TSTP Solution File: NUM925+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM925+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 14:31:43 EDT 2022
% Result : Theorem 61.55s 61.80s
% Output : Refutation 63.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 65
% Syntax : Number of clauses : 180 ( 155 unt; 0 nHn; 180 RR)
% Number of literals : 208 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
is_int(one_one_int),
file('NUM925+3.p',unknown),
[] ).
cnf(3,axiom,
is_int(min),
file('NUM925+3.p',unknown),
[] ).
cnf(4,axiom,
is_int(pls),
file('NUM925+3.p',unknown),
[] ).
cnf(25,axiom,
equal(zero_zero_int,pls),
file('NUM925+3.p',unknown),
[] ).
cnf(32,axiom,
is_int(hAPP_nat_int(u,v)),
file('NUM925+3.p',unknown),
[] ).
cnf(37,axiom,
equal(bit0(pls),pls),
file('NUM925+3.p',unknown),
[] ).
cnf(45,axiom,
equal(number267125858f_real(pls),zero_zero_real),
file('NUM925+3.p',unknown),
[] ).
cnf(53,axiom,
~ equal(zero_zero_real,one_one_real),
file('NUM925+3.p',unknown),
[] ).
cnf(59,axiom,
equal(bit1(min),min),
file('NUM925+3.p',unknown),
[] ).
cnf(76,axiom,
equal(number_number_of_int(bit1(pls)),one_one_int),
file('NUM925+3.p',unknown),
[] ).
cnf(78,axiom,
equal(number267125858f_real(bit1(pls)),one_one_real),
file('NUM925+3.p',unknown),
[] ).
cnf(85,axiom,
equal(hAPP_nat_int(semiri1621563631at_int,one_one_nat),one_one_int),
file('NUM925+3.p',unknown),
[] ).
cnf(88,axiom,
equal(hAPP_nat_real(semiri132038758t_real,zero_zero_nat),zero_zero_real),
file('NUM925+3.p',unknown),
[] ).
cnf(103,axiom,
equal(minus_minus_real(u,zero_zero_real),u),
file('NUM925+3.p',unknown),
[] ).
cnf(116,axiom,
equal(minus_minus_nat(u,u),zero_zero_nat),
file('NUM925+3.p',unknown),
[] ).
cnf(131,axiom,
equal(times_times_int(pls,u),pls),
file('NUM925+3.p',unknown),
[] ).
cnf(132,axiom,
equal(bit1(pls),succ(pls)),
file('NUM925+3.p',unknown),
[] ).
cnf(142,axiom,
( ~ is_int(u)
| is_int(bit0(u)) ),
file('NUM925+3.p',unknown),
[] ).
cnf(145,axiom,
( ~ is_int(u)
| is_int(succ(u)) ),
file('NUM925+3.p',unknown),
[] ).
cnf(151,axiom,
equal(plus_plus_int(u,u),bit0(u)),
file('NUM925+3.p',unknown),
[] ).
cnf(157,axiom,
equal(hAPP_nat_int(power_power_int(one_one_int),u),one_one_int),
file('NUM925+3.p',unknown),
[] ).
cnf(174,axiom,
equal(nat(hAPP_nat_int(semiri1621563631at_int,u)),u),
file('NUM925+3.p',unknown),
[] ).
cnf(178,axiom,
equal(number_number_of_nat(u),nat(number_number_of_int(u))),
file('NUM925+3.p',unknown),
[] ).
cnf(180,axiom,
equal(succ(bit0(u)),bit1(u)),
file('NUM925+3.p',unknown),
[] ).
cnf(181,axiom,
equal(plus_plus_int(u,one_one_int),succ(u)),
file('NUM925+3.p',unknown),
[] ).
cnf(189,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
file('NUM925+3.p',unknown),
[] ).
cnf(192,axiom,
equal(minus_minus_int(u,min),succ(u)),
file('NUM925+3.p',unknown),
[] ).
cnf(209,axiom,
( ~ is_int(u)
| equal(number_number_of_int(u),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(226,axiom,
equal(plus_plus_int(u,v),plus_plus_int(v,u)),
file('NUM925+3.p',unknown),
[] ).
cnf(227,axiom,
equal(plus_plus_nat(u,v),plus_plus_nat(v,u)),
file('NUM925+3.p',unknown),
[] ).
cnf(228,axiom,
equal(plus_plus_real(u,v),plus_plus_real(v,u)),
file('NUM925+3.p',unknown),
[] ).
cnf(237,axiom,
equal(minus_minus_real(plus_plus_real(u,v),v),u),
file('NUM925+3.p',unknown),
[] ).
cnf(238,axiom,
equal(plus_plus_real(minus_minus_real(u,v),v),u),
file('NUM925+3.p',unknown),
[] ).
cnf(240,axiom,
equal(minus_minus_nat(plus_plus_nat(u,v),u),v),
file('NUM925+3.p',unknown),
[] ).
cnf(242,axiom,
equal(bit0(succ(u)),succ(bit1(u))),
file('NUM925+3.p',unknown),
[] ).
cnf(252,axiom,
equal(plus_plus_int(one_one_int,one_one_int),number_number_of_int(bit0(bit1(pls)))),
file('NUM925+3.p',unknown),
[] ).
cnf(260,axiom,
equal(plus_plus_int(plus_plus_int(one_one_int,u),u),bit1(u)),
file('NUM925+3.p',unknown),
[] ).
cnf(263,axiom,
equal(number_number_of_int(hAPP_nat_int(semiri1621563631at_int,u)),hAPP_nat_int(semiri1621563631at_int,u)),
file('NUM925+3.p',unknown),
[] ).
