/15.55 [1446]~P59(x14461)+~P8(x14461,x14463,x14464)+~P8(x14461,f3(x14461),x14462)+P8(x14461,f21(f21(f5(x14461),x14462),x14463),f21(f21(f5(x14461),x14462),x14464))
% 15.40/15.55 [1447]~P58(x14471)+~P8(x14471,x14473,x14474)+~P8(x14471,f3(x14471),x14472)+P8(x14471,f21(f21(f5(x14471),x14472),x14473),f21(f21(f5(x14471),x14472),x14474))
% 15.40/15.55 [1448]~P55(x14481)+~P8(x14481,x14482,x14484)+~P8(x14481,f3(x14481),x14483)+P8(x14481,f21(f21(f5(x14481),x14482),x14483),f21(f21(f5(x14481),x14484),x14483))
% 15.40/15.55 [1449]~P59(x14491)+~P8(x14491,x14492,x14494)+~P8(x14491,f3(x14491),x14493)+P8(x14491,f21(f21(f5(x14491),x14492),x14493),f21(f21(f5(x14491),x14494),x14493))
% 15.40/15.55 [1450]~P55(x14501)+~P8(x14501,x14503,x14504)+~P8(x14501,f3(x14501),x14502)+P8(x14501,f21(f21(f5(x14501),x14502),x14503),f21(f21(f5(x14501),x14502),x14504))
% 15.40/15.55 [1451]~P1(x14511)+~P73(f21(f21(f22(x14511),x14512),x14514))+P73(f21(f21(f22(x14511),x14512),x14513))+~P73(f21(f21(f22(x14511),x14514),x14513))
% 15.40/15.55 [1521]P8(x15211,x15213,x15212)+~P55(x15211)+P8(x15211,x15212,x15213)+~P8(x15211,f21(f21(f5(x15211),x15214),x15212),f21(f21(f5(x15211),x15214),x15213))
% 15.40/15.55 [1522]P8(x15221,x15223,x15222)+~P55(x15221)+P8(x15221,x15222,x15223)+~P8(x15221,f21(f21(f5(x15221),x15222),x15224),f21(f21(f5(x15221),x15223),x15224))
% 15.40/15.55 [1526]~P55(x15261)+P8(x15261,x15262,x15263)+P8(x15261,x15264,f3(x15261))+~P8(x15261,f21(f21(f5(x15261),x15262),x15264),f21(f21(f5(x15261),x15263),x15264))
% 15.40/15.55 [1527]~P55(x15271)+P8(x15271,x15272,x15273)+P8(x15271,x15274,f3(x15271))+~P8(x15271,f21(f21(f5(x15271),x15274),x15272),f21(f21(f5(x15271),x15274),x15273))
% 15.40/15.55 [1528]~P55(x15281)+P8(x15281,x15282,x15283)+P8(x15281,f3(x15281),x15284)+~P8(x15281,f21(f21(f5(x15281),x15284),x15283),f21(f21(f5(x15281),x15284),x15282))
% 15.40/15.55 [1529]~P55(x15291)+P8(x15291,x15292,x15293)+P8(x15291,f3(x15291),x15294)+~P8(x15291,f21(f21(f5(x15291),x15293),x15294),f21(f21(f5(x15291),x15292),x15294))
% 15.40/15.55 [1537]~P55(x15371)+P8(x15371,f3(x15371),x15372)+P8(x15371,x15372,f3(x15371))+~P8(x15371,f21(f21(f5(x15371),x15373),x15372),f21(f21(f5(x15371),x15374),x15372))
% 15.40/15.55 [1538]~P55(x15381)+P8(x15381,f3(x15381),x15382)+P8(x15381,x15382,f3(x15381))+~P8(x15381,f21(f21(f5(x15381),x15382),x15383),f21(f21(f5(x15381),x15382),x15384))
% 15.40/15.55 [1562]~P54(x15623)+P7(a58,x15621,x15622)+~P8(x15623,f6(x15623),x15624)+~P7(x15623,f21(f21(f27(x15623),x15624),x15621),f21(f21(f27(x15623),x15624),x15622))
% 15.40/15.55 [1564]~P54(x15643)+P8(a58,x15641,x15642)+~P8(x15643,f6(x15643),x15644)+~P8(x15643,f21(f21(f27(x15643),x15644),x15641),f21(f21(f27(x15643),x15644),x15642))
% 15.40/15.55 [1565]~P55(x15651)+P7(x15651,x15652,x15653)+~P8(x15651,x15654,f3(x15651))+~P7(x15651,f21(f21(f5(x15651),x15654),x15653),f21(f21(f5(x15651),x15654),x15652))
% 15.40/15.55 [1566]~P55(x15661)+P8(x15661,x15662,x15663)+~P8(x15661,x15664,f3(x15661))+~P8(x15661,f21(f21(f5(x15661),x15664),x15663),f21(f21(f5(x15661),x15664),x15662))
% 15.40/15.55 [1567]~P55(x15671)+P7(x15671,x15672,x15673)+~P8(x15671,f3(x15671),x15674)+~P7(x15671,f21(f21(f5(x15671),x15674),x15672),f21(f21(f5(x15671),x15674),x15673))
% 15.40/15.55 [1568]~P59(x15681)+P7(x15681,x15682,x15683)+~P8(x15681,f3(x15681),x15684)+~P7(x15681,f21(f21(f5(x15681),x15684),x15682),f21(f21(f5(x15681),x15684),x15683))
% 15.40/15.55 [1569]~P59(x15691)+P7(x15691,x15692,x15693)+~P8(x15691,f3(x15691),x15694)+~P7(x15691,f21(f21(f5(x15691),x15692),x15694),f21(f21(f5(x15691),x15693),x15694))
% 15.40/15.55 [1570]~P55(x15701)+P8(x15701,x15702,x15703)+~P8(x15701,f3(x15701),x15704)+~P8(x15701,f21(f21(f5(x15701),x15704),x15702),f21(f21(f5(x15701),x15704),x15703))
% 15.40/15.55 [1571]~P59(x15711)+P8(x15711,x15712,x15713)+~P7(x15711,f3(x15711),x15714)+~P8(x15711,f21(f21(f5(x15711),x15714),x15712),f21(f21(f5(x15711),x15714),x15713))
% 15.40/15.55 [1572]~P60(x15721)+P8(x15721,x15722,x15723)+~P7(x15721,f3(x15721),x15724)+~P8(x15721,f21(f21(f5(x15721),x15724),x15722),f21(f21(f5(x15721),x15724),x15723))
% 15.40/15.55 [1573]~P54(x15731)+P8(x15731,x15732,x15733)+~P7(x15731,f3(x15731),x15733)+~P8(x15731,f21(f21(f27(x15731),x15732),x15734),f21(f21(f27(x15731),x15733),x15734))
% 15.40/15.55 [1574]~P59(x15741)+P8(x15741,x15742,x15743)+~P7(x15741,f3(x15741),x15744)+~P8(x15741,f21(f21(f5(x15741),x15742),x15744),f21(f21(f5(x15741),x15743),x15744))
% 15.40/15.55 [1575]~P60(x15751)+P8(x15751,x15752,x15753)+~P7(x15751,f3(x15751),x15754)+~P8(x15751,f21(f21(f5(x15751),x15752),x15754),f21(f21(f5(x15751),x15753),x15754))
% 15.40/15.55 [1580]~P15(x15801)+~P7(a58,f2(x15801,x15803),x15804)+~P7(a58,f2(x15801,x15802),x15804)+P7(a58,f2(x15801,f11(f65(x15801),x15802,x15803)),x15804)
% 15.40/15.55 [1581]~P3(x15811)+~P7(a58,f2(x15811,x15813),x15814)+~P7(a58,f2(x15811,x15812),x15814)+P7(a58,f2(x15811,f7(f65(x15811),x15812,x15813)),x15814)
% 15.40/15.55 [1582]~P15(x15821)+~P8(a58,f2(x15821,x15823),x15824)+~P8(a58,f2(x15821,x15822),x15824)+P8(a58,f2(x15821,f11(f65(x15821),x15822,x15823)),x15824)
% 15.40/15.55 [1583]~P3(x15831)+~P8(a58,f2(x15831,x15833),x15834)+~P8(a58,f2(x15831,x15832),x15834)+P8(a58,f2(x15831,f7(f65(x15831),x15832,x15833)),x15834)
% 15.40/15.55 [1633]~P41(x16331)+P7(x16331,f21(x16332,x16333),f21(x16332,x16334))+~P10(a58,x16331,f22(a58),x16332)+~P73(f21(f21(f22(a58),x16333),x16334))
% 15.40/15.55 [1640]~P1(x16401)+P73(f21(f21(f22(x16401),x16402),f11(x16401,x16403,x16404)))+~P73(f21(f21(f22(x16401),x16402),x16404))+~P73(f21(f21(f22(x16401),x16402),x16403))
% 15.40/15.55 [1641]~P32(x16411)+P73(f21(f21(f22(x16411),x16412),f7(x16411,x16413,x16414)))+~P73(f21(f21(f22(x16411),x16412),x16414))+~P73(f21(f21(f22(x16411),x16412),x16413))
% 15.40/15.55 [1684]~P5(x16841)+E(f11(x16841,f9(x16841,x16842,x16843),f9(x16841,x16844,x16843)),f9(x16841,f11(x16841,x16842,x16844),x16843))+~P73(f21(f21(f22(x16841),x16843),x16844))+~P73(f21(f21(f22(x16841),x16843),x16842))
% 15.40/15.55 [1737]~P73(f21(x17371,x17374))+~P7(a58,f21(f21(f5(a58),x17373),x17374),x17372)+~P8(a58,x17372,f21(f21(f5(a58),x17373),f11(a58,x17374,f6(a58))))+P73(f21(x17371,f9(a58,x17372,x17373)))
% 15.40/15.55 [1768]~P54(x17681)+P7(x17681,x17682,x17683)+~P7(x17681,f3(x17681),x17683)+~P7(x17681,f21(f21(f27(x17681),x17682),f11(a58,x17684,f6(a58))),f21(f21(f27(x17681),x17683),f11(a58,x17684,f6(a58))))
% 15.40/15.55 [1614]~P50(x16143)+~P70(x16143)+P73(f21(x16141,f56(x16142,x16141,x16143)))+~P73(f21(x16141,f21(f21(f5(x16143),x16142),x16144)))
% 15.40/15.55 [1705]~P4(x17051)+P73(f21(f21(f22(f65(x17051)),x17052),f24(x17051,x17053,x17054)))+~P73(f21(f21(f22(f65(x17051)),x17052),x17054))+~P73(f21(f21(f22(f65(x17051)),x17052),x17053))
% 15.40/15.55 [1752]~P50(x17521)+~P70(x17521)+P73(f21(f21(f22(x17521),x17522),f11(x17521,f56(x17522,x17523,x17521),f3(x17521))))+~P73(f21(x17523,f21(f21(f5(x17521),x17522),x17524)))
% 15.40/15.55 [1766]~P51(x17662)+E(x17661,f3(x17662))+P73(f21(f21(f22(x17662),x17663),x17664))+~P73(f21(f21(f22(x17662),f21(f21(f5(x17662),x17663),x17661)),f21(f21(f5(x17662),x17664),x17661)))
% 15.40/15.55 [1767]~P51(x17672)+E(x17671,f3(x17672))+P73(f21(f21(f22(x17672),x17673),x17674))+~P73(f21(f21(f22(x17672),f21(f21(f5(x17672),x17671),x17673)),f21(f21(f5(x17672),x17671),x17674)))
% 15.40/15.55 [941]~P3(x9415)+E(x9411,x9412)+~E(x9413,x9414)+~E(f7(x9415,x9413,x9414),f7(x9415,x9411,x9412))
% 15.40/15.55 [1202]~P25(x12021)+~P7(x12021,x12024,x12025)+P7(x12021,x12022,x12023)+~E(f7(x12021,x12024,x12025),f7(x12021,x12022,x12023))
% 15.40/15.55 [1204]~P25(x12041)+~P8(x12041,x12044,x12045)+P8(x12041,x12042,x12043)+~E(f7(x12041,x12044,x12045),f7(x12041,x12042,x12043))
% 15.40/15.55 [1427]~P28(x14271)+~P7(x14271,x14273,x14275)+~P7(x14271,x14272,x14274)+P7(x14271,f11(x14271,x14272,x14273),f11(x14271,x14274,x14275))
% 15.40/15.55 [1428]~P29(x14281)+~P7(x14281,x14283,x14285)+~P8(x14281,x14282,x14284)+P8(x14281,f11(x14281,x14282,x14283),f11(x14281,x14284,x14285))
% 15.40/15.55 [1429]~P29(x14291)+~P7(x14291,x14292,x14294)+~P8(x14291,x14293,x14295)+P8(x14291,f11(x14291,x14292,x14293),f11(x14291,x14294,x14295))
% 15.40/15.55 [1430]~P29(x14301)+~P8(x14301,x14303,x14305)+~P8(x14301,x14302,x14304)+P8(x14301,f11(x14301,x14302,x14303),f11(x14301,x14304,x14305))
% 15.40/15.55 [1798]~P4(x17982)+~P11(x17982,x17984,x17983,x17981,x17985)+E(x17981,f3(f65(x17982)))+~E(x17983,f3(f65(x17982)))
% 15.40/15.55 [1700]~P72(x17005)+E(x17001,x17002)+E(x17003,x17004)+~E(f11(x17005,f21(f21(f5(x17005),x17003),x17001),f21(f21(f5(x17005),x17004),x17002)),f11(x17005,f21(f21(f5(x17005),x17003),x17002),f21(f21(f5(x17005),x17004),x17001)))
% 15.40/15.55 [1725]~P5(x17251)+E(f9(x17251,f21(f21(f5(x17251),x17252),x17253),f21(f21(f5(x17251),x17254),x17255)),f21(f21(f5(x17251),f9(x17251,x17252,x17254)),f9(x17251,x17253,x17255)))+~P73(f21(f21(f22(x17251),x17255),x17253))+~P73(f21(f21(f22(x17251),x17254),x17252))
% 15.40/15.55 [1726]~P1(x17261)+~P7(a58,x17263,x17265)+~P73(f21(f21(f22(x17261),x17262),x17264))+P73(f21(f21(f22(x17261),f21(f21(f27(x17261),x17262),x17263)),f21(f21(f27(x17261),x17264),x17265)))
% 15.40/15.55 [1733]~P1(x17331)+~P73(f21(f21(f22(x17331),x17333),x17335))+~P73(f21(f21(f22(x17331),x17332),x17334))+P73(f21(f21(f22(x17331),f21(f21(f5(x17331),x17332),x17333)),f21(f21(f5(x17331),x17334),x17335)))
% 15.40/15.55 [1780]~P1(x17801)+~P7(a58,x17803,x17805)+~P73(f21(f21(f22(x17801),f21(f21(f27(x17801),x17802),x17805)),x17804))+P73(f21(f21(f22(x17801),f21(f21(f27(x17801),x17802),x17803)),x17804))
% 15.40/15.55 [1848]E(x18481,x18482)+~P11(x18483,x18484,x18485,x18486,x18481)+~P11(x18483,x18484,x18485,x18487,x18482)+~P4(x18483)
% 15.40/15.55 [1849]E(x18491,x18492)+~P11(x18493,x18494,x18495,x18492,x18496)+~P11(x18493,x18494,x18495,x18491,x18497)+~P4(x18493)
% 15.40/15.55 [1855]~P4(x18551)+~P11(x18551,x18552,x18553,x18558,x18557)+~P11(x18551,x18558,x18554,x18555,x18556)+P11(x18551,x18552,f21(f21(f5(f65(x18551)),x18553),x18554),x18555,f11(f65(x18551),f21(f21(f5(f65(x18551)),x18553),x18556),x18557))
% 15.40/15.55 [1472]E(x14721,x14722)+~P7(a59,f3(a59),x14722)+~P7(a59,f3(a59),x14721)+~P73(f21(f21(f22(a59),x14722),x14721))+~P73(f21(f21(f22(a59),x14721),x14722))
