%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP280_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:12:34 AM UTC 2025
% Result : Theorem 183.07s 183.42s
% Output : Proof 183.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 64
% Syntax : Number of formulae : 173 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 503 ( 257 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 465 ( 157 ~; 171 |; 12 &)
% ( 97 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 18 con; 0-2 aty)
% Number of variables : 273 ( 242 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
tff(aa_real_real_type,type,
aa_real_real: ( fun_real_real * real ) > real ).
tff(aa_VEBT_VEBT_real_type,type,
aa_VEBT_VEBT_real: ( fun_VEBT_VEBT_real * vEBT_VEBT ) > real ).
tff(vEBT_vebt_buildup_type,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(aa_num_nat_type,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(aa_num_num_type,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(one_type,type,
one: num ).
tff(bit0_type,type,
bit0: fun_num_num ).
tff(numeral_numeral_nat_type,type,
numeral_numeral_nat: fun_num_nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(va_type,type,
va: nat ).
tff(divide_divide_nat_type,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(suc_type,type,
suc: fun_nat_nat ).
tff(vEBT_VEBT_cnt_type,type,
vEBT_VEBT_cnt: fun_VEBT_VEBT_real ).
tff(aa_rea7340605660300375871l_real_type,type,
aa_rea7340605660300375871l_real: ( fun_re7681423839302404990l_real * real ) > fun_real_real ).
tff(aa_num_real_type,type,
aa_num_real: ( fun_num_real * num ) > real ).
tff(bit1_type,type,
bit1: fun_num_num ).
tff(numeral_numeral_real_type,type,
numeral_numeral_real: fun_num_real ).
tff(times_times_real_type,type,
times_times_real: fun_re7681423839302404990l_real ).
tff(aa_nat_real_type,type,
aa_nat_real: ( fun_nat_real * nat ) > real ).
tff(vEBT_V8646137997579335489_i_l_d_type,type,
vEBT_V8646137997579335489_i_l_d: fun_nat_nat ).
tff(semiri5074537144036343181t_real_type,type,
semiri5074537144036343181t_real: fun_nat_real ).
tff(one_one_nat_type,type,
one_one_nat: nat ).
tff(plus_plus_nat_type,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(aa_fun1538629612289296340t_real_type,type,
aa_fun1538629612289296340t_real: ( fun_fu3106432010075488275t_real * fun_nat_nat ) > fun_nat_real ).
tff(aTP_Lamm_ht_type,type,
aTP_Lamm_ht: fun_nat_real > fun_fu3106432010075488275t_real ).
tff(ord_max_real_type,type,
ord_max_real: fun_re7681423839302404990l_real ).
tff(pp_type,type,
pp: bool > $o ).
tff(aa_real_bool_type,type,
aa_real_bool: ( fun_real_bool * real ) > bool ).
tff(aa_rea7809428808904475482l_bool_type,type,
aa_rea7809428808904475482l_bool: ( fun_re1255401033344146673l_bool * real ) > fun_real_bool ).
tff(ord_less_eq_real_type,type,
ord_less_eq_real: fun_re1255401033344146673l_bool ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(aa_nat_fun_nat_bool_type,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(dvd_dvd_nat_type,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(ord_less_real_type,type,
ord_less_real: fun_re1255401033344146673l_bool ).
tff(1,plain,
^ [A: real,B: real] :
refl(( ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) )
<=> ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) )
<=> ! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) )
<=> ! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_mult_Ocommute) ).
tff(5,plain,
! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: real,B: real] : ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,A),B) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,B),A) )
| ( aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [N: nat] :
refl(( ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) )
<=> ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) )
<=> ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) )
<=> ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3617_Suc__eq__plus1) ).
tff(14,plain,
! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) )
| ( aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: nat,B: nat] :
refl(( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
<=> ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
<=> ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
<=> ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3237_add_Ocommute) ).
tff(24,plain,
! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
| ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [A: nat,B: nat,C: nat] :
refl(( ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) )
<=> ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) )
<=> ! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) )
<=> ! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2935_add__left__cancel) ).
tff(34,plain,
! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [A: nat,B: nat,C: nat] :
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
<=> ( B = C ) )
| ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) )
<=> ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) )
<=> ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [M: nat] :
refl(( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) )
<=> ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) )
<=> ! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) )
<=> ! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_div2__Suc__Suc) ).
tff(43,plain,
! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [M: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,M))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) )
| ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) )
<=> ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) )
| ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) )
| ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) != aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(49,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(unit_resolution,[status(thm)],[48,47,38]) ).
tff(50,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [A: nat,B: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
| ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(unit_resolution,[status(thm)],[51,26]) ).
tff(53,plain,
( ~ ! [N: nat] : ( aa_nat_nat(suc,N) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) )
| ( aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat),
inference(unit_resolution,[status(thm)],[53,16]) ).
tff(55,plain,
aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(transitivity,[status(thm)],[54,52,50,29,19]) ).
tff(56,plain,
vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),
inference(transitivity,[status(thm)],[58,9]) ).
tff(60,plain,
^ [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] :
refl(( ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) )
<=> ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) )
<=> ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) )
<=> ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10413_ATP_Olambda__198) ).
tff(64,plain,
! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) )
| ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat) = aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(symmetry,[status(thm)],[54]) ).
tff(70,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat),
inference(symmetry,[status(thm)],[52]) ).
tff(71,plain,
aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(transitivity,[status(thm)],[18,28,49,70,69]) ).
tff(72,plain,
aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) = aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Uu: fun_nat_real,Uua: fun_nat_nat,Uub: nat] : ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(Uu),Uua),Uub) = aa_nat_real(Uu,aa_nat_nat(Uua,Uub)) )
| ( aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),
inference(unit_resolution,[status(thm)],[74,66]) ).