cnf(264,axiom,
equal(number267125858f_real(hAPP_nat_int(semiri1621563631at_int,u)),hAPP_nat_real(semiri132038758t_real,u)),
file('NUM925+3.p',unknown),
[] ).
cnf(265,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,one_one_int))),
file('NUM925+3.p',unknown),
[] ).
cnf(290,axiom,
( ~ is_int(u)
| equal(times_times_int(u,one_one_int),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(294,axiom,
( ~ is_int(u)
| equal(minus_minus_int(u,pls),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(347,axiom,
equal(times_times_int(bit0(u),v),bit0(times_times_int(u,v))),
file('NUM925+3.p',unknown),
[] ).
cnf(362,axiom,
equal(minus_minus_int(pls,bit1(u)),bit1(minus_minus_int(min,u))),
file('NUM925+3.p',unknown),
[] ).
cnf(364,axiom,
equal(minus_minus_int(min,bit0(u)),bit1(minus_minus_int(min,u))),
file('NUM925+3.p',unknown),
[] ).
cnf(373,axiom,
( ~ is_int(u)
| ~ is_int(v)
| is_int(plus_plus_int(v,u)) ),
file('NUM925+3.p',unknown),
[] ).
cnf(379,axiom,
equal(plus_plus_int(number_number_of_int(u),one_one_int),number_number_of_int(plus_plus_int(u,bit1(pls)))),
file('NUM925+3.p',unknown),
[] ).
cnf(382,axiom,
equal(plus_plus_int(bit0(u),bit0(v)),bit0(plus_plus_int(u,v))),
file('NUM925+3.p',unknown),
[] ).
cnf(385,axiom,
equal(plus_plus_int(number_number_of_int(u),number_number_of_int(v)),number_number_of_int(plus_plus_int(u,v))),
file('NUM925+3.p',unknown),
[] ).
cnf(386,axiom,
equal(number267125858f_real(plus_plus_int(u,v)),plus_plus_real(number267125858f_real(u),number267125858f_real(v))),
file('NUM925+3.p',unknown),
[] ).
cnf(387,axiom,
equal(plus_plus_int(bit1(u),bit0(v)),bit1(plus_plus_int(u,v))),
file('NUM925+3.p',unknown),
[] ).
cnf(408,axiom,
equal(number_number_of_int(minus_minus_int(u,v)),minus_minus_int(number_number_of_int(u),number_number_of_int(v))),
file('NUM925+3.p',unknown),
[] ).
cnf(409,axiom,
equal(number267125858f_real(minus_minus_int(u,v)),minus_minus_real(number267125858f_real(u),number267125858f_real(v))),
file('NUM925+3.p',unknown),
[] ).
cnf(411,axiom,
( ~ is_int(u)
| equal(minus_minus_int(plus_plus_int(u,v),v),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(430,axiom,
( ~ is_int(u)
| equal(plus_plus_int(minus_minus_int(u,v),v),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(460,axiom,
equal(plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(u)),number_number_of_int(u)),number_number_of_int(bit0(u))),
file('NUM925+3.p',unknown),
[] ).
cnf(510,axiom,
equal(plus_plus_int(plus_plus_int(u,v),w),plus_plus_int(u,plus_plus_int(v,w))),
file('NUM925+3.p',unknown),
[] ).
cnf(532,axiom,
equal(times_times_int(times_times_int(u,v),w),times_times_int(u,times_times_int(v,w))),
file('NUM925+3.p',unknown),
[] ).
cnf(548,axiom,
equal(times_times_int(bit1(u),v),plus_plus_int(bit0(times_times_int(u,v)),v)),
file('NUM925+3.p',unknown),
[] ).
cnf(608,axiom,
equal(hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('NUM925+3.p',unknown),
[] ).
cnf(629,axiom,
equal(hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(u,v)),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v))),
file('NUM925+3.p',unknown),
[] ).
cnf(630,axiom,
equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(u),v)),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v)),
file('NUM925+3.p',unknown),
[] ).
cnf(637,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,u),pls))
| equal(plus_plus_nat(one_one_nat,number_number_of_nat(u)),one_one_nat) ),
file('NUM925+3.p',unknown),
[] ).
cnf(974,axiom,
( ~ is_int(u)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),u))
| equal(hAPP_nat_int(semiri1621563631at_int,skf30(u)),u) ),
file('NUM925+3.p',unknown),
[] ).
cnf(1722,axiom,
equal(hAPP_nat_int(power_power_int(plus_plus_int(u,v)),number_number_of_nat(bit0(bit1(pls)))),plus_plus_int(plus_plus_int(hAPP_nat_int(power_power_int(u),number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),u),v)),hAPP_nat_int(power_power_int(v),number_number_of_nat(bit0(bit1(pls)))))),
file('NUM925+3.p',unknown),
[] ).
cnf(1779,plain,
equal(number267125858f_real(succ(pls)),one_one_real),
inference(rew,[status(thm),theory(equality)],[132,78]),
[iquote('0:Rew:132.0,78.0')] ).
cnf(1781,plain,
equal(number_number_of_int(succ(pls)),one_one_int),
inference(rew,[status(thm),theory(equality)],[132,76]),
[iquote('0:Rew:132.0,76.0')] ).
cnf(1795,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
inference(rew,[status(thm),theory(equality)],[25,189]),
[iquote('0:Rew:25.0,189.0')] ).
cnf(1809,plain,
equal(plus_plus_real(u,minus_minus_real(v,u)),v),
inference(rew,[status(thm),theory(equality)],[228,238]),
[iquote('0:Rew:228.0,238.0')] ).