% 15.40/15.55 [1147]~P30(x11472)+~P7(x11472,f3(x11472),x11473)+~P7(x11472,f3(x11472),x11471)+~E(f11(x11472,x11473,x11471),f3(x11472))+E(x11471,f3(x11472))
% 15.40/15.55 [1148]~P30(x11482)+~P7(x11482,f3(x11482),x11483)+~P7(x11482,f3(x11482),x11481)+~E(f11(x11482,x11481,x11483),f3(x11482))+E(x11481,f3(x11482))
% 15.40/15.55 [1143]~P2(x11432)+~P7(a58,f2(x11432,x11431),x11433)+P8(a58,f2(x11432,x11431),x11433)+~E(f21(f13(x11432,x11431),x11433),f3(x11432))+E(x11431,f3(f65(x11432)))
% 15.40/15.55 [1453]~P57(x14531)+~P7(x14531,x14532,f6(x14531))+~P7(x14531,f3(x14531),x14532)+~P7(x14531,f3(x14531),x14533)+P7(x14531,f21(f21(f5(x14531),x14532),x14533),x14533)
% 15.40/15.55 [1454]~P57(x14541)+~P7(x14541,x14543,f6(x14541))+~P7(x14541,f3(x14541),x14543)+~P7(x14541,f3(x14541),x14542)+P7(x14541,f21(f21(f5(x14541),x14542),x14543),x14542)
% 15.40/15.55 [1660]~P51(x16603)+E(x16601,x16602)+~E(f21(f13(x16603,x16601),f2(x16603,x16601)),f21(f13(x16603,x16602),f2(x16603,x16602)))+~P73(f21(f21(f22(f65(x16603)),x16602),x16601))+~P73(f21(f21(f22(f65(x16603)),x16601),x16602))
% 15.40/15.55 [1630]~E(f2(a1,x16302),x16301)+~P8(a58,x16301,a62)+E(x16301,f3(a58))+E(f21(f16(a1,x16302),f52(x16301,x16302,x16303)),f3(a1))+P73(f21(f21(f22(f65(a1)),x16302),f21(f21(f27(f65(a1)),x16303),x16301)))
% 15.40/15.55 [1667]~E(f2(a1,x16672),x16671)+~P8(a58,x16671,a62)+E(x16671,f3(a58))+~E(f21(f16(a1,x16673),f52(x16671,x16672,x16673)),f3(a1))+P73(f21(f21(f22(f65(a1)),x16672),f21(f21(f27(f65(a1)),x16673),x16671)))
% 15.40/15.55 [1205]~P5(x12052)+E(x12051,f3(x12052))+E(f9(x12052,x12053,x12051),x12054)+~E(x12053,f21(f21(f5(x12052),x12054),x12051))+~P73(f21(f21(f22(x12052),x12051),x12053))
% 15.40/15.55 [1206]~P5(x12062)+~E(f9(x12062,x12063,x12061),x12064)+E(x12061,f3(x12062))+E(x12063,f21(f21(f5(x12062),x12064),x12061))+~P73(f21(f21(f22(x12062),x12061),x12063))
% 15.40/15.55 [1540]~P54(x15401)+~P8(x15401,x15402,x15404)+~P7(x15401,f3(x15401),x15402)+~P8(a58,f3(a58),x15403)+P8(x15401,f21(f21(f27(x15401),x15402),x15403),f21(f21(f27(x15401),x15404),x15403))
% 15.40/15.55 [1546]~P54(x15461)+~P7(a58,x15464,x15463)+~P7(x15461,x15462,f6(x15461))+~P7(x15461,f3(x15461),x15462)+P7(x15461,f21(f21(f27(x15461),x15462),x15463),f21(f21(f27(x15461),x15462),x15464))
% 15.40/15.55 [1547]~P54(x15471)+~P8(a58,x15474,x15473)+~P8(x15471,x15472,f6(x15471))+~P8(x15471,f3(x15471),x15472)+P8(x15471,f21(f21(f27(x15471),x15472),x15473),f21(f21(f27(x15471),x15472),x15474))
% 15.40/15.55 [1662]~P54(x16623)+E(x16621,x16622)+~P7(x16623,f3(x16623),x16622)+~P7(x16623,f3(x16623),x16621)+~E(f21(f21(f27(x16623),x16621),f11(a58,x16624,f6(a58))),f21(f21(f27(x16623),x16622),f11(a58,x16624,f6(a58))))
% 15.40/15.55 [1770]~P5(x17701)+P73(f21(f21(f22(x17701),f9(x17701,x17702,x17703)),f9(x17701,x17704,x17703)))+~P73(f21(f21(f22(x17701),x17703),x17704))+~P73(f21(f21(f22(x17701),x17703),x17702))+~P73(f21(f21(f22(x17701),x17702),x17704))
% 15.40/15.55 [1774]~P50(x17742)+~P70(x17742)+~P73(f21(x17741,x17744))+~P73(f21(f21(f22(x17742),x17743),f11(x17742,x17744,f3(x17742))))+P73(f21(x17741,f21(f21(f5(x17742),x17743),f57(x17743,x17741,x17742))))
% 15.40/15.55 [1786]~P5(x17861)+~P73(f21(f21(f22(x17861),f9(x17861,x17862,x17864)),f9(x17861,x17863,x17864)))+P73(f21(f21(f22(x17861),x17862),x17863))+~P73(f21(f21(f22(x17861),x17864),x17863))+~P73(f21(f21(f22(x17861),x17864),x17862))
% 15.40/15.55 [1734]~P7(a59,f3(a59),x17342)+~P8(a59,f3(a59),x17343)+~P73(f21(x17341,x17344))+P73(f21(x17341,f37(x17342,x17341,x17343)))+P73(f21(x17341,f11(a59,x17344,f21(f21(f5(a59),x17342),x17343))))
% 15.40/15.55 [1735]~P7(a59,f3(a59),x17352)+~P8(a59,f3(a59),x17353)+~P73(f21(x17351,x17354))+P73(f21(x17351,f47(x17352,x17351,x17353)))+P73(f21(x17351,f7(a59,x17354,f21(f21(f5(a59),x17352),x17353))))
% 15.40/15.55 [1794]~P7(a59,f3(a59),x17943)+~P8(a59,f3(a59),x17944)+~P73(f21(x17941,x17942))+~P73(f21(x17941,f11(a59,f37(x17943,x17941,x17944),x17944)))+P73(f21(x17941,f11(a59,x17942,f21(f21(f5(a59),x17943),x17944))))
% 15.40/15.55 [1795]~P7(a59,f3(a59),x17953)+~P8(a59,f3(a59),x17954)+~P73(f21(x17951,x17952))+~P73(f21(x17951,f7(a59,f47(x17953,x17951,x17954),x17954)))+P73(f21(x17951,f7(a59,x17952,f21(f21(f5(a59),x17953),x17954))))
% 15.40/15.55 [1807]~P4(x18072)+~P11(x18072,x18074,x18073,x18075,x18071)+P8(a58,f2(x18072,x18071),f2(x18072,x18073))+E(x18071,f3(f65(x18072)))+E(x18073,f3(f65(x18072)))
% 15.40/15.55 [1664]~P8(a58,x16645,x16641)+E(x16641,f3(a58))+P73(f21(x16642,x16643))+~P73(f21(x16642,f9(a58,x16644,x16641)))+~E(x16644,f11(a58,f21(f21(f5(a58),x16641),x16643),x16645))
% 15.40/15.55 [1775]P7(a59,x17751,x17752)+~P8(a59,x17753,x17754)+~P8(a59,x17753,x17755)+~P7(a59,x17754,f3(a59))+~P7(a59,f11(a59,f21(f21(f5(a59),x17753),x17752),x17755),f11(a59,f21(f21(f5(a59),x17753),x17751),x17754))
% 15.40/15.55 [1776]P7(a59,x17761,x17762)+~P8(a59,x17763,x17764)+~P8(a59,x17765,x17764)+~P7(a59,f3(a59),x17765)+~P7(a59,f11(a59,f21(f21(f5(a59),x17764),x17761),x17765),f11(a59,f21(f21(f5(a59),x17764),x17762),x17763))
% 15.40/15.55 [1783]~P4(x17832)+P11(x17832,x17833,x17831,x17834,x17835)+E(x17831,f3(f65(x17832)))+~E(x17835,f3(f65(x17832)))+~E(x17833,f11(f65(x17832),f21(f21(f5(f65(x17832)),x17834),x17831),x17835))
% 15.40/15.55 [1784]~P4(x17841)+P11(x17841,x17842,x17843,x17844,x17845)+~E(x17844,f3(f65(x17841)))+~E(x17845,f3(f65(x17841)))+~E(x17842,f11(f65(x17841),f21(f21(f5(f65(x17841)),x17844),x17843),x17845))
% 15.40/15.55 [1785]~P4(x17851)+P11(x17851,x17852,x17853,x17854,x17855)+~E(x17854,f3(f65(x17851)))+~E(x17853,f3(f65(x17851)))+~E(x17852,f11(f65(x17851),f21(f21(f5(f65(x17851)),x17854),x17853),x17855))
% 15.40/15.55 [1789]~P4(x17892)+P11(x17892,x17893,x17891,x17894,x17895)+~P8(a58,f2(x17892,x17895),f2(x17892,x17891))+E(x17891,f3(f65(x17892)))+~E(x17893,f11(f65(x17892),f21(f21(f5(f65(x17892)),x17894),x17891),x17895))
% 15.40/15.55 [1790]~P4(x17901)+P11(x17901,x17902,x17903,x17904,x17905)+~P8(a58,f2(x17901,x17905),f2(x17901,x17903))+~E(x17904,f3(f65(x17901)))+~E(x17902,f11(f65(x17901),f21(f21(f5(f65(x17901)),x17904),x17903),x17905))
% 15.40/15.55 [1510]~P72(x15104)+E(x15101,x15102)+~E(x15105,x15106)+E(x15103,f3(x15104))+~E(f11(x15104,x15105,f21(f21(f5(x15104),x15103),x15101)),f11(x15104,x15106,f21(f21(f5(x15104),x15103),x15102)))
% 15.40/15.55 [1816]~P50(x18161)+~P42(x18161)+~P73(f21(f21(f22(x18161),x18162),f11(x18161,x18163,x18166)))+~P73(f21(f21(f22(x18161),x18162),x18165))+P73(f21(f21(f22(x18161),x18162),f11(x18161,f7(x18161,x18163,f21(f21(f5(x18161),x18164),x18165)),x18166)))
% 15.40/15.55 [1841]~P50(x18411)+~P42(x18411)+P73(f21(f21(f22(x18411),x18412),f11(x18411,x18413,x18414)))+~P73(f21(f21(f22(x18411),x18412),x18415))+~P73(f21(f21(f22(x18411),x18412),f11(x18411,f7(x18411,x18413,f21(f21(f5(x18411),x18416),x18415)),x18414)))
% 15.40/15.55 [1122]~P30(x11221)+~P7(x11221,f3(x11221),x11223)+~P7(x11221,f3(x11221),x11222)+~E(x11223,f3(x11221))+~E(x11222,f3(x11221))+E(f11(x11221,x11222,x11223),f3(x11221))
% 15.40/15.55 [811]~P52(x8112)+~P53(x8112)+~P69(x8112)+~P35(x8112)+E(x8111,f3(x8112))+~E(f21(f21(f27(x8112),x8111),x8113),f3(x8112))
% 15.40/15.55 [812]~P52(x8122)+~P53(x8122)+~P69(x8122)+~P35(x8122)+~E(x8121,f3(a58))+~E(f21(f21(f27(x8122),x8123),x8121),f3(x8122))
% 15.40/15.55 [1459]~P54(x14593)+E(x14591,x14592)+~P7(x14593,f3(x14593),x14592)+~P7(x14593,f3(x14593),x14591)+~P8(a58,f3(a58),x14594)+~E(f21(f21(f27(x14593),x14591),x14594),f21(f21(f27(x14593),x14592),x14594))
% 15.40/15.55 [1513]~P8(a59,x15131,x15134)+E(f9(a59,x15132,x15131),x15133)+E(x15131,f3(a59))+P8(a59,f3(a59),x15131)+~P7(a59,x15134,f3(a59))+~E(x15132,f11(a59,f21(f21(f5(a59),x15131),x15133),x15134))
% 15.40/15.55 [1551]~P8(a59,x15514,x15511)+E(f9(a59,x15512,x15511),x15513)+E(x15511,f3(a59))+~P7(a59,f3(a59),x15514)+~P8(a59,f3(a59),x15511)+~E(x15512,f11(a59,f21(f21(f5(a59),x15511),x15513),x15514))
% 15.40/15.55 [1617]~P66(x16171)+~P7(x16171,x16173,x16175)+~P7(x16171,x16172,x16174)+~P7(x16171,f3(x16171),x16173)+~P7(x16171,f3(x16171),x16174)+P7(x16171,f21(f21(f5(x16171),x16172),x16173),f21(f21(f5(x16171),x16174),x16175))
% 15.40/15.55 [1618]~P66(x16181)+~P7(x16181,x16183,x16185)+~P7(x16181,x16182,x16184)+~P7(x16181,f3(x16181),x16183)+~P7(x16181,f3(x16181),x16182)+P7(x16181,f21(f21(f5(x16181),x16182),x16183),f21(f21(f5(x16181),x16184),x16185))
% 15.40/15.55 [1619]~P59(x16191)+~P7(x16191,x16193,x16195)+~P8(x16191,x16192,x16194)+~P7(x16191,f3(x16191),x16192)+~P8(x16191,f3(x16191),x16193)+P8(x16191,f21(f21(f5(x16191),x16192),x16193),f21(f21(f5(x16191),x16194),x16195))
% 15.40/15.55 [1620]~P59(x16201)+~P7(x16201,x16202,x16204)+~P8(x16201,x16203,x16205)+~P7(x16201,f3(x16201),x16203)+~P8(x16201,f3(x16201),x16202)+P8(x16201,f21(f21(f5(x16201),x16202),x16203),f21(f21(f5(x16201),x16204),x16205))
% 15.40/15.55 [1621]~P59(x16211)+~P8(x16211,x16213,x16215)+~P8(x16211,x16212,x16214)+~P7(x16211,f3(x16211),x16213)+~P7(x16211,f3(x16211),x16212)+P8(x16211,f21(f21(f5(x16211),x16212),x16213),f21(f21(f5(x16211),x16214),x16215))
% 15.40/15.55 [1622]~P59(x16221)+~P8(x16221,x16223,x16225)+~P8(x16221,x16222,x16224)+~P7(x16221,f3(x16221),x16223)+~P8(x16221,f3(x16221),x16224)+P8(x16221,f21(f21(f5(x16221),x16222),x16223),f21(f21(f5(x16221),x16224),x16225))
% 15.40/15.55 [1605]~P74(x16051,x16054,x16053)+~P8(a59,x16054,x16055)+~P7(a59,x16055,f3(a59))+~P8(a59,x16054,f3(a59))+P73(f21(x16051,x16052))+~E(x16053,f11(a59,f21(f21(f5(a59),x16054),x16052),x16055))
% 15.40/15.55 [1606]~P74(x16061,x16064,x16063)+~P8(a59,x16065,x16064)+~P7(a59,f3(a59),x16065)+~P8(a59,f3(a59),x16064)+P73(f21(x16061,x16062))+~E(x16063,f11(a59,f21(f21(f5(a59),x16064),x16062),x16065))
% 15.40/15.55 [1788]~P8(a59,x17885,x17883)+~P7(a59,x17883,f3(a59))+~P8(a59,x17885,f3(a59))+P73(f21(f21(x17881,x17882),x17883))+~P73(f21(f21(x17881,f9(a59,x17884,x17885)),f8(a59,x17884,x17885)))+~E(x17884,f11(a59,f21(f21(f5(a59),x17885),x17882),x17883))
% 15.40/15.55 [744]~P52(x7442)+~P53(x7442)+~P69(x7442)+~P35(x7442)+~E(x7443,f3(x7442))+E(x7441,f3(a58))+E(f21(f21(f27(x7442),x7443),x7441),f3(x7442))
% 15.40/15.55 [1616]~P8(a59,x16164,x16161)+~P8(a59,x16161,x16164)+E(f9(a59,x16162,x16161),x16163)+E(x16161,f3(a59))+~P7(a59,x16164,f3(a59))+~P7(a59,f3(a59),x16164)+~E(x16162,f11(a59,f21(f21(f5(a59),x16161),x16163),x16164))
