%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM924^3 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:10:11 PM UTC 2025
% Result : Theorem 23.57s 23.80s
% Output : Proof 23.57s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_min,type,
min: int ).
thf(ty_one_one_int,type,
one_one_int: int ).
thf(ty_bit1,type,
bit1: int > int ).
thf(ty_dvd_dvd_int,type,
dvd_dvd_int: int > int > $o ).
thf(ty_eigen__0,type,
eigen__0: int ).
thf(ty_bit0,type,
bit0: int > int ).
thf(ty_s,type,
s: int ).
thf(ty_power_power_int,type,
power_power_int: int > nat > int ).
thf(ty_zero_zero_int,type,
zero_zero_int: int ).
thf(ty_number_number_of_nat,type,
number_number_of_nat: int > nat ).
thf(ty_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(ty_m,type,
m: int ).
thf(ty_times_times_int,type,
times_times_int: int > int > int ).
thf(ty_number_number_of_int,type,
number_number_of_int: int > int ).
thf(ty_eigen__1,type,
eigen__1: int ).
thf(ty_pls,type,
pls: int ).
thf(ty_zcong,type,
zcong: int > int > int > $o ).
thf(sP1,plain,
( sP1
<=> ( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int )
= zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: int] : ( dvd_dvd_int @ zero_zero_int @ ( times_times_int @ X1 @ zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( dvd_dvd_int @ zero_zero_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: int] :
( ( dvd_dvd_int @ zero_zero_int @ X1 )
=> ( X1 = zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: int,X2: int] : ( dvd_dvd_int @ X1 @ ( times_times_int @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
zcong @ ( power_power_int @ eigen__0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP10
| ~ sP1
| ~ sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP7
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP5 ),
inference(symeq,[status(thm)],[]) ).
thf(fact_537_dvd__triv__right,axiom,
sP8 ).
thf(fact_525_dvd__0__left,axiom,
sP4 ).
thf(fact_3_t,axiom,
sP9 ).
thf(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
sP6 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,h0,fact_537_dvd__triv__right,fact_525_dvd__0__left,fact_3_t,fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
thf(fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
~ ! [X1: int] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ X1 ) ) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,7,h2]) ).
thf(fact_455__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,axiom,
~ ! [X1: int] :
~ ( zcong @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_455__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,8,h1]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM924^3 : TPTP v9.2.0. Released v5.3.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 22:24:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 23.57/23.80 % SZS status Theorem
% 23.57/23.80 % Mode: cade22sinegrackle2xfaf3
% 23.57/23.80 % Steps: 9629
% 23.57/23.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------