cnf(1825,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(one_one_int))),
inference(rew,[status(thm),theory(equality)],[25,265,151]),
[iquote('0:Rew:25.0,265.0,151.0,265.0')] ).
cnf(1828,plain,
equal(plus_plus_int(u,plus_plus_int(one_one_int,u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[226,260]),
[iquote('0:Rew:226.0,260.0')] ).
cnf(1836,plain,
equal(number_number_of_int(succ(succ(pls))),bit0(one_one_int)),
inference(rew,[status(thm),theory(equality)],[151,252,132,242]),
[iquote('0:Rew:151.0,252.0,132.0,252.0,242.0,252.0,132.0,252.0')] ).
cnf(1864,plain,
( ~ is_int(u)
| equal(plus_plus_int(v,minus_minus_int(u,v)),u) ),
inference(rew,[status(thm),theory(equality)],[226,430]),
[iquote('0:Rew:226.0,430.1')] ).
cnf(1874,plain,
equal(plus_plus_int(one_one_int,number_number_of_int(u)),number_number_of_int(plus_plus_int(u,succ(pls)))),
inference(rew,[status(thm),theory(equality)],[226,379,132]),
[iquote('0:Rew:226.0,379.0,132.0,379.0')] ).
cnf(1882,plain,
equal(times_times_int(bit1(u),v),plus_plus_int(v,bit0(times_times_int(u,v)))),
inference(rew,[status(thm),theory(equality)],[226,548]),
[iquote('0:Rew:226.0,548.0')] ).
cnf(1908,plain,
equal(plus_plus_int(pls,number_number_of_int(bit0(u))),number_number_of_int(bit0(u))),
inference(rew,[status(thm),theory(equality)],[151,460,385,510,25]),
[iquote('0:Rew:151.0,460.0,385.0,460.0,510.0,460.0,25.0,460.0')] ).
cnf(1936,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,u),pls))
| equal(plus_plus_nat(one_one_nat,nat(number_number_of_int(u))),one_one_nat) ),
inference(rew,[status(thm),theory(equality)],[178,637]),
[iquote('0:Rew:178.0,637.1')] ).
cnf(1949,plain,
equal(hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(bit0(one_one_int))),pls),
inference(rew,[status(thm),theory(equality)],[1836,608,178,132,242,25]),
[iquote('0:Rew:1836.0,608.0,178.0,608.0,132.0,608.0,242.0,608.0,132.0,608.0,25.0,608.0')] ).
cnf(2074,plain,
( ~ is_int(u)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),u))
| equal(hAPP_nat_int(semiri1621563631at_int,skf30(u)),u) ),
inference(rew,[status(thm),theory(equality)],[25,974]),
[iquote('0:Rew:25.0,974.1')] ).
cnf(2364,plain,
equal(hAPP_nat_int(power_power_int(plus_plus_int(u,v)),nat(bit0(one_one_int))),plus_plus_int(hAPP_nat_int(power_power_int(u),nat(bit0(one_one_int))),plus_plus_int(bit0(times_times_int(one_one_int,times_times_int(u,v))),hAPP_nat_int(power_power_int(v),nat(bit0(one_one_int)))))),
inference(rew,[status(thm),theory(equality)],[510,1722,532,347,1836,178,132,242]),
[iquote('0:Rew:510.0,1722.0,532.0,1722.0,347.0,1722.0,347.0,1722.0,1836.0,1722.0,178.0,1722.0,132.0,1722.0,242.0,1722.0,132.0,1722.0')] ).
cnf(2365,plain,
equal(plus_plus_int(hAPP_nat_int(power_power_int(one_one_int),nat(bit0(one_one_int))),plus_plus_int(bit0(times_times_int(one_one_int,times_times_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(bit0(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[2364,1949]),
[iquote('0:Rew:2364.0,1949.0')] ).
cnf(2366,plain,
equal(plus_plus_int(one_one_int,plus_plus_int(bit0(times_times_int(one_one_int,times_times_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(bit0(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[157,2365]),
[iquote('0:Rew:157.0,2365.0')] ).
cnf(2568,plain,
equal(bit0(one_one_int),succ(one_one_int)),
inference(spr,[status(thm),theory(equality)],[151,181]),
[iquote('0:SpR:151.0,181.0')] ).
cnf(2616,plain,
equal(plus_plus_int(one_one_int,plus_plus_int(bit0(times_times_int(one_one_int,times_times_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[2568,2366]),
[iquote('0:Rew:2568.0,2366.0')] ).
cnf(2630,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),succ(one_one_int))),
inference(rew,[status(thm),theory(equality)],[2568,1825]),
[iquote('0:Rew:2568.0,1825.0')] ).
cnf(2661,plain,
equal(bit0(bit1(u)),succ(bit1(bit0(u)))),
inference(spr,[status(thm),theory(equality)],[180,242]),
[iquote('0:SpR:180.0,242.0')] ).
cnf(2764,plain,
( ~ is_int(succ(pls))
| equal(succ(pls),one_one_int) ),
inference(spr,[status(thm),theory(equality)],[209,1781]),
[iquote('0:SpR:209.1,1781.0')] ).
cnf(2768,plain,
equal(succ(pls),one_one_int),
inference(ssi,[status(thm)],[2764,145,4]),
[iquote('0:SSi:2764.0,145.0,4.1')] ).
cnf(2769,plain,
equal(number267125858f_real(one_one_int),one_one_real),
inference(rew,[status(thm),theory(equality)],[2768,1779]),
[iquote('0:Rew:2768.0,1779.0')] ).