% 15.40/15.55 [1831]~P4(x18312)+E(f24(x18312,x18313,x18311),x18314)+~E(f21(f13(x18312,x18314),f2(x18312,x18314)),f6(x18312))+E(x18311,f3(f65(x18312)))+P73(f21(f21(f22(f65(x18312)),f36(x18311,x18313,x18314,x18312)),x18313))+~P73(f21(f21(f22(f65(x18312)),x18314),x18313))+~P73(f21(f21(f22(f65(x18312)),x18314),x18311))
% 15.40/15.55 [1832]~P4(x18322)+E(f24(x18322,x18323,x18321),x18324)+~E(f21(f13(x18322,x18324),f2(x18322,x18324)),f6(x18322))+E(x18321,f3(f65(x18322)))+P73(f21(f21(f22(f65(x18322)),f36(x18321,x18323,x18324,x18322)),x18321))+~P73(f21(f21(f22(f65(x18322)),x18324),x18323))+~P73(f21(f21(f22(f65(x18322)),x18324),x18321))
% 15.40/15.55 [1833]~P4(x18332)+E(f24(x18332,x18331,x18333),x18334)+~E(f21(f13(x18332,x18334),f2(x18332,x18334)),f6(x18332))+E(x18331,f3(f65(x18332)))+P73(f21(f21(f22(f65(x18332)),f36(x18333,x18331,x18334,x18332)),x18333))+~P73(f21(f21(f22(f65(x18332)),x18334),x18333))+~P73(f21(f21(f22(f65(x18332)),x18334),x18331))
% 15.40/15.55 [1834]~P4(x18342)+E(f24(x18342,x18341,x18343),x18344)+~E(f21(f13(x18342,x18344),f2(x18342,x18344)),f6(x18342))+E(x18341,f3(f65(x18342)))+P73(f21(f21(f22(f65(x18342)),f36(x18343,x18341,x18344,x18342)),x18341))+~P73(f21(f21(f22(f65(x18342)),x18344),x18343))+~P73(f21(f21(f22(f65(x18342)),x18344),x18341))
% 15.40/15.55 [1837]~P4(x18371)+E(f24(x18371,x18372,x18373),x18374)+~E(f21(f13(x18371,x18374),f2(x18371,x18374)),f3(x18371))+~E(f21(f13(x18371,x18374),f2(x18371,x18374)),f6(x18371))+P73(f21(f21(f22(f65(x18371)),f36(x18373,x18372,x18374,x18371)),x18373))+~P73(f21(f21(f22(f65(x18371)),x18374),x18373))+~P73(f21(f21(f22(f65(x18371)),x18374),x18372))
% 15.40/15.55 [1838]~P4(x18381)+E(f24(x18381,x18382,x18383),x18384)+~E(f21(f13(x18381,x18384),f2(x18381,x18384)),f3(x18381))+~E(f21(f13(x18381,x18384),f2(x18381,x18384)),f6(x18381))+P73(f21(f21(f22(f65(x18381)),f36(x18383,x18382,x18384,x18381)),x18382))+~P73(f21(f21(f22(f65(x18381)),x18384),x18383))+~P73(f21(f21(f22(f65(x18381)),x18384),x18382))
% 15.40/15.55 [1850]~P4(x18502)+E(f24(x18502,x18503,x18501),x18504)+~E(f21(f13(x18502,x18504),f2(x18502,x18504)),f6(x18502))+E(x18501,f3(f65(x18502)))+~P73(f21(f21(f22(f65(x18502)),f36(x18501,x18503,x18504,x18502)),x18504))+~P73(f21(f21(f22(f65(x18502)),x18504),x18503))+~P73(f21(f21(f22(f65(x18502)),x18504),x18501))
% 15.40/15.55 [1851]~P4(x18512)+E(f24(x18512,x18511,x18513),x18514)+~E(f21(f13(x18512,x18514),f2(x18512,x18514)),f6(x18512))+E(x18511,f3(f65(x18512)))+~P73(f21(f21(f22(f65(x18512)),f36(x18513,x18511,x18514,x18512)),x18514))+~P73(f21(f21(f22(f65(x18512)),x18514),x18513))+~P73(f21(f21(f22(f65(x18512)),x18514),x18511))
% 15.40/15.55 [1854]~P4(x18541)+E(f24(x18541,x18542,x18543),x18544)+~E(f21(f13(x18541,x18544),f2(x18541,x18544)),f3(x18541))+~E(f21(f13(x18541,x18544),f2(x18541,x18544)),f6(x18541))+~P73(f21(f21(f22(f65(x18541)),f36(x18543,x18542,x18544,x18541)),x18544))+~P73(f21(f21(f22(f65(x18541)),x18544),x18543))+~P73(f21(f21(f22(f65(x18541)),x18544),x18542))
% 15.40/15.55 [1613]~P5(x16132)+E(f9(x16132,x16134,x16131),f9(x16132,x16135,x16133))+E(x16131,f3(x16132))+E(x16133,f3(x16132))+~E(f21(f21(f5(x16132),x16134),x16133),f21(f21(f5(x16132),x16131),x16135))+~P73(f21(f21(f22(x16132),x16131),x16134))+~P73(f21(f21(f22(x16132),x16133),x16135))
% 15.40/15.55 [1615]~P5(x16152)+~E(f9(x16152,x16154,x16153),f9(x16152,x16155,x16151))+E(x16151,f3(x16152))+E(x16153,f3(x16152))+E(f21(f21(f5(x16152),x16154),x16151),f21(f21(f5(x16152),x16153),x16155))+~P73(f21(f21(f22(x16152),x16151),x16155))+~P73(f21(f21(f22(x16152),x16153),x16154))
% 15.40/15.55 [1729]~P61(x17291)+~P7(x17291,x17295,x17296)+~P7(x17291,x17293,x17296)+~P7(x17291,f3(x17291),x17294)+~P7(x17291,f3(x17291),x17292)+~E(f11(x17291,x17292,x17294),f6(x17291))+P7(x17291,f11(x17291,f21(f21(f5(x17291),x17292),x17293),f21(f21(f5(x17291),x17294),x17295)),x17296)
% 15.40/15.55 [1730]~P62(x17301)+~P8(x17301,x17305,x17306)+~P8(x17301,x17303,x17306)+~P7(x17301,f3(x17301),x17304)+~P7(x17301,f3(x17301),x17302)+~E(f11(x17301,x17302,x17304),f6(x17301))+P8(x17301,f11(x17301,f21(f21(f5(x17301),x17302),x17303),f21(f21(f5(x17301),x17304),x17305)),x17306)
% 15.40/15.55 [1777]~P7(a59,x17775,x17773)+~P8(a59,x17776,x17775)+P7(a59,x17771,x17772)+~P7(a59,f3(a59),x17774)+~P8(a59,f3(a59),x17775)+~P7(a59,f3(a59),f11(a59,f21(f21(f5(a59),x17775),x17772),x17776))+~E(f11(a59,f21(f21(f5(a59),x17773),x17771),x17774),f11(a59,f21(f21(f5(a59),x17775),x17772),x17776))
% 15.40/15.55 [1778]~P7(a59,x17785,x17783)+~P8(a59,x17784,x17783)+P7(a59,x17781,x17782)+~P7(a59,f3(a59),x17786)+~P8(a59,f3(a59),x17785)+~P8(a59,f11(a59,f21(f21(f5(a59),x17785),x17781),x17786),f3(a59))+~E(f11(a59,f21(f21(f5(a59),x17783),x17782),x17784),f11(a59,f21(f21(f5(a59),x17785),x17781),x17786))
% 15.40/15.55 [1835]~P4(x18351)+E(f24(x18351,x18352,x18353),x18354)+~E(x18353,f3(f65(x18351)))+~E(x18352,f3(f65(x18351)))+~E(f21(f13(x18351,x18354),f2(x18351,x18354)),f3(x18351))+P73(f21(f21(f22(f65(x18351)),f36(x18353,x18352,x18354,x18351)),x18353))+~P73(f21(f21(f22(f65(x18351)),x18354),x18353))+~P73(f21(f21(f22(f65(x18351)),x18354),x18352))
% 15.40/15.55 [1836]~P4(x18361)+E(f24(x18361,x18362,x18363),x18364)+~E(x18363,f3(f65(x18361)))+~E(x18362,f3(f65(x18361)))+~E(f21(f13(x18361,x18364),f2(x18361,x18364)),f3(x18361))+P73(f21(f21(f22(f65(x18361)),f36(x18363,x18362,x18364,x18361)),x18362))+~P73(f21(f21(f22(f65(x18361)),x18364),x18363))+~P73(f21(f21(f22(f65(x18361)),x18364),x18362))
% 15.40/15.55 [1852]~P4(x18521)+E(f24(x18521,x18522,x18523),x18524)+~E(x18523,f3(f65(x18521)))+~E(x18522,f3(f65(x18521)))+~E(f21(f13(x18521,x18524),f2(x18521,x18524)),f3(x18521))+~P73(f21(f21(f22(f65(x18521)),f36(x18523,x18522,x18524,x18521)),x18524))+~P73(f21(f21(f22(f65(x18521)),x18524),x18523))+~P73(f21(f21(f22(f65(x18521)),x18524),x18522))
% 15.40/15.55 %EqnAxiom
% 15.40/15.55 [1]E(x11,x11)
% 15.40/15.55 [2]E(x22,x21)+~E(x21,x22)
% 15.40/15.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 15.40/15.55 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 15.40/15.55 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 15.40/15.55 [6]~E(x61,x62)+E(f21(x61,x63),f21(x62,x63))
% 15.40/15.55 [7]~E(x71,x72)+E(f21(x73,x71),f21(x73,x72))
% 15.40/15.55 [8]~E(x81,x82)+E(f3(x81),f3(x82))
% 15.40/15.55 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 15.40/15.55 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 15.40/15.55 [11]~E(x111,x112)+E(f11(x111,x113,x114),f11(x112,x113,x114))
% 15.40/15.55 [12]~E(x121,x122)+E(f11(x123,x121,x124),f11(x123,x122,x124))
% 15.40/15.55 [13]~E(x131,x132)+E(f11(x133,x134,x131),f11(x133,x134,x132))
% 15.40/15.55 [14]~E(x141,x142)+E(f16(x141,x143),f16(x142,x143))
% 15.40/15.55 [15]~E(x151,x152)+E(f16(x153,x151),f16(x153,x152))
% 15.40/15.55 [16]~E(x161,x162)+E(f65(x161),f65(x162))
% 15.40/15.55 [17]~E(x171,x172)+E(f42(x171,x173,x174),f42(x172,x173,x174))
% 15.40/15.55 [18]~E(x181,x182)+E(f42(x183,x181,x184),f42(x183,x182,x184))
% 15.40/15.55 [19]~E(x191,x192)+E(f42(x193,x194,x191),f42(x193,x194,x192))
% 15.40/15.55 [20]~E(x201,x202)+E(f7(x201,x203,x204),f7(x202,x203,x204))
% 15.40/15.55 [21]~E(x211,x212)+E(f7(x213,x211,x214),f7(x213,x212,x214))
% 15.40/15.55 [22]~E(x221,x222)+E(f7(x223,x224,x221),f7(x223,x224,x222))
% 15.40/15.55 [23]~E(x231,x232)+E(f27(x231),f27(x232))
% 15.40/15.55 [24]~E(x241,x242)+E(f5(x241),f5(x242))
% 15.40/15.55 [25]~E(x251,x252)+E(f6(x251),f6(x252))
% 15.40/15.55 [26]~E(x261,x262)+E(f12(x261,x263),f12(x262,x263))
% 15.40/15.55 [27]~E(x271,x272)+E(f12(x273,x271),f12(x273,x272))
% 15.40/15.55 [28]~E(x281,x282)+E(f22(x281),f22(x282))
% 15.40/15.55 [29]~E(x291,x292)+E(f39(x291,x293,x294),f39(x292,x293,x294))
% 15.40/15.55 [30]~E(x301,x302)+E(f39(x303,x301,x304),f39(x303,x302,x304))
% 15.40/15.55 [31]~E(x311,x312)+E(f39(x313,x314,x311),f39(x313,x314,x312))
% 15.40/15.55 [32]~E(x321,x322)+E(f13(x321,x323),f13(x322,x323))
% 15.40/15.55 [33]~E(x331,x332)+E(f13(x333,x331),f13(x333,x332))
% 15.40/15.55 [34]~E(x341,x342)+E(f9(x341,x343,x344),f9(x342,x343,x344))
% 15.40/15.55 [35]~E(x351,x352)+E(f9(x353,x351,x354),f9(x353,x352,x354))
% 15.40/15.55 [36]~E(x361,x362)+E(f9(x363,x364,x361),f9(x363,x364,x362))
% 15.40/15.55 [37]~E(x371,x372)+E(f50(x371,x373,x374),f50(x372,x373,x374))
% 15.40/15.55 [38]~E(x381,x382)+E(f50(x383,x381,x384),f50(x383,x382,x384))
% 15.40/15.55 [39]~E(x391,x392)+E(f50(x393,x394,x391),f50(x393,x394,x392))
% 15.40/15.55 [40]~E(x401,x402)+E(f45(x401,x403,x404),f45(x402,x403,x404))
% 15.40/15.55 [41]~E(x411,x412)+E(f45(x413,x411,x414),f45(x413,x412,x414))
% 15.40/15.55 [42]~E(x421,x422)+E(f45(x423,x424,x421),f45(x423,x424,x422))
% 15.40/15.55 [43]~E(x431,x432)+E(f24(x431,x433,x434),f24(x432,x433,x434))
% 15.40/15.55 [44]~E(x441,x442)+E(f24(x443,x441,x444),f24(x443,x442,x444))
% 15.40/15.55 [45]~E(x451,x452)+E(f24(x453,x454,x451),f24(x453,x454,x452))
% 15.40/15.55 [46]~E(x461,x462)+E(f31(x461,x463),f31(x462,x463))
% 15.40/15.55 [47]~E(x471,x472)+E(f31(x473,x471),f31(x473,x472))
% 15.40/15.55 [48]~E(x481,x482)+E(f44(x481,x483,x484),f44(x482,x483,x484))
% 15.40/15.55 [49]~E(x491,x492)+E(f44(x493,x491,x494),f44(x493,x492,x494))
% 15.40/15.55 [50]~E(x501,x502)+E(f44(x503,x504,x501),f44(x503,x504,x502))
% 15.40/15.55 [51]~E(x511,x512)+E(f36(x511,x513,x514,x515),f36(x512,x513,x514,x515))
% 15.40/15.55 [52]~E(x521,x522)+E(f36(x523,x521,x524,x525),f36(x523,x522,x524,x525))
% 15.40/15.55 [53]~E(x531,x532)+E(f36(x533,x534,x531,x535),f36(x533,x534,x532,x535))
% 15.40/15.55 [54]~E(x541,x542)+E(f36(x543,x544,x545,x541),f36(x543,x544,x545,x542))
% 15.40/15.55 [55]~E(x551,x552)+E(f19(x551,x553,x554),f19(x552,x553,x554))
% 15.40/15.55 [56]~E(x561,x562)+E(f19(x563,x561,x564),f19(x563,x562,x564))
% 15.40/15.55 [57]~E(x571,x572)+E(f19(x573,x574,x571),f19(x573,x574,x572))
% 15.40/15.55 [58]~E(x581,x582)+E(f49(x581,x583,x584),f49(x582,x583,x584))
% 15.40/15.55 [59]~E(x591,x592)+E(f49(x593,x591,x594),f49(x593,x592,x594))
% 15.40/15.55 [60]~E(x601,x602)+E(f49(x603,x604,x601),f49(x603,x604,x602))
% 15.40/15.55 [61]~E(x611,x612)+E(f8(x611,x613,x614),f8(x612,x613,x614))
% 15.40/15.55 [62]~E(x621,x622)+E(f8(x623,x621,x624),f8(x623,x622,x624))