tff(76,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(transitivity,[status(thm)],[76,73,68]) ).
tff(78,plain,
( ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) )
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) ),
inference(monotonicity,[status(thm)],[77,59]) ).
tff(79,plain,
( ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) )
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
^ [X: real,Y4: real] :
refl(( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
<=> ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
<=> ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
<=> ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
^ [X: real,Y4: real] :
rewrite(( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
<=> ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
<=> ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8942_max__absorb2) ).
tff(86,plain,
! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
<=> ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
tff(92,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ! [X: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(95,plain,
( ! [X: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) )
<=> ! [X: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(96,plain,
( ! [X: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
inference(transitivity,[status(thm)],[95,94]) ).
tff(97,plain,
^ [X: nat] :
trans(monotonicity(rewrite(( ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) )
<=> ( ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )),
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ) )),
rewrite(( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) ) )),
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [X: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )
<=> ! [X: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( X != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [X: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,axiom,
! [X: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,X)))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,X)))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C3_OIH_C_I3_J) ).
tff(101,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))) ),
inference(modus_ponens,[status(thm)],[101,93]) ).
tff(103,plain,
pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))))),
inference(unit_resolution,[status(thm)],[102,92]) ).
tff(104,plain,
( ( ~ ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) )
<=> ( ~ ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,X),Y4) = Y4 ) )
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),
inference(unit_resolution,[status(thm)],[106,103,89]) ).
tff(108,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),
inference(symmetry,[status(thm)],[58]) ).
tff(109,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),
inference(symmetry,[status(thm)],[9]) ).
tff(110,plain,
aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),
inference(transitivity,[status(thm)],[109,108]) ).
tff(111,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_nat_real(aa_fun1538629612289296340t_real(aTP_Lamm_ht(semiri5074537144036343181t_real),vEBT_V8646137997579335489_i_l_d),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),
inference(symmetry,[status(thm)],[68]) ).
tff(112,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),
inference(transitivity,[status(thm)],[111,72,75]) ).
tff(113,plain,
aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))),
inference(monotonicity,[status(thm)],[113,110]) ).
tff(115,plain,
aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [A: real,B: real] :
refl(( ~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
^ [A: real,B: real] :
rewrite(( ( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
^ [A: real,B: real] :
rewrite(( ( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [A: real,B: real] :
( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
<=> ! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [A: real,B: real] :
( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
=> ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8953_max__def) ).
tff(124,plain,
! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [A: real,B: real] :
( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
& ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) ),
inference(modus_ponens,[status(thm)],[127,117]) ).
tff(129,plain,
( ~ ! [A: real,B: real] :
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = B ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,A),B))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,A),B) = A ) ) )
| ~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
~ ( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ) ),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ~ ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) )
| ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(135,plain,
~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
( ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) )
| ( aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))) = aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),
inference(unit_resolution,[status(thm)],[137,132]) ).
tff(139,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(ord_max_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))),aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),
inference(transitivity,[status(thm)],[111,72,75,139,115,107]) ).
tff(141,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),
inference(modus_ponens,[status(thm)],[140,79]) ).
tff(142,plain,
^ [X: real,Y4: real] :
refl(( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
<=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
^ [X: real,Y4: real] :
rewrite(( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4)) )
<=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4)) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,axiom,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1753_order__less__imp__le) ).
tff(148,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,plain,
( ( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))) )
<=> ( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4)) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))))),
inference(unit_resolution,[status(thm)],[154,151,135]) ).
tff(156,plain,
^ [X: real,Y4: real] :
refl(( ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
<=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
^ [X: real,Y4: real] :
rewrite(( ( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
<=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
<=> ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [X: real,Y4: real] :
( ~ pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
=> ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1628_antisym__conv1) ).
tff(162,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
( ( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ) )
<=> ( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [X: real,Y4: real] :
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,X),Y4))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,X),Y4))
<=> ( X = Y4 ) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ),
inference(unit_resolution,[status(thm)],[168,165,155]) ).
tff(170,plain,
( ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) )
| pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
| ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) != aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(171,plain,
( ~ ( pp(aa_real_bool(aa_rea7809428808904475482l_bool(ord_less_eq_real,aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))))))
<=> ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) = aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) )
| ( aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) != aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))) ) ),
inference(unit_resolution,[status(thm)],[170,135]) ).
tff(172,plain,
aa_nat_real(semiri5074537144036343181t_real,aa_nat_nat(vEBT_V8646137997579335489_i_l_d,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) != aa_real_real(aa_rea7340605660300375871l_real(times_times_real,aa_num_real(numeral_numeral_real,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one))))),aa_VEBT_VEBT_real(vEBT_VEBT_cnt,vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))))),
inference(unit_resolution,[status(thm)],[171,169]) ).
tff(173,plain,
$false,
inference(unit_resolution,[status(thm)],[172,141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.21 % Problem : ITP280_1 : TPTP v9.0.0. Released v8.0.0.
% 0.13/0.21 % Command : run_E %s %d THM
% 0.14/0.45 % Computer : n011.cluster.edu
% 0.14/0.45 % Model : x86_64 x86_64
% 0.14/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.45 % Memory : 8042.1875MB
% 0.14/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.46 % CPULimit : 300
% 0.14/0.46 % WCLimit : 300
% 0.14/0.46 % DateTime : Thu Jun 19 18:42:12 EDT 2025
% 0.14/0.46 % CPUTime :
% 183.07/183.42 % SZS status Theorem
% 183.07/183.42 % SZS output start Proof
% See solution above
% 183.83/184.15 % E exiting
%------------------------------------------------------------------------------