cnf(2771,plain,
equal(bit1(pls),one_one_int),
inference(rew,[status(thm),theory(equality)],[2768,132]),
[iquote('0:Rew:2768.0,132.0')] ).
cnf(2830,plain,
equal(plus_plus_int(one_one_int,number_number_of_int(u)),number_number_of_int(plus_plus_int(u,one_one_int))),
inference(rew,[status(thm),theory(equality)],[2768,1874]),
[iquote('0:Rew:2768.0,1874.0')] ).
cnf(2835,plain,
equal(plus_plus_int(one_one_int,number_number_of_int(u)),number_number_of_int(succ(u))),
inference(rew,[status(thm),theory(equality)],[181,2830]),
[iquote('0:Rew:181.0,2830.0')] ).
cnf(2883,plain,
equal(minus_minus_real(u,minus_minus_real(u,v)),v),
inference(spr,[status(thm),theory(equality)],[1809,237]),
[iquote('0:SpR:1809.0,237.0')] ).
cnf(2944,plain,
equal(plus_plus_int(one_one_int,u),succ(u)),
inference(spr,[status(thm),theory(equality)],[226,181]),
[iquote('0:SpR:226.0,181.0')] ).
cnf(2952,plain,
equal(succ(plus_plus_int(bit0(times_times_int(one_one_int,times_times_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[2944,2616]),
[iquote('0:Rew:2944.0,2616.0')] ).
cnf(2954,plain,
equal(number_number_of_int(succ(u)),succ(number_number_of_int(u))),
inference(rew,[status(thm),theory(equality)],[2944,2835]),
[iquote('0:Rew:2944.0,2835.0')] ).
cnf(2982,plain,
equal(plus_plus_int(u,succ(u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[2944,1828]),
[iquote('0:Rew:2944.0,1828.0')] ).
cnf(3082,plain,
equal(succ(number_number_of_int(bit0(u))),number_number_of_int(bit1(u))),
inference(spr,[status(thm),theory(equality)],[180,2954]),
[iquote('0:SpR:180.0,2954.0')] ).
cnf(3565,plain,
equal(succ(bit1(bit0(min))),bit0(min)),
inference(spr,[status(thm),theory(equality)],[59,2661]),
[iquote('0:SpR:59.0,2661.0')] ).
cnf(3577,plain,
equal(succ(number_number_of_int(bit1(bit0(min)))),number_number_of_int(bit0(min))),
inference(spr,[status(thm),theory(equality)],[3565,2954]),
[iquote('0:SpR:3565.0,2954.0')] ).
cnf(3622,plain,
equal(succ(bit1(number_number_of_int(bit0(u)))),bit0(number_number_of_int(bit1(u)))),
inference(spr,[status(thm),theory(equality)],[3082,242]),
[iquote('0:SpR:3082.0,242.0')] ).
cnf(3625,plain,
equal(plus_plus_int(number_number_of_int(bit0(u)),number_number_of_int(bit1(u))),bit1(number_number_of_int(bit0(u)))),
inference(spr,[status(thm),theory(equality)],[3082,2982]),
[iquote('0:SpR:3082.0,2982.0')] ).
cnf(3639,plain,
equal(plus_plus_int(number_number_of_int(bit1(u)),number_number_of_int(bit0(u))),bit1(number_number_of_int(bit0(u)))),
inference(rew,[status(thm),theory(equality)],[226,3625]),
[iquote('0:Rew:226.0,3625.0')] ).
cnf(3640,plain,
equal(number_number_of_int(bit1(plus_plus_int(u,u))),bit1(number_number_of_int(bit0(u)))),
inference(rew,[status(thm),theory(equality)],[387,3639,385]),
[iquote('0:Rew:387.0,3639.0,385.0,3639.0')] ).
cnf(3641,plain,
equal(number_number_of_int(bit1(bit0(u))),bit1(number_number_of_int(bit0(u)))),
inference(rew,[status(thm),theory(equality)],[151,3640]),
[iquote('0:Rew:151.0,3640.0')] ).
cnf(3643,plain,
equal(succ(bit1(number_number_of_int(bit0(min)))),number_number_of_int(bit0(min))),
inference(rew,[status(thm),theory(equality)],[3641,3577]),
[iquote('0:Rew:3641.0,3577.0')] ).
cnf(3644,plain,
equal(number_number_of_int(bit0(min)),bit0(number_number_of_int(bit1(min)))),
inference(rew,[status(thm),theory(equality)],[3622,3643]),
[iquote('0:Rew:3622.0,3643.0')] ).
cnf(3645,plain,
equal(number_number_of_int(bit0(min)),bit0(number_number_of_int(min))),
inference(rew,[status(thm),theory(equality)],[59,3644]),
[iquote('0:Rew:59.0,3644.0')] ).
cnf(3656,plain,
( ~ is_int(bit0(min))
| equal(bit0(number_number_of_int(min)),bit0(min)) ),
inference(spr,[status(thm),theory(equality)],[3645,209]),
[iquote('0:SpR:3645.0,209.1')] ).
cnf(3657,plain,
equal(number_number_of_int(bit1(min)),succ(bit0(number_number_of_int(min)))),
inference(spr,[status(thm),theory(equality)],[3645,3082]),
[iquote('0:SpR:3645.0,3082.0')] ).
cnf(3659,plain,
equal(bit1(number_number_of_int(min)),number_number_of_int(min)),
inference(rew,[status(thm),theory(equality)],[59,3657,180]),
[iquote('0:Rew:59.0,3657.0,180.0,3657.0')] ).