% 15.40/15.55 [63]~E(x631,x632)+E(f8(x633,x634,x631),f8(x633,x634,x632))
% 15.40/15.55 [64]~E(x641,x642)+E(f66(x641,x643),f66(x642,x643))
% 15.40/15.55 [65]~E(x651,x652)+E(f66(x653,x651),f66(x653,x652))
% 15.40/15.55 [66]~E(x661,x662)+E(f20(x661,x663,x664),f20(x662,x663,x664))
% 15.40/15.55 [67]~E(x671,x672)+E(f20(x673,x671,x674),f20(x673,x672,x674))
% 15.40/15.55 [68]~E(x681,x682)+E(f20(x683,x684,x681),f20(x683,x684,x682))
% 15.40/15.55 [69]~E(x691,x692)+E(f17(x691,x693,x694),f17(x692,x693,x694))
% 15.40/15.55 [70]~E(x701,x702)+E(f17(x703,x701,x704),f17(x703,x702,x704))
% 15.40/15.55 [71]~E(x711,x712)+E(f17(x713,x714,x711),f17(x713,x714,x712))
% 15.40/15.55 [72]~E(x721,x722)+E(f43(x721,x723,x724),f43(x722,x723,x724))
% 15.40/15.55 [73]~E(x731,x732)+E(f43(x733,x731,x734),f43(x733,x732,x734))
% 15.40/15.55 [74]~E(x741,x742)+E(f43(x743,x744,x741),f43(x743,x744,x742))
% 15.40/15.55 [75]~E(x751,x752)+E(f26(x751,x753,x754,x755,x756),f26(x752,x753,x754,x755,x756))
% 15.40/15.55 [76]~E(x761,x762)+E(f26(x763,x761,x764,x765,x766),f26(x763,x762,x764,x765,x766))
% 15.40/15.55 [77]~E(x771,x772)+E(f26(x773,x774,x771,x775,x776),f26(x773,x774,x772,x775,x776))
% 15.40/15.55 [78]~E(x781,x782)+E(f26(x783,x784,x785,x781,x786),f26(x783,x784,x785,x782,x786))
% 15.40/15.55 [79]~E(x791,x792)+E(f26(x793,x794,x795,x796,x791),f26(x793,x794,x795,x796,x792))
% 15.40/15.55 [80]~E(x801,x802)+E(f46(x801,x803,x804),f46(x802,x803,x804))
% 15.40/15.55 [81]~E(x811,x812)+E(f46(x813,x811,x814),f46(x813,x812,x814))
% 15.40/15.55 [82]~E(x821,x822)+E(f46(x823,x824,x821),f46(x823,x824,x822))
% 15.40/15.55 [83]~E(x831,x832)+E(f18(x831,x833,x834),f18(x832,x833,x834))
% 15.40/15.55 [84]~E(x841,x842)+E(f18(x843,x841,x844),f18(x843,x842,x844))
% 15.40/15.55 [85]~E(x851,x852)+E(f18(x853,x854,x851),f18(x853,x854,x852))
% 15.40/15.55 [86]~E(x861,x862)+E(f10(x861,x863),f10(x862,x863))
% 15.40/15.55 [87]~E(x871,x872)+E(f10(x873,x871),f10(x873,x872))
% 15.40/15.55 [88]~E(x881,x882)+E(f53(x881,x883,x884),f53(x882,x883,x884))
% 15.40/15.55 [89]~E(x891,x892)+E(f53(x893,x891,x894),f53(x893,x892,x894))
% 15.40/15.55 [90]~E(x901,x902)+E(f53(x903,x904,x901),f53(x903,x904,x902))
% 15.40/15.55 [91]~E(x911,x912)+E(f40(x911,x913,x914),f40(x912,x913,x914))
% 15.40/15.55 [92]~E(x921,x922)+E(f40(x923,x921,x924),f40(x923,x922,x924))
% 15.40/15.55 [93]~E(x931,x932)+E(f40(x933,x934,x931),f40(x933,x934,x932))
% 15.40/15.55 [94]~E(x941,x942)+E(f51(x941,x943),f51(x942,x943))
% 15.40/15.55 [95]~E(x951,x952)+E(f51(x953,x951),f51(x953,x952))
% 15.40/15.55 [96]~E(x961,x962)+E(f37(x961,x963,x964),f37(x962,x963,x964))
% 15.40/15.55 [97]~E(x971,x972)+E(f37(x973,x971,x974),f37(x973,x972,x974))
% 15.40/15.55 [98]~E(x981,x982)+E(f37(x983,x984,x981),f37(x983,x984,x982))
% 15.40/15.55 [99]~E(x991,x992)+E(f30(x991,x993),f30(x992,x993))
% 15.40/15.55 [100]~E(x1001,x1002)+E(f30(x1003,x1001),f30(x1003,x1002))
% 15.40/15.55 [101]~E(x1011,x1012)+E(f48(x1011,x1013,x1014),f48(x1012,x1013,x1014))
% 15.40/15.55 [102]~E(x1021,x1022)+E(f48(x1023,x1021,x1024),f48(x1023,x1022,x1024))
% 15.40/15.55 [103]~E(x1031,x1032)+E(f48(x1033,x1034,x1031),f48(x1033,x1034,x1032))
% 15.40/15.55 [104]~E(x1041,x1042)+E(f28(x1041,x1043),f28(x1042,x1043))
% 15.40/15.55 [105]~E(x1051,x1052)+E(f28(x1053,x1051),f28(x1053,x1052))
% 15.40/15.55 [106]~E(x1061,x1062)+E(f23(x1061,x1063,x1064),f23(x1062,x1063,x1064))
% 15.40/15.55 [107]~E(x1071,x1072)+E(f23(x1073,x1071,x1074),f23(x1073,x1072,x1074))
% 15.40/15.55 [108]~E(x1081,x1082)+E(f23(x1083,x1084,x1081),f23(x1083,x1084,x1082))
% 15.40/15.55 [109]~E(x1091,x1092)+E(f56(x1091,x1093,x1094),f56(x1092,x1093,x1094))
% 15.40/15.55 [110]~E(x1101,x1102)+E(f56(x1103,x1101,x1104),f56(x1103,x1102,x1104))
% 15.40/15.55 [111]~E(x1111,x1112)+E(f56(x1113,x1114,x1111),f56(x1113,x1114,x1112))
% 15.40/15.55 [112]~E(x1121,x1122)+E(f29(x1121,x1123),f29(x1122,x1123))
% 15.40/15.55 [113]~E(x1131,x1132)+E(f29(x1133,x1131),f29(x1133,x1132))
% 15.40/15.55 [114]~E(x1141,x1142)+E(f55(x1141,x1143,x1144,x1145),f55(x1142,x1143,x1144,x1145))
% 15.40/15.55 [115]~E(x1151,x1152)+E(f55(x1153,x1151,x1154,x1155),f55(x1153,x1152,x1154,x1155))
% 15.40/15.55 [116]~E(x1161,x1162)+E(f55(x1163,x1164,x1161,x1165),f55(x1163,x1164,x1162,x1165))
% 15.40/15.55 [117]~E(x1171,x1172)+E(f55(x1173,x1174,x1175,x1171),f55(x1173,x1174,x1175,x1172))
% 15.40/15.55 [118]~E(x1181,x1182)+E(f25(x1181,x1183,x1184),f25(x1182,x1183,x1184))
% 15.40/15.55 [119]~E(x1191,x1192)+E(f25(x1193,x1191,x1194),f25(x1193,x1192,x1194))
% 15.40/15.55 [120]~E(x1201,x1202)+E(f25(x1203,x1204,x1201),f25(x1203,x1204,x1202))
% 15.40/15.55 [121]~E(x1211,x1212)+E(f14(x1211,x1213),f14(x1212,x1213))
% 15.40/15.55 [122]~E(x1221,x1222)+E(f14(x1223,x1221),f14(x1223,x1222))
% 15.40/15.55 [123]~E(x1231,x1232)+E(f33(x1231,x1233,x1234),f33(x1232,x1233,x1234))
% 15.40/15.55 [124]~E(x1241,x1242)+E(f33(x1243,x1241,x1244),f33(x1243,x1242,x1244))
% 15.40/15.55 [125]~E(x1251,x1252)+E(f33(x1253,x1254,x1251),f33(x1253,x1254,x1252))
% 15.40/15.55 [126]~E(x1261,x1262)+E(f38(x1261,x1263,x1264),f38(x1262,x1263,x1264))
% 15.40/15.55 [127]~E(x1271,x1272)+E(f38(x1273,x1271,x1274),f38(x1273,x1272,x1274))
% 15.40/15.55 [128]~E(x1281,x1282)+E(f38(x1283,x1284,x1281),f38(x1283,x1284,x1282))
% 15.40/15.55 [129]~E(x1291,x1292)+E(f41(x1291),f41(x1292))
% 15.40/15.55 [130]~E(x1301,x1302)+E(f34(x1301,x1303),f34(x1302,x1303))
% 15.40/15.55 [131]~E(x1311,x1312)+E(f34(x1313,x1311),f34(x1313,x1312))
% 15.40/15.55 [132]~E(x1321,x1322)+E(f47(x1321,x1323,x1324),f47(x1322,x1323,x1324))
% 15.40/15.55 [133]~E(x1331,x1332)+E(f47(x1333,x1331,x1334),f47(x1333,x1332,x1334))
% 15.40/15.55 [134]~E(x1341,x1342)+E(f47(x1343,x1344,x1341),f47(x1343,x1344,x1342))
% 15.40/15.55 [135]~E(x1351,x1352)+E(f52(x1351,x1353,x1354),f52(x1352,x1353,x1354))
% 15.40/15.55 [136]~E(x1361,x1362)+E(f52(x1363,x1361,x1364),f52(x1363,x1362,x1364))
% 15.40/15.55 [137]~E(x1371,x1372)+E(f52(x1373,x1374,x1371),f52(x1373,x1374,x1372))
% 15.40/15.55 [138]~E(x1381,x1382)+E(f32(x1381,x1383),f32(x1382,x1383))
% 15.40/15.55 [139]~E(x1391,x1392)+E(f32(x1393,x1391),f32(x1393,x1392))
% 15.40/15.55 [140]~E(x1401,x1402)+E(f15(x1401,x1403,x1404,x1405),f15(x1402,x1403,x1404,x1405))
% 15.40/15.55 [141]~E(x1411,x1412)+E(f15(x1413,x1411,x1414,x1415),f15(x1413,x1412,x1414,x1415))
% 15.40/15.55 [142]~E(x1421,x1422)+E(f15(x1423,x1424,x1421,x1425),f15(x1423,x1424,x1422,x1425))
% 15.40/15.55 [143]~E(x1431,x1432)+E(f15(x1433,x1434,x1435,x1431),f15(x1433,x1434,x1435,x1432))
% 15.40/15.55 [144]~E(x1441,x1442)+E(f57(x1441,x1443,x1444),f57(x1442,x1443,x1444))
% 15.40/15.55 [145]~E(x1451,x1452)+E(f57(x1453,x1451,x1454),f57(x1453,x1452,x1454))
% 15.40/15.55 [146]~E(x1461,x1462)+E(f57(x1463,x1464,x1461),f57(x1463,x1464,x1462))
% 15.40/15.55 [147]~E(x1471,x1472)+E(f54(x1471,x1473,x1474),f54(x1472,x1473,x1474))
% 15.40/15.55 [148]~E(x1481,x1482)+E(f54(x1483,x1481,x1484),f54(x1483,x1482,x1484))
% 15.40/15.55 [149]~E(x1491,x1492)+E(f54(x1493,x1494,x1491),f54(x1493,x1494,x1492))
% 15.40/15.55 [150]~E(x1501,x1502)+E(f35(x1501,x1503),f35(x1502,x1503))
% 15.40/15.55 [151]~E(x1511,x1512)+E(f35(x1513,x1511),f35(x1513,x1512))
% 15.40/15.55 [152]~P1(x1521)+P1(x1522)+~E(x1521,x1522)
% 15.40/15.55 [153]~P73(x1531)+P73(x1532)+~E(x1531,x1532)
% 15.40/15.55 [154]~P51(x1541)+P51(x1542)+~E(x1541,x1542)
% 15.40/15.55 [155]~P2(x1551)+P2(x1552)+~E(x1551,x1552)
% 15.40/15.55 [156]P7(x1562,x1563,x1564)+~E(x1561,x1562)+~P7(x1561,x1563,x1564)
% 15.40/15.55 [157]P7(x1573,x1572,x1574)+~E(x1571,x1572)+~P7(x1573,x1571,x1574)
% 15.40/15.55 [158]P7(x1583,x1584,x1582)+~E(x1581,x1582)+~P7(x1583,x1584,x1581)
% 15.40/15.55 [159]P74(x1592,x1593,x1594)+~E(x1591,x1592)+~P74(x1591,x1593,x1594)
% 15.40/15.55 [160]P74(x1603,x1602,x1604)+~E(x1601,x1602)+~P74(x1603,x1601,x1604)
% 15.40/15.55 [161]P74(x1613,x1614,x1612)+~E(x1611,x1612)+~P74(x1613,x1614,x1611)
% 15.40/15.55 [162]~P32(x1621)+P32(x1622)+~E(x1621,x1622)
% 15.40/15.55 [163]P11(x1632,x1633,x1634,x1635,x1636)+~E(x1631,x1632)+~P11(x1631,x1633,x1634,x1635,x1636)
% 15.40/15.55 [164]P11(x1643,x1642,x1644,x1645,x1646)+~E(x1641,x1642)+~P11(x1643,x1641,x1644,x1645,x1646)
% 15.40/15.55 [165]P11(x1653,x1654,x1652,x1655,x1656)+~E(x1651,x1652)+~P11(x1653,x1654,x1651,x1655,x1656)
% 15.40/15.55 [166]P11(x1663,x1664,x1665,x1662,x1666)+~E(x1661,x1662)+~P11(x1663,x1664,x1665,x1661,x1666)
% 15.40/15.55 [167]P11(x1673,x1674,x1675,x1676,x1672)+~E(x1671,x1672)+~P11(x1673,x1674,x1675,x1676,x1671)
% 15.40/15.55 [168]~P48(x1681)+P48(x1682)+~E(x1681,x1682)
% 15.40/15.55 [169]~P4(x1691)+P4(x1692)+~E(x1691,x1692)
% 15.40/15.55 [170]~P46(x1701)+P46(x1702)+~E(x1701,x1702)
% 15.40/15.55 [171]P8(x1712,x1713,x1714)+~E(x1711,x1712)+~P8(x1711,x1713,x1714)
% 15.40/15.55 [172]P8(x1723,x1722,x1724)+~E(x1721,x1722)+~P8(x1723,x1721,x1724)
% 15.40/15.55 [173]P8(x1733,x1734,x1732)+~E(x1731,x1732)+~P8(x1733,x1734,x1731)
% 15.40/15.55 [174]~P30(x1741)+P30(x1742)+~E(x1741,x1742)
% 15.40/15.55 [175]~P3(x1751)+P3(x1752)+~E(x1751,x1752)
% 15.40/15.55 [176]~P20(x1761)+P20(x1762)+~E(x1761,x1762)
% 15.40/15.55 [177]~P49(x1771)+P49(x1772)+~E(x1771,x1772)
% 15.40/15.55 [178]~P25(x1781)+P25(x1782)+~E(x1781,x1782)
% 15.40/15.55 [179]~P50(x1791)+P50(x1792)+~E(x1791,x1792)
% 15.40/15.55 [180]P9(x1802,x1803)+~E(x1801,x1802)+~P9(x1801,x1803)
% 15.40/15.55 [181]P9(x1813,x1812)+~E(x1811,x1812)+~P9(x1813,x1811)
% 15.40/15.55 [182]~P57(x1821)+P57(x1822)+~E(x1821,x1822)
% 15.40/15.55 [183]~P59(x1831)+P59(x1832)+~E(x1831,x1832)
% 15.40/15.55 [184]~P47(x1841)+P47(x1842)+~E(x1841,x1842)
% 15.40/15.55 [185]~P52(x1851)+P52(x1852)+~E(x1851,x1852)
% 15.40/15.55 [186]~P35(x1861)+P35(x1862)+~E(x1861,x1862)
% 15.40/15.55 [187]~P69(x1871)+P69(x1872)+~E(x1871,x1872)
% 15.40/15.55 [188]~P68(x1881)+P68(x1882)+~E(x1881,x1882)
% 15.40/15.55 [189]~P37(x1891)+P37(x1892)+~E(x1891,x1892)
% 15.40/15.55 [190]~P53(x1901)+P53(x1902)+~E(x1901,x1902)
% 15.40/15.55 [191]~P21(x1911)+P21(x1912)+~E(x1911,x1912)
% 15.40/15.55 [192]~P54(x1921)+P54(x1922)+~E(x1921,x1922)
% 15.40/15.55 [193]~P72(x1931)+P72(x1932)+~E(x1931,x1932)
% 15.40/15.55 [194]~P40(x1941)+P40(x1942)+~E(x1941,x1942)
% 15.40/15.55 [195]~P34(x1951)+P34(x1952)+~E(x1951,x1952)
% 15.40/15.55 [196]~P33(x1961)+P33(x1962)+~E(x1961,x1962)
% 15.40/15.55 [197]~P12(x1971)+P12(x1972)+~E(x1971,x1972)
% 15.40/15.55 [198]~P55(x1981)+P55(x1982)+~E(x1981,x1982)
% 15.40/15.55 [199]~P67(x1991)+P67(x1992)+~E(x1991,x1992)
% 15.40/15.55 [200]~P19(x2001)+P19(x2002)+~E(x2001,x2002)
% 15.40/15.55 [201]~P39(x2011)+P39(x2012)+~E(x2011,x2012)
% 15.40/15.55 [202]~P36(x2021)+P36(x2022)+~E(x2021,x2022)
% 15.40/15.55 [203]~P16(x2031)+P16(x2032)+~E(x2031,x2032)
% 15.40/15.55 [204]~P66(x2041)+P66(x2042)+~E(x2041,x2042)
% 15.40/15.55 [205]~P5(x2051)+P5(x2052)+~E(x2051,x2052)
% 15.40/15.55 [206]~P43(x2061)+P43(x2062)+~E(x2061,x2062)
% 15.40/15.55 [207]~P15(x2071)+P15(x2072)+~E(x2071,x2072)
% 15.40/15.55 [208]~P42(x2081)+P42(x2082)+~E(x2081,x2082)
% 15.40/15.55 [209]~P41(x2091)+P41(x2092)+~E(x2091,x2092)
% 15.40/15.55 [210]~P13(x2101)+P13(x2102)+~E(x2101,x2102)
% 15.40/15.55 [211]~P29(x2111)+P29(x2112)+~E(x2111,x2112)
% 15.40/15.55 [212]~P27(x2121)+P27(x2122)+~E(x2121,x2122)
% 15.40/15.55 [213]~P24(x2131)+P24(x2132)+~E(x2131,x2132)
% 15.40/15.55 [214]~P58(x2141)+P58(x2142)+~E(x2141,x2142)
% 15.40/15.55 [215]~P64(x2151)+P64(x2152)+~E(x2151,x2152)
% 15.40/15.55 [216]~P38(x2161)+P38(x2162)+~E(x2161,x2162)
% 15.40/15.55 [217]~P56(x2171)+P56(x2172)+~E(x2171,x2172)
% 15.40/15.55 [218]~P18(x2181)+P18(x2182)+~E(x2181,x2182)
% 15.40/15.55 [219]~P70(x2191)+P70(x2192)+~E(x2191,x2192)
% 15.40/15.55 [220]~P22(x2201)+P22(x2202)+~E(x2201,x2202)
% 15.40/15.55 [221]~P14(x2211)+P14(x2212)+~E(x2211,x2212)
% 15.40/15.55 [222]~P65(x2221)+P65(x2222)+~E(x2221,x2222)
% 15.40/15.55 [223]~P71(x2231)+P71(x2232)+~E(x2231,x2232)
% 15.40/15.55 [224]~P28(x2241)+P28(x2242)+~E(x2241,x2242)
% 15.40/15.55 [225]~P45(x2251)+P45(x2252)+~E(x2251,x2252)
% 15.40/15.55 [226]~P61(x2261)+P61(x2262)+~E(x2261,x2262)
% 15.40/15.55 [227]~P63(x2271)+P63(x2272)+~E(x2271,x2272)
% 15.40/15.55 [228]~P60(x2281)+P60(x2282)+~E(x2281,x2282)
% 15.40/15.55 [229]~P44(x2291)+P44(x2292)+~E(x2291,x2292)
% 15.40/15.55 [230]~P75(x2301)+P75(x2302)+~E(x2301,x2302)
% 15.40/15.55 [231]~P31(x2311)+P31(x2312)+~E(x2311,x2312)
% 15.40/15.55 [232]~P23(x2321)+P23(x2322)+~E(x2321,x2322)
% 15.40/15.55 [233]~P26(x2331)+P26(x2332)+~E(x2331,x2332)
% 15.40/15.55 [234]~P62(x2341)+P62(x2342)+~E(x2341,x2342)
% 15.40/15.55 [235]P10(x2352,x2353,x2354,x2355)+~E(x2351,x2352)+~P10(x2351,x2353,x2354,x2355)
% 15.40/15.55 [236]P10(x2363,x2362,x2364,x2365)+~E(x2361,x2362)+~P10(x2363,x2361,x2364,x2365)
% 15.40/15.55 [237]P10(x2373,x2374,x2372,x2375)+~E(x2371,x2372)+~P10(x2373,x2374,x2371,x2375)
% 15.40/15.55 [238]P10(x2383,x2384,x2385,x2382)+~E(x2381,x2382)+~P10(x2383,x2384,x2385,x2381)
% 15.40/15.55 [239]~P17(x2391)+P17(x2392)+~E(x2391,x2392)
% 15.40/15.55 [240]~P6(x2401)+P6(x2402)+~E(x2401,x2402)
% 15.40/15.55
% 15.40/15.55 %-------------------------------------------
% 15.40/15.58 cnf(1861,plain,
% 15.40/15.58 (E(a62,f2(a1,a61))),
% 15.40/15.58 inference(scs_inference,[],[385,2])).
% 15.40/15.58 cnf(1862,plain,
% 15.40/15.58 (~P8(a59,x18621,x18621)),
% 15.40/15.58 inference(scs_inference,[],[322,385,2,727])).
% 15.40/15.58 cnf(1870,plain,
% 15.40/15.58 (~P7(a59,f6(a59),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[322,385,412,398,437,2,727,707,706,715,850])).
% 15.40/15.58 cnf(1873,plain,
% 15.40/15.58 (P7(a58,f9(a58,x18731,x18732),x18731)),
% 15.40/15.58 inference(rename_variables,[],[432])).
% 15.40/15.58 cnf(1876,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x18761,x18762),x18762)),
% 15.40/15.58 inference(rename_variables,[],[506])).
% 15.40/15.58 cnf(1879,plain,
% 15.40/15.58 (E(f11(a58,x18791,x18792),f11(a58,x18792,x18791))),
% 15.40/15.58 inference(rename_variables,[],[419])).
% 15.40/15.58 cnf(1882,plain,
% 15.40/15.58 (P7(a58,x18821,f11(a58,x18822,x18821))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(1886,plain,
% 15.40/15.58 (P8(a59,x18861,f11(a59,x18861,f6(a59)))),
% 15.40/15.58 inference(scs_inference,[],[394,322,385,412,429,432,506,419,398,437,444,2,727,707,706,715,850,726,890,851,1261,1260,1184])).
% 15.40/15.58 cnf(1887,plain,
% 15.40/15.58 (P7(a59,x18871,x18871)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(1890,plain,
% 15.40/15.58 (P7(a58,x18901,f11(a58,x18902,x18901))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(1893,plain,
% 15.40/15.58 (P7(a59,x18931,x18931)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(1898,plain,
% 15.40/15.58 (E(f11(a58,x18981,x18982),f11(a58,x18982,x18981))),
% 15.40/15.58 inference(rename_variables,[],[419])).
% 15.40/15.58 cnf(1901,plain,
% 15.40/15.58 (P8(a58,x19011,f11(a58,f11(a58,x19012,x19011),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(1904,plain,
% 15.40/15.58 (P7(a58,x19041,f11(a58,x19042,x19041))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(1907,plain,
% 15.40/15.58 (P7(a58,x19071,f11(a58,x19072,x19071))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(1910,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x19101,x19102),x19101)),
% 15.40/15.58 inference(rename_variables,[],[507])).
% 15.40/15.58 cnf(1915,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x19151,x19152),x19152)),
% 15.40/15.58 inference(rename_variables,[],[506])).
% 15.40/15.58 cnf(1918,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x19181,x19182),x19182)),
% 15.40/15.58 inference(rename_variables,[],[506])).
% 15.40/15.58 cnf(1921,plain,
% 15.40/15.58 (~P7(a58,f11(a58,x19211,f6(a58)),x19211)),
% 15.40/15.58 inference(rename_variables,[],[508])).
% 15.40/15.58 cnf(1924,plain,
% 15.40/15.58 (~P7(a58,f11(a58,x19241,f6(a58)),x19241)),
% 15.40/15.58 inference(rename_variables,[],[508])).
% 15.40/15.58 cnf(1927,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x19271,x19272),x19271)),
% 15.40/15.58 inference(rename_variables,[],[507])).
% 15.40/15.58 cnf(1929,plain,
% 15.40/15.58 (~E(f11(a58,x19291,f11(a58,x19292,f6(a58))),x19292)),
% 15.40/15.58 inference(scs_inference,[],[394,1887,322,385,412,429,1882,1890,1904,432,506,1876,1915,1918,507,1910,419,1879,398,437,508,1921,465,444,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885])).
% 15.40/15.58 cnf(1930,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x19301,x19302),x19302)),
% 15.40/15.58 inference(rename_variables,[],[506])).
% 15.40/15.58 cnf(1933,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x19331,x19332),x19332),x19331)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(1935,plain,
% 15.40/15.58 (~E(f11(a58,x19351,f17(a1,a64,a61)),x19351)),
% 15.40/15.58 inference(scs_inference,[],[394,1887,322,385,412,492,429,1882,1890,1904,432,506,1876,1915,1918,507,1910,419,1879,398,437,508,1921,433,465,444,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711])).
% 15.40/15.58 cnf(1940,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),f6(a58)),x19401))),
% 15.40/15.58 inference(rename_variables,[],[421])).
% 15.40/15.58 cnf(1952,plain,
% 15.40/15.58 (~E(f11(a58,x19521,f6(a58)),f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[505])).
% 15.40/15.58 cnf(1955,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x19551,x19552),x19552),x19551)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(1960,plain,
% 15.40/15.58 (P7(a59,x19601,x19601)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(1963,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x19631),x19631))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(1966,plain,
% 15.40/15.58 (~E(f11(a58,x19661,f6(a58)),f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[505])).
% 15.40/15.58 cnf(1969,plain,
% 15.40/15.58 (~E(f11(a58,x19691,f6(a58)),f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[505])).
% 15.40/15.58 cnf(1972,plain,
% 15.40/15.58 (~P8(a58,x19721,x19721)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(1975,plain,
% 15.40/15.58 (~P8(a58,x19751,x19751)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(1978,plain,
% 15.40/15.58 (~P7(a58,f11(a58,x19781,f6(a58)),x19781)),
% 15.40/15.58 inference(rename_variables,[],[508])).
% 15.40/15.58 cnf(1983,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x19831,x19832),x19832),x19831)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(1985,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x19851,x19852),x19852),x19851)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(1987,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x19871,x19872),x19872),x19871)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(1989,plain,
% 15.40/15.58 (P8(a58,x19891,f11(a58,f11(a58,x19891,x19892),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[466])).
% 15.40/15.58 cnf(1991,plain,
% 15.40/15.58 (~P8(a58,x19911,x19911)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(1995,plain,
% 15.40/15.58 (P7(a58,x19951,f11(a58,x19951,x19952))),
% 15.40/15.58 inference(rename_variables,[],[430])).
% 15.40/15.58 cnf(1997,plain,
% 15.40/15.58 (P7(a58,f3(a58),x19971)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(1999,plain,
% 15.40/15.58 (E(f11(a58,x19991,f3(a58)),x19991)),
% 15.40/15.58 inference(rename_variables,[],[401])).
% 15.40/15.58 cnf(2001,plain,
% 15.40/15.58 (~P8(a59,f6(a59),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,394,1887,1893,494,1972,1975,322,330,400,385,487,412,492,510,429,1882,1890,1904,430,432,506,1876,1915,1918,507,1910,419,1879,398,437,508,1921,1924,1978,433,1933,1955,1983,1985,401,465,1901,466,444,505,1952,1966,417,1963,421,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918])).
% 15.40/15.58 cnf(2004,plain,
% 15.40/15.58 (P7(a58,f7(a58,x20041,x20042),x20041)),
% 15.40/15.58 inference(rename_variables,[],[431])).
% 15.40/15.58 cnf(2005,plain,
% 15.40/15.58 (P7(a58,f3(a58),x20051)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2012,plain,
% 15.40/15.58 (P7(a58,f3(a58),x20121)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2020,plain,
% 15.40/15.58 (~E(f6(a58),f3(a58))),
% 15.40/15.58 inference(scs_inference,[],[486,394,1887,1893,494,1972,1975,321,322,324,329,330,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,508,1921,1924,1978,433,1933,1955,1983,1985,401,465,1901,466,444,505,1952,1966,417,1963,421,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640])).