cnf(3690,plain,
equal(bit0(number_number_of_int(min)),bit0(min)),
inference(ssi,[status(thm)],[3656,142,3]),
[iquote('0:SSi:3656.0,142.0,3.1')] ).
cnf(3723,plain,
equal(bit1(number_number_of_int(min)),succ(bit0(min))),
inference(spr,[status(thm),theory(equality)],[3690,180]),
[iquote('0:SpR:3690.0,180.0')] ).
cnf(3731,plain,
equal(number_number_of_int(min),min),
inference(rew,[status(thm),theory(equality)],[3659,3723,59,180]),
[iquote('0:Rew:3659.0,3723.0,59.0,3723.0,180.0,3723.0')] ).
cnf(3968,plain,
equal(minus_minus_int(pls,one_one_int),bit1(minus_minus_int(min,pls))),
inference(spr,[status(thm),theory(equality)],[2771,362]),
[iquote('0:SpR:2771.0,362.0')] ).
cnf(3975,plain,
equal(bit1(minus_minus_int(min,pls)),minus_minus_int(min,pls)),
inference(spr,[status(thm),theory(equality)],[37,364]),
[iquote('0:SpR:37.0,364.0')] ).
cnf(3980,plain,
equal(minus_minus_int(pls,one_one_int),minus_minus_int(min,pls)),
inference(rew,[status(thm),theory(equality)],[3975,3968]),
[iquote('0:Rew:3975.0,3968.0')] ).
cnf(4472,plain,
equal(times_times_int(succ(one_one_int),u),bit0(times_times_int(one_one_int,u))),
inference(spr,[status(thm),theory(equality)],[2568,347]),
[iquote('0:SpR:2568.0,347.0')] ).
cnf(4493,plain,
( ~ is_int(succ(one_one_int))
| equal(bit0(times_times_int(one_one_int,one_one_int)),succ(one_one_int)) ),
inference(spr,[status(thm),theory(equality)],[4472,290]),
[iquote('0:SpR:4472.0,290.1')] ).
cnf(4497,plain,
equal(bit0(times_times_int(one_one_int,one_one_int)),succ(one_one_int)),
inference(ssi,[status(thm)],[4493,145,1]),
[iquote('0:SSi:4493.0,145.0,1.1')] ).
cnf(4512,plain,
equal(bit0(times_times_int(times_times_int(one_one_int,one_one_int),u)),times_times_int(succ(one_one_int),u)),
inference(spr,[status(thm),theory(equality)],[4497,347]),
[iquote('0:SpR:4497.0,347.0')] ).
cnf(4537,plain,
equal(bit0(times_times_int(times_times_int(one_one_int,one_one_int),u)),bit0(times_times_int(one_one_int,u))),
inference(rew,[status(thm),theory(equality)],[4472,4512]),
[iquote('0:Rew:4472.0,4512.0')] ).
cnf(4538,plain,
equal(bit0(times_times_int(one_one_int,times_times_int(one_one_int,u))),bit0(times_times_int(one_one_int,u))),
inference(rew,[status(thm),theory(equality)],[532,4537]),
[iquote('0:Rew:532.0,4537.0')] ).
cnf(4539,plain,
equal(succ(plus_plus_int(bit0(times_times_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[4538,2952]),
[iquote('0:Rew:4538.0,2952.0')] ).
cnf(6616,plain,
equal(number_number_of_int(plus_plus_int(u,u)),bit0(number_number_of_int(u))),
inference(spr,[status(thm),theory(equality)],[385,151]),
[iquote('0:SpR:385.0,151.0')] ).
cnf(6637,plain,
equal(plus_plus_int(min,number_number_of_int(u)),number_number_of_int(plus_plus_int(min,u))),
inference(spr,[status(thm),theory(equality)],[3731,385]),
[iquote('0:SpR:3731.0,385.0')] ).
cnf(6638,plain,
equal(number_number_of_int(bit0(u)),bit0(number_number_of_int(u))),
inference(rew,[status(thm),theory(equality)],[151,6616]),
[iquote('0:Rew:151.0,6616.0')] ).
cnf(6642,plain,
equal(plus_plus_int(pls,bit0(number_number_of_int(u))),bit0(number_number_of_int(u))),
inference(rew,[status(thm),theory(equality)],[6638,1908]),
[iquote('0:Rew:6638.0,1908.0')] ).
cnf(6878,plain,
equal(plus_plus_int(pls,bit0(hAPP_nat_int(semiri1621563631at_int,u))),bit0(hAPP_nat_int(semiri1621563631at_int,u))),
inference(spr,[status(thm),theory(equality)],[263,6642]),
[iquote('0:SpR:263.0,6642.0')] ).
cnf(7070,plain,
equal(plus_plus_int(pls,bit0(u)),bit0(plus_plus_int(pls,u))),
inference(spr,[status(thm),theory(equality)],[37,382]),
[iquote('0:SpR:37.0,382.0')] ).
cnf(7086,plain,
equal(bit0(plus_plus_int(pls,hAPP_nat_int(semiri1621563631at_int,u))),bit0(hAPP_nat_int(semiri1621563631at_int,u))),
inference(rew,[status(thm),theory(equality)],[7070,6878]),
[iquote('0:Rew:7070.0,6878.0')] ).
cnf(7261,plain,
equal(number267125858f_real(succ(u)),minus_minus_real(number267125858f_real(u),number267125858f_real(min))),
inference(spr,[status(thm),theory(equality)],[192,409]),
[iquote('0:SpR:192.0,409.0')] ).