% 15.40/15.58 cnf(2024,plain,
% 15.40/15.58 (E(x20241,f11(a58,f3(a58),x20241))),
% 15.40/15.58 inference(scs_inference,[],[486,394,1887,1893,494,1972,1975,321,322,324,329,330,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,508,1921,1924,1978,433,1933,1955,1983,1985,401,465,1901,466,444,505,1952,1966,417,1963,421,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264])).
% 15.40/15.58 cnf(2025,plain,
% 15.40/15.58 (P8(a58,x20251,f11(a58,f11(a58,x20252,x20251),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(2028,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x20281,x20282),x20282),x20281)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2033,plain,
% 15.40/15.58 (P8(a58,x20331,f11(a58,x20331,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2034,plain,
% 15.40/15.58 (P8(a58,x20341,f11(a58,f11(a58,x20342,x20341),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(2037,plain,
% 15.40/15.58 (P8(a58,x20371,f11(a58,x20371,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2039,plain,
% 15.40/15.58 (P8(a58,f3(a58),f6(a58))),
% 15.40/15.58 inference(scs_inference,[],[486,394,1887,1893,494,1972,1975,321,322,324,329,330,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,2033,2037,508,1921,1924,1978,433,1933,1955,1983,1985,1987,401,465,1901,2025,466,444,505,1952,1966,417,1963,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144])).
% 15.40/15.58 cnf(2040,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),f6(a58)),x20401))),
% 15.40/15.58 inference(rename_variables,[],[421])).
% 15.40/15.58 cnf(2041,plain,
% 15.40/15.58 (P8(a58,x20411,f11(a58,x20411,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2044,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x20441),x20441))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2045,plain,
% 15.40/15.58 (E(f7(a58,x20451,x20451),f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[398])).
% 15.40/15.58 cnf(2050,plain,
% 15.40/15.58 (~E(f11(a58,x20501,f6(a58)),x20501)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2053,plain,
% 15.40/15.58 (~E(f11(a58,x20531,f6(a58)),x20531)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2056,plain,
% 15.40/15.58 (~E(f11(a58,x20561,f6(a58)),x20561)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2061,plain,
% 15.40/15.58 (E(f11(a58,f3(a58),x20611),x20611)),
% 15.40/15.58 inference(rename_variables,[],[405])).
% 15.40/15.58 cnf(2062,plain,
% 15.40/15.58 (P8(a58,x20621,f11(a58,x20621,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2065,plain,
% 15.40/15.58 (P8(a58,x20651,f11(a58,x20651,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2069,plain,
% 15.40/15.58 (~P8(a59,f4(a59,f3(a59)),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,281,321,322,324,329,330,370,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,2033,2037,2041,2062,508,1921,1924,1978,433,1933,1955,1983,1985,1987,401,405,499,2050,2053,465,1901,2025,466,444,505,1952,1966,417,1963,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957])).
% 15.40/15.58 cnf(2071,plain,
% 15.40/15.58 (~P8(a59,f3(a59),f4(a59,f3(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,281,314,321,322,324,329,330,370,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,2033,2037,2041,2062,508,1921,1924,1978,433,1933,1955,1983,1985,1987,401,405,499,2050,2053,465,1901,2025,466,444,505,1952,1966,417,1963,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955])).
% 15.40/15.58 cnf(2073,plain,
% 15.40/15.58 (~P7(a59,f6(a59),f4(a59,f6(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,281,314,321,322,324,329,330,370,400,1997,2005,385,386,487,412,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,2033,2037,2041,2062,508,1921,1924,1978,433,1933,1955,1983,1985,1987,401,405,499,2050,2053,465,1901,2025,466,444,505,1952,1966,417,1963,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954])).
% 15.40/15.58 cnf(2078,plain,
% 15.40/15.58 (~E(f11(a58,x20781,f6(a58)),x20781)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2081,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x20811,x20812),x20812),x20811)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2090,plain,
% 15.40/15.58 (~P8(a58,x20901,f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[497])).
% 15.40/15.58 cnf(2093,plain,
% 15.40/15.58 (~E(f11(a58,x20931,f6(a58)),x20931)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2095,plain,
% 15.40/15.58 (~E(x20951,f9(a58,f21(f21(f5(a58),f11(a58,f3(a58),f6(a58))),f11(a58,x20951,f6(a58))),f11(a58,f3(a58),f6(a58))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,1991,244,281,282,304,314,321,322,324,329,330,336,345,370,400,1997,2005,497,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,401,405,499,2050,2053,2056,2078,465,1901,2025,466,444,505,1952,1966,417,1963,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539])).
% 15.40/15.58 cnf(2096,plain,
% 15.40/15.58 (~P8(a58,x20961,x20961)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2097,plain,
% 15.40/15.58 (P8(a58,x20971,f11(a58,x20971,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2100,plain,
% 15.40/15.58 (~E(f11(a58,x21001,f6(a58)),x21001)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2103,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x21031),x21031))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2108,plain,
% 15.40/15.58 (~P7(a58,f11(a58,x21081,f6(a58)),x21081)),
% 15.40/15.58 inference(rename_variables,[],[508])).
% 15.40/15.58 cnf(2113,plain,
% 15.40/15.58 (P7(a58,f3(a58),x21131)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2125,plain,
% 15.40/15.58 (~P7(a59,f3(a59),f4(a59,f6(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,1991,242,244,281,282,304,314,321,322,324,329,330,336,345,370,400,1997,2005,2012,497,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,1898,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,401,405,499,2050,2053,2056,2078,2093,465,1901,2025,466,444,505,1952,1966,417,1963,2044,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976])).
% 15.40/15.58 cnf(2128,plain,
% 15.40/15.58 (~E(f11(a58,x21281,f6(a58)),x21281)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2131,plain,
% 15.40/15.58 (~E(f11(a58,x21311,f6(a58)),x21311)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2134,plain,
% 15.40/15.58 (~E(f11(a58,x21341,f6(a58)),x21341)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2136,plain,
% 15.40/15.58 (~E(f4(a59,f6(a59)),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,1991,242,244,281,282,283,304,314,321,322,324,329,330,336,345,370,400,1997,2005,2012,497,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,1898,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,401,405,499,2050,2053,2056,2078,2093,2100,2128,2131,465,1901,2025,466,444,505,1952,1966,417,1963,2044,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596])).
% 15.40/15.58 cnf(2139,plain,
% 15.40/15.58 (~E(f11(a58,x21391,f6(a58)),x21391)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2144,plain,
% 15.40/15.58 (~E(f11(a58,x21441,f6(a58)),x21441)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2146,plain,
% 15.40/15.58 (~P8(a59,f3(a59),f11(a59,f3(a59),f3(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,1991,242,244,281,282,283,304,314,321,322,324,329,330,336,345,370,378,400,1997,2005,2012,497,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,1898,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,401,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,465,1901,2025,466,444,505,1952,1966,417,1963,2044,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237])).
% 15.40/15.58 cnf(2150,plain,
% 15.40/15.58 (~P8(a59,f11(a59,f3(a59),f3(a59)),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,394,1887,1893,494,1972,1975,1991,242,244,281,282,283,304,314,321,322,324,329,330,336,345,370,378,400,1997,2005,2012,497,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,1898,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,401,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,465,1901,2025,466,444,505,1952,1966,417,1963,2044,421,1940,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235])).
% 15.40/15.58 cnf(2157,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),f6(a58)),x21571))),
% 15.40/15.58 inference(rename_variables,[],[421])).
% 15.40/15.58 cnf(2160,plain,
% 15.40/15.58 (~E(f11(a58,x21601,f6(a58)),x21601)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2163,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x21631,x21632),x21631),x21632)),
% 15.40/15.58 inference(rename_variables,[],[434])).
% 15.40/15.58 cnf(2173,plain,
% 15.40/15.58 (~E(f11(a58,x21731,f6(a58)),x21731)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2176,plain,
% 15.40/15.58 (~E(f11(a58,x21761,f6(a58)),x21761)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2183,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x21831),x21831))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2186,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x21861),x21861))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2189,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x21891),x21891))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2198,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x21981),x21981))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2199,plain,
% 15.40/15.58 (~P8(a58,x21991,f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[497])).
% 15.40/15.58 cnf(2202,plain,
% 15.40/15.58 (~E(f11(a58,x22021,f6(a58)),x22021)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2205,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x22051),x22051))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2208,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x22081),x22081))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2211,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x22111),x22111))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2222,plain,
% 15.40/15.58 (~P8(a58,x22221,x22221)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2229,plain,
% 15.40/15.58 (P7(a58,x22291,x22291)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2230,plain,
% 15.40/15.58 (P7(a58,f3(a58),x22301)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2239,plain,
% 15.40/15.58 (E(f11(a58,x22391,f11(a58,x22392,x22393)),f11(a58,x22392,f11(a58,x22391,x22393)))),
% 15.40/15.58 inference(rename_variables,[],[447])).
% 15.40/15.58 cnf(2244,plain,
% 15.40/15.58 (P7(f66(x22441,a58),x22442,x22442)),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,394,1887,1893,494,1972,1975,1991,2096,242,244,261,281,282,283,304,314,321,322,324,326,329,330,336,345,370,375,376,378,400,1997,2005,2012,2113,497,2090,385,386,487,412,489,492,510,429,1882,1890,1904,430,431,432,506,1876,1915,1918,507,1910,419,1879,1898,398,437,2033,2037,2041,2062,2065,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,434,401,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,465,1901,2025,466,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,447,2239,509,421,1940,2040,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844])).
% 15.40/15.58 cnf(2245,plain,
% 15.40/15.58 (P7(a58,x22451,x22451)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2260,plain,
% 15.40/15.58 (~E(f11(a58,x22601,f6(a58)),x22601)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2263,plain,
% 15.40/15.58 (P8(a58,x22631,f11(a58,f11(a58,x22631,x22632),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[466])).
% 15.40/15.58 cnf(2268,plain,
% 15.40/15.58 (P7(a58,f9(a58,x22681,x22682),x22681)),
% 15.40/15.58 inference(rename_variables,[],[432])).
% 15.40/15.58 cnf(2271,plain,
% 15.40/15.58 (P8(a58,x22711,f11(a58,x22711,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2274,plain,
% 15.40/15.58 (P7(a58,f17(a1,x22741,a61),a62)),
% 15.40/15.58 inference(rename_variables,[],[428])).
% 15.40/15.58 cnf(2277,plain,
% 15.40/15.58 (P7(a58,f9(a58,x22771,x22772),x22771)),
% 15.40/15.58 inference(rename_variables,[],[432])).
% 15.40/15.58 cnf(2280,plain,
% 15.40/15.58 (P7(a58,f3(a58),x22801)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2283,plain,
% 15.40/15.58 (P7(a58,f3(a58),x22831)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2286,plain,
% 15.40/15.58 (P7(a58,f3(a58),x22861)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2289,plain,
% 15.40/15.58 (~P8(a58,x22891,f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[497])).
% 15.40/15.58 cnf(2294,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x22941),x22941))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(2297,plain,
% 15.40/15.58 (~E(f11(a58,x22971,f6(a58)),x22971)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2298,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x22981,x22982),x22982),x22981)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2301,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x23011,x23012),x23011),x23012)),
% 15.40/15.58 inference(rename_variables,[],[434])).
% 15.40/15.58 cnf(2302,plain,
% 15.40/15.58 (P7(a58,f3(a58),x23021)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2303,plain,
% 15.40/15.58 (P7(a58,x23031,x23031)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2306,plain,
% 15.40/15.58 (P7(a58,x23061,x23061)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2309,plain,
% 15.40/15.58 (~P8(a58,x23091,x23091)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2310,plain,
% 15.40/15.58 (P8(a58,x23101,f11(a58,x23101,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2313,plain,
% 15.40/15.58 (P8(a58,x23131,f11(a58,x23131,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2316,plain,
% 15.40/15.58 (P7(a58,f3(a58),x23161)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2319,plain,
% 15.40/15.58 (P7(a58,x23191,x23191)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2322,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x23221,x23222),x23222),x23221)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2323,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x23231,x23232),x23232),x23231)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2326,plain,
% 15.40/15.58 (P8(a58,x23261,f11(a58,x23261,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2329,plain,
% 15.40/15.58 (~P8(a58,f11(a58,x23291,x23292),x23291)),
% 15.40/15.58 inference(rename_variables,[],[507])).
% 15.40/15.58 cnf(2332,plain,
% 15.40/15.58 (P7(a58,f3(a58),x23321)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2335,plain,
% 15.40/15.58 (P7(a58,x23351,f11(a58,x23352,x23351))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(2340,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x23401,x23402),x23402),x23401)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2343,plain,
% 15.40/15.58 (P7(a58,f3(a58),x23431)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2350,plain,
% 15.40/15.58 (P7(a58,x23501,x23501)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2365,plain,
% 15.40/15.58 (E(f11(a59,x23651,x23652),f11(a59,x23652,x23651))),
% 15.40/15.58 inference(rename_variables,[],[420])).
% 15.40/15.58 cnf(2368,plain,
% 15.40/15.58 (~E(f11(a58,x23681,f6(a58)),x23681)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2369,plain,
% 15.40/15.58 (~E(f11(a58,x23691,f6(a58)),x23691)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2370,plain,
% 15.40/15.58 (~P8(a58,x23701,x23701)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2373,plain,
% 15.40/15.58 (E(f11(a58,x23731,f3(a58)),x23731)),
% 15.40/15.58 inference(rename_variables,[],[401])).
% 15.40/15.58 cnf(2374,plain,
% 15.40/15.58 (~E(f11(a58,x23741,f6(a58)),x23741)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2375,plain,
% 15.40/15.58 (E(f7(a58,f11(a58,x23751,x23752),x23752),x23751)),
% 15.40/15.58 inference(rename_variables,[],[433])).
% 15.40/15.58 cnf(2383,plain,
% 15.40/15.58 (~P74(f21(f22(f65(a1)),f21(f21(f27(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),f11(a58,f17(a1,a64,a61),f6(a58)))),f6(a59),f11(a59,f3(a59),f21(f21(f5(a59),f6(a59)),a61)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,394,1887,1893,1960,494,1972,1975,1991,2096,2222,2309,242,244,247,256,257,258,261,281,282,283,299,302,304,314,319,321,322,324,326,329,330,336,338,345,349,366,370,375,376,378,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,398,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606])).
% 15.40/15.58 cnf(2384,plain,
% 15.40/15.58 (E(f11(a59,x23841,x23842),f11(a59,x23842,x23841))),
% 15.40/15.58 inference(rename_variables,[],[420])).
% 15.40/15.58 cnf(2385,plain,
% 15.40/15.58 (P7(a59,x23851,x23851)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(2388,plain,
% 15.40/15.58 (E(f11(a59,x23881,x23882),f11(a59,x23882,x23881))),
% 15.40/15.58 inference(rename_variables,[],[420])).
% 15.40/15.58 cnf(2389,plain,
% 15.40/15.58 (P7(a59,x23891,x23891)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(2392,plain,
% 15.40/15.58 (P7(a58,x23921,x23921)),
% 15.40/15.58 inference(rename_variables,[],[393])).
% 15.40/15.58 cnf(2393,plain,
% 15.40/15.58 (P8(a58,x23931,f11(a58,x23931,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2394,plain,
% 15.40/15.58 (P8(a58,x23941,f11(a58,x23941,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2397,plain,
% 15.40/15.58 (P7(a58,f3(a58),x23971)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(2415,plain,
% 15.40/15.58 (~E(f21(f21(f5(f65(a1)),f19(a1,f4(a1,a64),f19(a1,f6(a1),f3(f65(a1))))),x24151),a68)),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,242,244,247,256,257,258,261,281,282,283,299,302,304,314,315,319,321,322,323,324,326,329,330,336,338,345,349,366,370,375,376,378,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779])).