cnf(7268,plain,
equal(number267125858f_real(minus_minus_int(min,pls)),minus_minus_real(number267125858f_real(pls),number267125858f_real(one_one_int))),
inference(spr,[status(thm),theory(equality)],[3980,409]),
[iquote('0:SpR:3980.0,409.0')] ).
cnf(7288,plain,
equal(number267125858f_real(min),minus_minus_real(zero_zero_real,one_one_real)),
inference(rew,[status(thm),theory(equality)],[103,7268,45,409,2769]),
[iquote('0:Rew:103.0,7268.0,45.0,7268.0,409.0,7268.0,45.0,7268.0,2769.0,7268.0')] ).
cnf(7289,plain,
equal(number267125858f_real(succ(u)),minus_minus_real(number267125858f_real(u),minus_minus_real(zero_zero_real,one_one_real))),
inference(rew,[status(thm),theory(equality)],[7288,7261]),
[iquote('0:Rew:7288.0,7261.0')] ).
cnf(8680,plain,
( ~ is_int(min)
| equal(minus_minus_int(number_number_of_int(plus_plus_int(min,u)),number_number_of_int(u)),min) ),
inference(spr,[status(thm),theory(equality)],[6637,411]),
[iquote('0:SpR:6637.0,411.1')] ).
cnf(8696,plain,
equal(minus_minus_int(number_number_of_int(plus_plus_int(min,u)),number_number_of_int(u)),min),
inference(ssi,[status(thm)],[8680,3]),
[iquote('0:SSi:8680.0,3.0')] ).
cnf(9635,plain,
( ~ is_int(u)
| equal(minus_minus_int(number_number_of_int(u),number_number_of_int(minus_minus_int(u,min))),min) ),
inference(spr,[status(thm),theory(equality)],[1864,8696]),
[iquote('0:SpR:1864.1,8696.0')] ).
cnf(9922,plain,
( ~ is_int(u)
| equal(minus_minus_int(u,succ(u)),min) ),
inference(rew,[status(thm),theory(equality)],[209,9635,192,3731,408]),
[iquote('0:Rew:209.1,9635.1,192.0,9635.1,3731.0,9635.1,408.0,9635.1')] ).
cnf(13197,plain,
equal(times_times_int(one_one_int,u),plus_plus_int(u,bit0(times_times_int(pls,u)))),
inference(spr,[status(thm),theory(equality)],[2771,1882]),
[iquote('0:SpR:2771.0,1882.0')] ).
cnf(13221,plain,
equal(times_times_int(one_one_int,u),plus_plus_int(u,pls)),
inference(rew,[status(thm),theory(equality)],[37,13197,131]),
[iquote('0:Rew:37.0,13197.0,131.0,13197.0')] ).
cnf(13272,plain,
equal(succ(plus_plus_int(bit0(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),pls)),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[13221,4539]),
[iquote('0:Rew:13221.0,4539.0')] ).
cnf(13467,plain,
equal(succ(plus_plus_int(bit0(plus_plus_int(pls,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[226,13272]),
[iquote('0:Rew:226.0,13272.0')] ).
cnf(13468,plain,
equal(succ(plus_plus_int(bit0(hAPP_nat_int(semiri1621563631at_int,n)),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int))))),pls),
inference(rew,[status(thm),theory(equality)],[7086,13467]),
[iquote('0:Rew:7086.0,13467.0')] ).
cnf(15685,plain,
equal(plus_plus_int(u,plus_plus_int(v,w)),plus_plus_int(w,plus_plus_int(u,v))),
inference(spr,[status(thm),theory(equality)],[510,226]),
[iquote('0:SpR:510.0,226.0')] ).
cnf(15717,plain,
equal(plus_plus_int(bit0(u),v),plus_plus_int(u,plus_plus_int(u,v))),
inference(spr,[status(thm),theory(equality)],[151,510]),
[iquote('0:SpR:151.0,510.0')] ).
cnf(15875,plain,
equal(succ(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),nat(succ(one_one_int)))))),pls),
inference(rew,[status(thm),theory(equality)],[15717,13468]),
[iquote('0:Rew:15717.0,13468.0')] ).
cnf(28095,plain,
equal(hAPP_nat_nat(power_power_nat(u),v),nat(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v))),
inference(spr,[status(thm),theory(equality)],[630,174]),
[iquote('0:SpR:630.0,174.0')] ).
cnf(28097,plain,
equal(number267125858f_real(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v)),hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(u),v))),
inference(spr,[status(thm),theory(equality)],[630,264]),
[iquote('0:SpR:630.0,264.0')] ).
cnf(28138,plain,
equal(hAPP_nat_int(semiri1621563631at_int,nat(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v))),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v)),
inference(rew,[status(thm),theory(equality)],[28095,630]),
[iquote('0:Rew:28095.0,630.0')] ).
cnf(28182,plain,
equal(number267125858f_real(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v)),hAPP_nat_real(semiri132038758t_real,nat(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,u)),v)))),
inference(rew,[status(thm),theory(equality)],[28095,28097]),
[iquote('0:Rew:28095.0,28097.0')] ).
cnf(29466,plain,
equal(plus_plus_nat(u,v),nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v)))),
inference(spr,[status(thm),theory(equality)],[629,174]),
[iquote('0:SpR:629.0,174.0')] ).
cnf(29468,plain,
equal(number267125858f_real(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v))),hAPP_nat_real(semiri132038758t_real,plus_plus_nat(u,v))),
inference(spr,[status(thm),theory(equality)],[629,264]),
[iquote('0:SpR:629.0,264.0')] ).