% 15.40/15.58 cnf(2432,plain,
% 15.40/15.58 (P73(f21(f21(f22(a1),x24321),x24321))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,256,257,258,261,281,282,283,299,302,304,314,315,319,321,322,323,324,326,329,330,336,338,345,349,366,370,375,376,378,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780])).
% 15.40/15.58 cnf(2458,plain,
% 15.40/15.58 (P5(f65(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,256,257,258,261,278,281,282,283,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567])).
% 15.40/15.58 cnf(2506,plain,
% 15.40/15.58 (P57(f65(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543])).
% 15.40/15.58 cnf(2522,plain,
% 15.40/15.58 (P54(f65(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535])).
% 15.40/15.58 cnf(2538,plain,
% 15.40/15.58 (P21(f65(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527])).
% 15.40/15.58 cnf(2554,plain,
% 15.40/15.58 (P51(f65(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519])).
% 15.40/15.58 cnf(2566,plain,
% 15.40/15.58 (P32(f65(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513])).
% 15.40/15.58 cnf(2570,plain,
% 15.40/15.58 (P1(f65(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511])).
% 15.40/15.58 cnf(2573,plain,
% 15.40/15.58 (P8(a58,x25731,f11(a58,x25731,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2576,plain,
% 15.40/15.58 (P8(a58,x25761,f11(a58,x25761,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2579,plain,
% 15.40/15.58 (P8(a58,x25791,f11(a58,x25791,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2582,plain,
% 15.40/15.58 (~E(f11(a58,x25821,f6(a58)),x25821)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2585,plain,
% 15.40/15.58 (P8(a58,x25851,f11(a58,x25851,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2589,plain,
% 15.40/15.58 (~E(f11(a58,f17(a1,a64,a61),x25891),f3(a58))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,394,1887,1893,1960,2385,494,1972,1975,1991,2096,2222,2309,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,497,2090,2199,385,386,487,488,411,412,489,492,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,508,1921,1924,1978,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721])).
% 15.40/15.58 cnf(2594,plain,
% 15.40/15.58 (~E(f11(a58,x25941,f6(a58)),x25941)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2597,plain,
% 15.40/15.58 (~E(f11(a58,x25971,f6(a58)),x25971)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2608,plain,
% 15.40/15.58 (~P8(a58,x26081,x26081)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2611,plain,
% 15.40/15.58 (~P8(a58,x26111,x26111)),
% 15.40/15.58 inference(rename_variables,[],[494])).
% 15.40/15.58 cnf(2614,plain,
% 15.40/15.58 (P7(a59,x26141,x26141)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(2617,plain,
% 15.40/15.58 (P8(a58,x26171,f11(a58,x26171,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2620,plain,
% 15.40/15.58 (P7(a59,x26201,x26201)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(2625,plain,
% 15.40/15.58 (~E(f11(a58,x26251,f6(a58)),x26251)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2628,plain,
% 15.40/15.58 (~E(f11(a58,x26281,f6(a58)),x26281)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(2631,plain,
% 15.40/15.58 (E(f11(a58,x26311,x26312),f11(a58,x26312,x26311))),
% 15.40/15.58 inference(rename_variables,[],[419])).
% 15.40/15.58 cnf(2836,plain,
% 15.40/15.58 (P8(f65(a59),x28361,f11(f65(a59),x28361,f6(f65(a59))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,494,1972,1975,1991,2096,2222,2309,2370,2608,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927])).
% 15.40/15.58 cnf(2838,plain,
% 15.40/15.58 (P7(a59,f3(a59),f21(f21(f5(a59),x28381),x28381))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,494,1972,1975,1991,2096,2222,2309,2370,2608,241,242,244,247,251,254,256,257,258,261,278,281,282,283,286,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897])).
% 15.40/15.58 cnf(2916,plain,
% 15.40/15.58 (~P8(a59,f11(a59,f11(a59,f6(a59),f3(a59)),f3(a59)),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,494,1972,1975,1991,2096,2222,2309,2370,2608,241,242,244,247,251,254,256,257,258,261,271,278,281,282,283,286,296,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,346,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632])).
% 15.40/15.58 cnf(2935,plain,
% 15.40/15.58 (P8(a58,x29351,f11(a58,x29351,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2948,plain,
% 15.40/15.58 (P8(a58,x29481,f11(a58,x29481,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2951,plain,
% 15.40/15.58 (P8(a58,x29511,f11(a58,x29511,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[437])).
% 15.40/15.58 cnf(2960,plain,
% 15.40/15.58 (~E(f11(a58,x29601,f6(a58)),x29601)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(3044,plain,
% 15.40/15.58 (E(f21(f13(a1,f3(f65(a1))),x30441),f3(a1))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,271,278,279,281,282,283,286,296,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,346,349,366,370,371,375,376,378,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710])).
% 15.40/15.58 cnf(3092,plain,
% 15.40/15.58 (E(f11(a58,f21(f21(f5(a58),f9(a58,x30921,x30922)),x30922),f8(a58,x30921,x30922)),x30921)),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,270,271,274,278,279,281,282,283,286,296,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,346,349,366,370,371,375,376,378,379,381,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657])).
% 15.40/15.58 cnf(3270,plain,
% 15.40/15.58 (P73(f21(f21(f22(f65(a1)),f21(f21(f27(f65(a1)),f19(a1,f4(a1,x32701),f19(a1,f6(a1),f3(f65(a1))))),f17(a1,x32701,x32702))),x32702))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,270,271,274,275,278,279,281,282,283,286,288,294,296,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,346,349,351,363,366,370,371,375,376,378,379,380,381,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857])).
% 15.40/15.58 cnf(3283,plain,
% 15.40/15.58 (~E(a1,x32831)+P17(x32831)),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,270,271,274,275,278,279,281,282,283,286,288,294,296,299,302,304,313,314,315,319,321,322,323,324,326,329,330,332,333,336,338,340,345,346,349,351,360,363,366,370,371,375,376,377,378,379,380,381,382,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239])).
% 15.40/15.58 cnf(3307,plain,
% 15.40/15.58 (P15(f11(a58,a59,f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,270,271,274,275,278,279,281,282,283,286,287,288,290,293,294,296,299,301,302,304,306,307,311,313,314,315,318,319,320,321,322,323,324,326,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,360,363,365,366,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207])).
% 15.40/15.58 cnf(3328,plain,
% 15.40/15.58 (P57(f11(a58,a59,f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,251,254,256,257,258,261,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,434,2163,401,1999,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182])).
% 15.40/15.58 cnf(3344,plain,
% 15.40/15.58 (P32(f11(a58,a59,f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,244,247,248,250,251,253,254,256,257,258,260,261,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162])).
% 15.40/15.58 cnf(3349,plain,
% 15.40/15.58 (P1(f11(a58,a59,f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,405,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,465,1901,2025,2034,466,1989,2263,444,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152])).
% 15.40/15.58 cnf(3410,plain,
% 15.40/15.58 (~P7(a59,f3(a59),f9(a59,f6(a59),f7(a59,f6(a59),f11(a59,f6(a59),f6(a59)))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,425,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349])).
% 15.40/15.58 cnf(3428,plain,
% 15.40/15.58 (~E(f11(a58,f11(a58,f11(a58,f3(a58),f6(a58)),f17(a1,a64,a61)),x34281),f11(a58,f3(a58),f6(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,425,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051])).
% 15.40/15.58 cnf(3456,plain,
% 15.40/15.58 (~P73(f21(f21(f22(a58),f21(f21(f5(a58),f7(a58,f11(a58,f11(a58,f6(a58),x34561),f6(a58)),x34561)),f11(a58,f3(a58),f6(a58)))),f11(a58,f3(a58),f6(a58))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,425,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695])).
% 15.40/15.58 cnf(3474,plain,
% 15.40/15.58 (~E(f11(a58,f3(a58),f3(a58)),f11(a58,f3(a58),f6(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,425,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150])).
% 15.40/15.58 cnf(3497,plain,
% 15.40/15.58 (P8(a58,f3(a58),f11(a58,x34971,f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[438])).
% 15.40/15.58 cnf(3533,plain,
% 15.40/15.58 (~P7(a58,f21(f21(f5(a58),f11(a58,f3(a58),f6(a58))),f11(a58,f3(a58),f6(a58))),f21(f21(f5(a58),f3(a58)),f11(a58,f3(a58),f6(a58))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507])).
% 15.40/15.58 cnf(3547,plain,
% 15.40/15.58 (~E(f21(f21(f5(a58),f11(a58,f6(a58),x35471)),f3(a58)),f21(f21(f5(a58),f11(a58,f6(a58),x35471)),a62))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047])).
% 15.40/15.58 cnf(3551,plain,
% 15.40/15.58 (~E(f21(f21(f5(a58),f17(a1,a64,a61)),f17(a1,a64,a61)),f21(f21(f5(a58),f17(a1,a64,a61)),f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871])).
% 15.40/15.58 cnf(3599,plain,
% 15.40/15.58 (~P8(f65(a59),f7(f65(a59),f6(f65(a59)),f3(f65(a59))),f3(f65(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218])).
% 15.40/15.58 cnf(3605,plain,
% 15.40/15.58 (P9(a59,f7(f65(a59),f11(f65(a59),x36051,f6(f65(a59))),x36051))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048])).
% 15.40/15.58 cnf(3649,plain,
% 15.40/15.58 (P8(a59,f4(a59,f6(a59)),f3(a59))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,425,435,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951])).
% 15.40/15.58 cnf(3735,plain,
% 15.40/15.58 (P73(f21(f21(f22(a59),f21(f21(f5(a59),f4(a59,f3(a59))),x37351)),f21(f21(f5(a59),f4(a59,f3(a59))),x37352)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672])).
% 15.40/15.58 cnf(3737,plain,
% 15.40/15.58 (P73(f21(f21(f22(a59),f21(f21(f5(a59),x37371),f4(a59,f3(a59)))),f21(f21(f5(a59),x37372),f4(a59,f3(a59)))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,509,418,421,1940,2040,2157,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671])).
% 15.40/15.58 cnf(3836,plain,
% 15.40/15.58 (~P8(a58,x38361,f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[497])).
% 15.40/15.58 cnf(3870,plain,
% 15.40/15.58 (~P7(a59,f21(f21(f27(a59),f11(a59,f6(a59),f6(a59))),f11(a58,f3(a58),f6(a58))),f21(f21(f27(a59),f11(a59,f6(a59),f6(a59))),f3(a58)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,510,429,1882,1890,1904,1907,2335,430,1995,431,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,509,418,421,1940,2040,2157,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562])).
% 15.40/15.58 cnf(3958,plain,
% 15.40/15.58 (~P7(a59,f3(a59),f21(f21(f5(a59),f6(a59)),f4(a59,f6(a59))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,509,418,421,1940,2040,2157,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338])).
% 15.40/15.58 cnf(3984,plain,
% 15.40/15.58 (P8(a59,f6(a59),f21(f21(f5(a59),f11(a59,f6(a59),f6(a59))),f11(a59,f6(a59),f6(a59))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,301,302,303,304,305,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,509,418,421,1940,2040,2157,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300])).
% 15.40/15.58 cnf(4051,plain,
% 15.40/15.58 (P11(a1,f21(f21(f5(a59),f6(a59)),f11(f65(a1),f21(f21(f5(f65(a1)),f25(a1,f3(f65(a1)),x40511)),x40512),f25(a1,f3(f65(a1)),x40511))),x40512,f25(a1,f3(f65(a1)),x40511),f25(a1,f3(f65(a1)),x40511))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,259,260,261,262,264,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,300,301,302,303,304,305,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,396,509,418,421,1940,2040,2157,457,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300,1299,1298,1297,1295,815,769,764,763,753,1720,1583,1582,1581,1580,1538,1537,1323,768,810,1767,1766,1733,1719,1602,1163,1133,1543,1776,1775,1540,1774,1785,1784])).
% 15.40/15.58 cnf(4054,plain,
% 15.40/15.58 (P7(a59,x40541,x40541)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(4057,plain,
% 15.40/15.58 (P7(a58,f3(a58),x40571)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(4059,plain,
% 15.40/15.58 (~P7(a58,f2(a1,f19(a1,f3(a1),f11(a58,f3(f65(a1)),f6(a58)))),f3(a58))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,259,260,261,262,264,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,300,301,302,303,304,305,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,3836,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,396,509,418,421,1940,2040,2157,457,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300,1299,1298,1297,1295,815,769,764,763,753,1720,1583,1582,1581,1580,1538,1537,1323,768,810,1767,1766,1733,1719,1602,1163,1133,1543,1776,1775,1540,1774,1785,1784,1148,1147,1143])).
% 15.40/15.58 cnf(4064,plain,
% 15.40/15.58 (~P74(f21(f22(a58),f11(a58,f6(a58),f6(a58))),f7(a59,f6(a59),f11(a59,f6(a59),f6(a59))),f9(a58,f11(a59,f21(f21(f5(a59),f7(a59,f6(a59),f11(a59,f6(a59),f6(a59)))),f6(a58)),f3(a59)),f11(a58,f3(a58),f6(a58))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,4054,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,259,260,261,262,264,265,267,270,271,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,298,299,300,301,302,303,304,305,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,3836,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,396,440,509,418,421,1940,2040,2157,457,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300,1299,1298,1297,1295,815,769,764,763,753,1720,1583,1582,1581,1580,1538,1537,1323,768,810,1767,1766,1733,1719,1602,1163,1133,1543,1776,1775,1540,1774,1785,1784,1148,1147,1143,1816,1605])).
% 15.40/15.58 cnf(4072,plain,
% 15.40/15.58 (P8(a59,f21(f21(f5(a59),f3(a59)),f3(a59)),f21(f21(f5(a59),f6(a59)),f6(a59)))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,4054,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,259,260,261,262,263,264,265,267,268,269,270,271,272,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,497,2090,2199,2289,3836,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,396,440,509,418,421,1940,2040,2157,457,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300,1299,1298,1297,1295,815,769,764,763,753,1720,1583,1582,1581,1580,1538,1537,1323,768,810,1767,1766,1733,1719,1602,1163,1133,1543,1776,1775,1540,1774,1785,1784,1148,1147,1143,1816,1605,812,1513,811,1622])).