cnf(29496,plain,
equal(hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(u,v)),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,v),hAPP_nat_int(semiri1621563631at_int,u))),
inference(spr,[status(thm),theory(equality)],[227,629]),
[iquote('0:SpR:227.0,629.0')] ).
cnf(29562,plain,
equal(minus_minus_nat(nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v))),u),v),
inference(rew,[status(thm),theory(equality)],[29466,240]),
[iquote('0:Rew:29466.0,240.0')] ).
cnf(29888,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,u),pls))
| equal(nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,one_one_nat),hAPP_nat_int(semiri1621563631at_int,nat(number_number_of_int(u))))),one_one_nat) ),
inference(rew,[status(thm),theory(equality)],[29466,1936]),
[iquote('0:Rew:29466.0,1936.1')] ).
cnf(29984,plain,
equal(hAPP_nat_int(semiri1621563631at_int,nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v)))),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,v),hAPP_nat_int(semiri1621563631at_int,u))),
inference(rew,[status(thm),theory(equality)],[29466,29496]),
[iquote('0:Rew:29466.0,29496.0')] ).
cnf(29999,plain,
equal(plus_plus_real(hAPP_nat_real(semiri132038758t_real,u),hAPP_nat_real(semiri132038758t_real,v)),hAPP_nat_real(semiri132038758t_real,plus_plus_nat(u,v))),
inference(rew,[status(thm),theory(equality)],[264,29468,386]),
[iquote('0:Rew:264.0,29468.0,264.0,29468.0,386.0,29468.0')] ).
cnf(30000,plain,
equal(plus_plus_real(hAPP_nat_real(semiri132038758t_real,u),hAPP_nat_real(semiri132038758t_real,v)),hAPP_nat_real(semiri132038758t_real,nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,u),hAPP_nat_int(semiri1621563631at_int,v))))),
inference(rew,[status(thm),theory(equality)],[29466,29999]),
[iquote('0:Rew:29466.0,29999.0')] ).
cnf(30235,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,u),pls))
| equal(nat(succ(hAPP_nat_int(semiri1621563631at_int,nat(number_number_of_int(u))))),one_one_nat) ),
inference(rew,[status(thm),theory(equality)],[2944,29888,85]),
[iquote('0:Rew:2944.0,29888.1,85.0,29888.1')] ).
cnf(30616,plain,
equal(minus_minus_nat(nat(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,u))),one_one_nat),u),
inference(spr,[status(thm),theory(equality)],[85,29562]),
[iquote('0:SpR:85.0,29562.0')] ).
cnf(30636,plain,
equal(minus_minus_nat(nat(succ(hAPP_nat_int(semiri1621563631at_int,u))),one_one_nat),u),
inference(rew,[status(thm),theory(equality)],[2944,30616]),
[iquote('0:Rew:2944.0,30616.0')] ).
cnf(63242,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls))
| equal(nat(succ(hAPP_nat_int(semiri1621563631at_int,nat(min)))),one_one_nat) ),
inference(spr,[status(thm),theory(equality)],[3731,30235]),
[iquote('0:SpR:3731.0,30235.1')] ).
cnf(63275,plain,
equal(nat(succ(hAPP_nat_int(semiri1621563631at_int,nat(min)))),one_one_nat),
inference(mrr,[status(thm)],[63242,1795]),
[iquote('0:MRR:63242.0,1795.0')] ).
cnf(63299,plain,
equal(nat(min),minus_minus_nat(one_one_nat,one_one_nat)),
inference(spr,[status(thm),theory(equality)],[63275,30636]),
[iquote('0:SpR:63275.0,30636.0')] ).
cnf(63318,plain,
equal(nat(min),zero_zero_nat),
inference(rew,[status(thm),theory(equality)],[116,63299]),
[iquote('0:Rew:116.0,63299.0')] ).
cnf(64344,plain,
( ~ is_int(succ(one_one_int))
| equal(hAPP_nat_int(semiri1621563631at_int,skf30(succ(one_one_int))),succ(one_one_int)) ),
inference(res,[status(thm),theory(equality)],[2630,2074]),
[iquote('0:Res:2630.0,2074.1')] ).
cnf(64392,plain,
equal(hAPP_nat_int(semiri1621563631at_int,skf30(succ(one_one_int))),succ(one_one_int)),
inference(ssi,[status(thm)],[64344,145,1]),
[iquote('0:SSi:64344.0,145.0,1.1')] ).
cnf(73180,plain,
equal(nat(succ(one_one_int)),skf30(succ(one_one_int))),
inference(spr,[status(thm),theory(equality)],[64392,174]),
[iquote('0:SpR:64392.0,174.0')] ).
cnf(73842,plain,
equal(succ(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int)))))),pls),
inference(rew,[status(thm),theory(equality)],[73180,15875]),
[iquote('0:Rew:73180.0,15875.0')] ).
cnf(82394,plain,
( ~ is_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))))
| equal(minus_minus_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))),pls),min) ),
inference(spr,[status(thm),theory(equality)],[73842,9922]),
[iquote('0:SpR:73842.0,9922.1')] ).
cnf(82412,plain,
equal(minus_minus_real(number267125858f_real(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int)))))),minus_minus_real(zero_zero_real,one_one_real)),number267125858f_real(pls)),
inference(spr,[status(thm),theory(equality)],[73842,7289]),
[iquote('0:SpR:73842.0,7289.0')] ).