% 15.40/15.58 cnf(4088,plain,
% 15.40/15.58 (~P73(f21(f21(f22(a59),f11(a59,f6(a59),f6(a59))),f4(a59,f6(a59))))),
% 15.40/15.58 inference(scs_inference,[],[486,393,2229,2245,2303,2306,2319,2350,2392,394,1887,1893,1960,2385,2389,2614,2620,4054,494,1972,1975,1991,2096,2222,2309,2370,2608,2611,241,242,243,244,246,247,248,249,250,251,253,254,255,256,257,258,259,260,261,262,263,264,265,267,268,269,270,271,272,273,274,275,277,278,279,280,281,282,283,284,285,286,287,288,290,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,329,330,332,333,334,336,337,338,339,340,342,343,345,346,348,349,350,351,353,356,357,359,360,363,365,366,367,368,369,370,371,373,375,376,377,378,379,380,381,382,384,400,1997,2005,2012,2113,2230,2280,2283,2286,2302,2316,2332,2343,2397,4057,497,2090,2199,2289,3836,385,386,487,488,411,412,489,492,387,388,483,485,510,429,1882,1890,1904,1907,2335,430,1995,431,2004,432,1873,2268,2277,506,1876,1915,1918,1930,507,1910,1927,2329,428,2274,419,1879,1898,2631,420,2365,2384,2388,398,2045,437,2033,2037,2041,2062,2065,2097,2271,2310,2313,2326,2394,2573,2576,2579,2585,2617,2935,2948,2951,2393,508,1921,1924,1978,2108,433,1933,1955,1983,1985,1987,2028,2081,2298,2323,2340,2375,2322,434,2163,2301,401,1999,2373,402,403,404,405,2061,406,499,2050,2053,2056,2078,2093,2100,2128,2131,2134,2139,2144,2160,2173,2176,2202,2260,2297,2369,2374,2368,2582,2594,2597,2625,2628,2960,389,465,1901,2025,2034,466,1989,2263,444,438,3497,425,435,436,505,1952,1966,1969,417,1963,2044,2103,2183,2186,2189,2198,2205,2208,2211,2294,443,390,391,447,2239,448,395,396,440,509,418,421,1940,2040,2157,457,478,2,727,707,706,715,850,726,890,851,1261,1260,1184,1182,1178,1177,1175,1168,1167,1166,1081,1062,1061,1059,1057,1055,1001,885,835,711,623,1579,13,1477,1467,1466,1272,893,844,1072,879,1408,1069,723,1365,1363,1362,1452,230,191,175,173,172,161,160,158,157,153,3,918,895,855,853,842,773,742,741,640,638,1264,1248,1244,1243,1242,1144,1170,1805,1803,1802,1801,1404,1171,1259,1406,957,955,954,755,601,598,586,1483,1217,1105,603,1539,1809,1495,1493,1492,1013,1012,1004,981,979,978,977,976,805,804,803,596,595,594,593,1237,1236,1235,1234,1233,1160,975,905,760,665,786,785,784,714,713,1609,1717,1716,1679,1678,1601,1461,819,1754,1670,1463,1419,1246,1824,1823,1822,1821,1814,1813,1812,1811,1763,1741,1740,1844,1600,1496,1658,1842,1839,1739,1738,1043,1042,1041,1040,1039,1038,931,867,861,859,806,1015,1798,1247,1279,1278,1277,1276,1275,1772,1430,1429,1428,1427,1614,1070,1572,1855,1451,1317,1752,1705,1641,1640,1725,1684,1510,1807,1783,1206,1205,1770,1606,1551,1620,1122,829,828,767,766,633,620,625,1115,1779,1176,1090,1088,1085,1084,1079,1002,886,780,636,635,621,592,591,590,589,588,587,570,569,568,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,529,528,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,1474,1468,1101,881,874,775,721,720,692,691,632,615,614,612,1132,1131,1099,1046,1044,876,1017,1016,962,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,12,11,10,9,8,7,6,5,4,1791,1762,1758,1702,1597,1596,1475,1431,1387,1386,1274,1273,1271,1270,1269,1268,1267,1266,1198,1197,1196,1194,1174,1162,1130,1108,1107,1073,927,897,894,889,888,839,838,836,833,814,788,787,779,778,776,748,700,699,698,678,677,675,674,664,655,652,651,650,646,645,644,643,641,608,607,606,600,599,584,572,1632,1631,1625,1469,1415,1393,1392,1366,1345,1326,1173,1137,1136,1135,1066,1032,1031,1030,751,749,622,1586,1585,1523,1773,1592,1465,1400,1399,1379,1375,1374,1216,1212,1211,1149,1068,1067,1009,983,982,958,932,901,887,884,883,878,877,848,847,846,832,820,777,761,724,722,719,718,717,716,710,709,708,693,687,685,684,682,676,669,668,663,661,631,617,578,577,576,575,1856,1713,1686,1666,1665,1657,1656,1599,1593,1556,1550,1518,1517,1516,1486,1385,1384,1383,1380,1364,1359,1358,1356,1355,1330,1258,1231,1230,1229,1228,1226,1225,1191,1075,1074,1020,1018,1000,999,989,972,970,961,945,944,869,858,770,734,733,701,686,1652,1642,1628,1611,1610,1578,1536,1535,1502,1501,1500,1499,1458,1457,1421,1420,1398,1396,1394,1378,1327,1098,1097,1095,1035,1034,1033,1806,1793,1782,1736,1669,1558,1557,1549,1548,816,1845,1787,1732,1685,1673,1857,1753,1587,1728,1829,1843,240,239,234,233,232,231,228,227,226,224,223,222,221,220,219,218,217,215,214,213,212,211,210,209,208,207,205,204,203,202,200,199,198,197,195,194,193,192,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,174,171,170,168,167,166,165,164,163,162,159,156,155,154,152,1008,1007,917,916,913,909,843,795,790,774,1653,1799,1232,667,1189,1188,1351,1350,1257,1255,1254,1253,934,891,695,694,647,629,1353,1352,1349,1312,1252,1251,1250,1249,1215,1139,1103,1051,1050,1026,985,984,873,1381,1377,1208,1207,1140,1025,935,659,1695,1694,1646,1645,1553,1552,1348,1347,1240,1150,1145,1053,1052,987,986,1498,1407,1403,1360,1322,1172,1109,926,925,924,922,921,920,758,757,658,657,611,610,609,1751,1691,1690,1507,1506,1373,1372,1371,1265,1151,1047,872,871,728,725,1697,1405,1113,939,938,937,936,666,574,1703,1416,1659,1485,1481,1479,1346,1291,1289,1288,1287,1285,1218,1126,1104,1048,1029,1027,997,993,967,964,953,605,1756,1748,1746,1745,1743,1687,1192,1750,1487,1112,1111,1110,959,951,950,949,948,947,946,856,822,808,782,781,756,735,688,671,670,656,616,583,582,581,580,1473,1222,1209,1120,1119,1118,1117,1116,899,898,783,752,680,672,1598,1560,1698,904,831,821,809,1672,1671,1525,1489,1488,1471,1470,1422,1335,1311,1011,743,732,1759,1576,823,1715,1714,1710,1709,1708,1595,1594,1402,1401,1221,1219,1129,1515,1514,1542,1541,1263,1262,1860,1810,1804,1828,1827,1826,1825,1820,1819,1818,1817,1761,1760,1849,1848,973,802,1683,857,1765,1460,968,1681,1520,1519,942,941,630,1123,697,1504,1503,1280,1562,1426,1424,1121,1114,1771,1204,1202,1780,1726,1700,1584,1768,1573,1444,1737,1575,1571,1570,1569,1568,1567,1565,1529,1528,1527,1526,1450,1449,1448,1447,1446,1443,1442,1441,1440,1439,1438,1434,1432,943,1389,1388,1343,1338,1337,1336,1320,1319,1318,1316,1310,1309,1307,1306,1305,1303,1300,1299,1298,1297,1295,815,769,764,763,753,1720,1583,1582,1581,1580,1538,1537,1323,768,810,1767,1766,1733,1719,1602,1163,1133,1543,1776,1775,1540,1774,1785,1784,1148,1147,1143,1816,1605,812,1513,811,1622,1621,1619,1618,1617,744,1730,1729,1190])).
% 15.40/15.58 cnf(4149,plain,
% 15.40/15.58 (E(x41491,f11(a58,f3(a58),x41491))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4161,plain,
% 15.40/15.58 (E(x41611,f11(a58,f3(a58),x41611))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4163,plain,
% 15.40/15.58 (E(x41631,f11(a58,f3(a58),x41631))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4165,plain,
% 15.40/15.58 (E(x41651,f11(a58,f3(a58),x41651))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4167,plain,
% 15.40/15.58 (E(x41671,f11(a58,f3(a58),x41671))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4169,plain,
% 15.40/15.58 (E(x41691,f11(a58,f3(a58),x41691))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4171,plain,
% 15.40/15.58 (E(x41711,f11(a58,f3(a58),x41711))),
% 15.40/15.58 inference(rename_variables,[],[2024])).
% 15.40/15.58 cnf(4181,plain,
% 15.40/15.58 (~E(f11(a58,f11(a58,f11(a58,f3(a58),f6(a58)),f17(a1,a64,a61)),x41811),f11(a58,f3(a58),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[3428])).
% 15.40/15.58 cnf(4182,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x41821),x41821))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(4185,plain,
% 15.40/15.58 (E(f21(f13(a1,f3(f65(a1))),x41851),f3(a1))),
% 15.40/15.58 inference(rename_variables,[],[3044])).
% 15.40/15.58 cnf(4201,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),f11(a58,f3(a58),f6(a58))),x42011))),
% 15.40/15.58 inference(rename_variables,[],[478])).
% 15.40/15.58 cnf(4206,plain,
% 15.40/15.58 (P8(a58,x42061,f11(a58,f11(a58,x42062,x42061),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(4209,plain,
% 15.40/15.58 (P8(a58,x42091,f11(a58,f11(a58,x42092,x42091),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(4216,plain,
% 15.40/15.58 (P7(a59,f3(a59),f21(f21(f5(a59),x42161),x42161))),
% 15.40/15.58 inference(rename_variables,[],[2838])).
% 15.40/15.58 cnf(4219,plain,
% 15.40/15.58 (P7(a59,f3(a59),f21(f21(f5(a59),x42191),x42191))),
% 15.40/15.58 inference(rename_variables,[],[2838])).
% 15.40/15.58 cnf(4222,plain,
% 15.40/15.58 (P7(a58,x42221,f11(a58,x42222,x42221))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(4223,plain,
% 15.40/15.58 (P7(a58,f3(a58),x42231)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(4226,plain,
% 15.40/15.58 (P7(a59,x42261,x42261)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(4229,plain,
% 15.40/15.58 (P7(a59,x42291,x42291)),
% 15.40/15.58 inference(rename_variables,[],[394])).
% 15.40/15.58 cnf(4235,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x42351),x42351))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(4236,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x42361),f3(a58)))),
% 15.40/15.58 inference(rename_variables,[],[418])).
% 15.40/15.58 cnf(4240,plain,
% 15.40/15.58 (~E(f11(a58,x42401,f6(a58)),x42401)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(4241,plain,
% 15.40/15.58 (P73(f21(f21(f22(a58),x42411),x42411))),
% 15.40/15.58 inference(rename_variables,[],[417])).
% 15.40/15.58 cnf(4245,plain,
% 15.40/15.58 (~E(f11(a58,x42451,f11(a58,x42452,f6(a58))),x42452)),
% 15.40/15.58 inference(rename_variables,[],[1929])).
% 15.40/15.58 cnf(4256,plain,
% 15.40/15.58 (P7(a58,f3(a58),x42561)),
% 15.40/15.58 inference(rename_variables,[],[400])).
% 15.40/15.58 cnf(4258,plain,
% 15.40/15.58 (P7(a58,x42581,f11(a58,x42582,x42581))),
% 15.40/15.58 inference(rename_variables,[],[429])).
% 15.40/15.58 cnf(4279,plain,
% 15.40/15.58 (~E(f11(a58,x42791,f6(a58)),x42791)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(4281,plain,
% 15.40/15.58 (E(f11(a58,f21(f21(f5(a58),x42811),x42812),f11(a58,f21(f21(f5(a58),x42813),x42812),x42814)),f11(a58,f21(f21(f5(a58),f11(a58,x42811,x42813)),x42812),x42814))),
% 15.40/15.58 inference(rename_variables,[],[481])).
% 15.40/15.58 cnf(4291,plain,
% 15.40/15.58 (~E(f11(a58,x42911,f6(a58)),x42911)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(4300,plain,
% 15.40/15.58 (~E(f11(a58,f11(a58,f11(a58,f3(a58),f6(a58)),f17(a1,a64,a61)),x43001),f11(a58,f3(a58),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[3428])).
% 15.40/15.58 cnf(4311,plain,
% 15.40/15.58 (~E(f11(a59,f11(a59,f6(a59),x43111),x43111),f3(a59))),
% 15.40/15.58 inference(rename_variables,[],[509])).
% 15.40/15.58 cnf(4318,plain,
% 15.40/15.58 (~E(f11(a58,x43181,f11(a58,x43182,f6(a58))),x43182)),
% 15.40/15.58 inference(rename_variables,[],[1929])).
% 15.40/15.58 cnf(4325,plain,
% 15.40/15.58 (~E(f11(a58,x43251,f17(a1,a64,a61)),x43251)),
% 15.40/15.58 inference(rename_variables,[],[1935])).
% 15.40/15.58 cnf(4328,plain,
% 15.40/15.58 (E(f11(a59,f21(f21(f5(a59),x43281),f9(a59,x43282,x43281)),f8(a59,x43282,x43281)),x43282)),
% 15.40/15.58 inference(rename_variables,[],[472])).
% 15.40/15.58 cnf(4329,plain,
% 15.40/15.58 (P8(a58,x43291,f11(a58,f11(a58,x43292,x43291),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(4332,plain,
% 15.40/15.58 (E(f11(a59,f21(f21(f5(a59),x43321),f9(a59,x43322,x43321)),f8(a59,x43322,x43321)),x43322)),
% 15.40/15.58 inference(rename_variables,[],[472])).
% 15.40/15.58 cnf(4333,plain,
% 15.40/15.58 (P8(a58,x43331,f11(a58,f11(a58,x43332,x43331),f6(a58)))),
% 15.40/15.58 inference(rename_variables,[],[465])).
% 15.40/15.58 cnf(4340,plain,
% 15.40/15.58 (~E(f11(a58,x43401,f6(a58)),f3(a58))),
% 15.40/15.58 inference(rename_variables,[],[505])).
% 15.40/15.58 cnf(4341,plain,
% 15.40/15.58 (~E(f11(a58,x43411,f6(a58)),x43411)),
% 15.40/15.58 inference(rename_variables,[],[499])).
% 15.40/15.58 cnf(4427,plain,
% 15.40/15.58 ($false),
% 15.40/15.58 inference(scs_inference,[],[1861,245,266,490,408,446,481,4281,472,4328,4332,394,4226,4229,494,243,248,297,300,379,380,400,4223,4256,497,429,4222,4258,431,432,508,433,434,401,499,4240,4279,4291,4341,465,4206,4209,4329,4333,505,4340,417,4182,4235,4241,438,478,4201,390,509,4311,330,488,283,332,378,510,302,326,321,247,274,483,418,4236,393,329,303,304,261,411,375,312,244,492,489,370,412,314,3349,3344,3328,3307,2001,3474,1870,2125,2039,2020,3551,4088,3270,2073,2432,3456,3735,3737,3649,2071,2244,1935,4325,3428,4181,4300,2095,4064,3092,1929,4245,4318,4072,2024,4149,4161,4163,4165,4167,4169,4171,2136,2150,2069,2836,4051,3547,2383,3044,4185,3599,1862,3533,2589,3870,1886,2458,2506,2522,2538,2554,2566,2570,3958,3984,2415,2838,4216,4219,3410,3605,2916,4059,2146,3283,1797,1796,1344,1245,1749,229,225,216,206,196,169,1076,980,1006,1241,1462,1324,1213,1037,1036,796,1003,1633,1127,1564,1423,1522,1521,1340,1339,1662,1546,1454,1453,1615,1613,1764,969,849,579,1623,845,1693,673,654,649,642,681,660,1664,706,1175,721,1579,748,751,1408,1067,883,1134,1248,1189,1244,1349,1050,1025,935,1553,1552,1347,1150,1052,1805,1065,922,658,611,610,1259,1697,1416,1218,1125,1106,998,964,953,605,1748,1539,1809,1495,1112,1111,782,671,616,905,1598,1698,809,1717,1716,1679,1672,1671,1422,1335,1311,1011,1246]),
% 15.40/15.58 ['proof']).
% 15.40/15.59 % SZS output end Proof
% 15.40/15.59 % Total time :14.210000s
%------------------------------------------------------------------------------