cnf(82467,plain,
equal(minus_minus_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,n),plus_plus_real(hAPP_nat_real(semiri132038758t_real,n),number267125858f_real(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int)))))),minus_minus_real(zero_zero_real,one_one_real)),zero_zero_real),
inference(rew,[status(thm),theory(equality)],[264,82412,386,45]),
[iquote('0:Rew:264.0,82412.0,386.0,82412.0,386.0,82412.0,45.0,82412.0')] ).
cnf(82468,plain,
equal(minus_minus_real(hAPP_nat_real(semiri132038758t_real,nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(semiri1621563631at_int,nat(hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))))))),minus_minus_real(zero_zero_real,one_one_real)),zero_zero_real),
inference(rew,[status(thm),theory(equality)],[15685,82467,29984,30000,28182]),
[iquote('0:Rew:15685.0,82467.0,29984.0,82467.0,30000.0,82467.0,30000.0,82467.0,28182.0,82467.0')] ).
cnf(82469,plain,
equal(minus_minus_real(hAPP_nat_real(semiri132038758t_real,nat(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))))),minus_minus_real(zero_zero_real,one_one_real)),zero_zero_real),
inference(rew,[status(thm),theory(equality)],[28138,82468]),
[iquote('0:Rew:28138.0,82468.0')] ).
cnf(82477,plain,
( ~ is_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))))
| equal(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))),min) ),
inference(rew,[status(thm),theory(equality)],[294,82394]),
[iquote('0:Rew:294.1,82394.1')] ).
cnf(82478,plain,
equal(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),plus_plus_int(hAPP_nat_int(semiri1621563631at_int,n),hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,n)),skf30(succ(one_one_int))))),min),
inference(ssi,[status(thm)],[82477,373,32]),
[iquote('0:SSi:82477.0,373.0,32.0,373.2,32.0,32.2')] ).
cnf(82499,plain,
equal(minus_minus_real(hAPP_nat_real(semiri132038758t_real,nat(min)),minus_minus_real(zero_zero_real,one_one_real)),zero_zero_real),
inference(rew,[status(thm),theory(equality)],[82478,82469]),
[iquote('0:Rew:82478.0,82469.0')] ).
cnf(82510,plain,
equal(zero_zero_real,one_one_real),
inference(rew,[status(thm),theory(equality)],[2883,82499,88,63318]),
[iquote('0:Rew:2883.0,82499.0,88.0,82499.0,63318.0,82499.0')] ).
cnf(82511,plain,
$false,
inference(mrr,[status(thm)],[82510,53]),
[iquote('0:MRR:82510.0,53.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM925+3 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 11:48:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 61.55/61.80
% 61.55/61.80 SPASS V 3.9
% 61.55/61.80 SPASS beiseite: Proof found.
% 61.55/61.80 % SZS status Theorem
% 61.55/61.80 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.55/61.80 SPASS derived 53749 clauses, backtracked 0 clauses, performed 0 splits and kept 19500 clauses.
% 61.55/61.80 SPASS allocated 175629 KBytes.
% 61.55/61.80 SPASS spent 0:01:01.38 on the problem.
% 61.55/61.80 0:00:00.06 for the input.
% 61.55/61.80 0:00:00.46 for the FLOTTER CNF translation.
% 61.55/61.80 0:00:00.81 for inferences.
% 61.55/61.80 0:00:00.00 for the backtracking.
% 61.55/61.80 0:0:59.14 for the reduction.
% 61.55/61.80
% 61.55/61.80
% 61.55/61.80 Here is a proof with depth 9, length 180 :
% 61.55/61.80 % SZS output start Refutation
% See solution above
% 63.35/63.52 Formulae used in the proof : gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint gsy_c_Int_OMin gsy_c_Int_OPls fact_98_Pls__def gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint fact_97_Bit0__Pls fact_112_semiring__norm_I112_J fact_230_zero__neq__one fact_1017_Bit1__Min fact_145_semiring__numeral__1__eq__1 fact_147_semiring__numeral__1__eq__1 fact_254_transfer__int__nat__numerals_I2_J fact_295_of__nat__0 fact_597_diff__0__right fact_628_diff__self__eq__0 fact_708_mult__Pls fact_808_succ__Pls gsy_c_Int_OBit0 gsy_c_Int_Osucc fact_103_Bit0__def fact_233_power__one fact_652_nat__int fact_767_nat__number__of__def fact_809_succ__Bit0 fact_814_succ__def fact_1007_bin__less__0__simps_I2_J fact_1021_diff__bin__simps_I2_J fact_177_number__of__is__id fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_603_add__diff__cancel fact_605_diff__add__cancel fact_704_diff__add__inverse fact_810_succ__Bit1 fact_18_semiring__one__add__one__is__two fact_128_Bit1__def fact_131_number__of__int fact_132_number__of__int fact_166_zero__less__two fact_717_zmult__1__right fact_861_diff__bin__simps_I1_J fact_709_mult__Bit0 fact_1026_diff__bin__simps_I4_J fact_1028_diff__bin__simps_I5_J gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint fact_14_add__special_I3_J fact_102_add__Bit0__Bit0 fact_124_number__of__add fact_125_number__of__add fact_126_add__Bit1__Bit0 fact_467_number__of__diff fact_468_number__of__diff fact_604_add__diff__cancel fact_984_Int2_Oaux1 fact_141_number__of__Bit0 fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J fact_451_zmult__assoc fact_804_mult__Bit1 conj_0 fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J fact_407_nat__1__add__number__of fact_297_zero__less__imp__eq__int fact_264_zero__less__one fact_409_zadd__power2
% 63.35/63.52
%------------------------------------------------------------------------------