TSTP Solution File: NUM926^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM926^1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 13:57:44 EDT 2022
% Result : Theorem 185.54s 181.33s
% Output : Proof 185.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_int,type,
int: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_bit1,type,
bit1: int > int ).
thf(ty_bit0,type,
bit0: int > int ).
thf(ty_times_times_int,type,
times_times_int: int > int > int ).
thf(ty_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(ty_t,type,
t: int ).
thf(ty_one_one_int,type,
one_one_int: int ).
thf(ty_pls,type,
pls: int ).
thf(ty_power_power_int,type,
power_power_int: int > nat > int ).
thf(ty_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(ty_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(ty_number_number_of_int,type,
number_number_of_int: int > int ).
thf(ty_m,type,
m: int ).
thf(ty_number_number_of_nat,type,
number_number_of_nat: int > nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: int,X2: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ X1 @ one_one_int ) @ X2 )
= ( ord_less_int @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ord_less_int @ t @ one_one_int ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: int,X2: int] :
( ( ord_less_eq_int @ X1 @ X2 )
=> ( ( ord_less_eq_int @ X2 @ t )
=> ( ord_less_eq_int @ X1 @ t ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ord_less_eq_int @ ( plus_plus_int @ t @ one_one_int ) @ one_one_int ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: int] :
( ( ord_less_int @ t @ X1 )
= ( ~ ( ( ord_less_eq_int @ t @ X1 )
=> ( t = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: int,X2: int] :
( ( ord_less_int @ X1 @ X2 )
=> ( ord_less_eq_int @ ( plus_plus_int @ X1 @ one_one_int ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ord_less_eq_int @ ( plus_plus_int @ t @ one_one_int ) @ t ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ord_less_eq_int @ one_one_int @ t )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_less_eq_int @ t @ t ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: int,X2: int,X3: int] :
( ( ord_less_eq_int @ X2 @ X3 )
=> ( ( ord_less_eq_int @ X3 @ X1 )
=> ( ord_less_eq_int @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: int,X2: int] :
( ( ord_less_eq_int @ X1 @ X2 )
=> ( ( ord_less_eq_int @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ~ sP2
=> ( t = one_one_int ) )
=> ( ord_less_int @ one_one_int @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: int] :
( ( ord_less_eq_int @ t @ X1 )
=> ( ( ord_less_eq_int @ X1 @ t )
=> ( t = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: int] :
( ( ord_less_int @ t @ X1 )
=> ( ord_less_eq_int @ ( plus_plus_int @ t @ one_one_int ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: int] :
( ~ ( ~ ( ord_less_int @ t @ X1 )
=> ( t = X1 ) )
=> ( ord_less_int @ X1 @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP10
=> ( sP10
=> ( t = t ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( t = one_one_int ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP10
=> ( t = t ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: int,X2: int] :
( ~ ( ~ ( ord_less_int @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ord_less_int @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP2
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ord_less_int @ t @ t ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: int,X2: int] :
( ( ord_less_int @ X1 @ X2 )
= ( ~ ( ( ord_less_eq_int @ X1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ t @ one_one_int ) @ X1 )
= ( ord_less_int @ t @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP23
= ( ~ sP20 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( ord_less_int @ one_one_int @ t )
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ t @ one_one_int ) @ X1 )
=> ( ( ord_less_eq_int @ X1 @ t )
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: int] : ( ord_less_eq_int @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP7 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ord_less_int @ one_one_int @ t ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP19
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ord_less_eq_int @ one_one_int @ t ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(conj_0,conjecture,
~ sP25 ).
thf(h0,negated_conjecture,
sP25,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP31
| ~ sP7
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP27
| ~ sP23
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP26
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP29
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP34
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| ~ sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP24
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP30
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP21
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP16
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| sP22
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| sP2
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP33
| ~ sP19
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP28
| ~ sP32
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_0_tpos,axiom,
sP34 ).
thf(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
sP33 ).
thf(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
sP28 ).
thf(fact_26_zle__refl,axiom,
sP30 ).
thf(fact_28_zless__le,axiom,
sP24 ).
thf(fact_29_zless__linear,axiom,
sP21 ).
thf(fact_30_zle__trans,axiom,
sP11 ).
thf(fact_31_zle__antisym,axiom,
sP12 ).
thf(fact_71_zless__imp__add1__zle,axiom,
sP6 ).
thf(fact_72_add1__zle__eq,axiom,
sP1 ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,fact_0_tpos,fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,fact_26_zle__refl,fact_28_zless__le,fact_29_zless__linear,fact_30_zle__trans,fact_31_zle__antisym,fact_71_zless__imp__add1__zle,fact_72_add1__zle__eq,h0]) ).
thf(0,theorem,
~ sP25,
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926^1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.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 : 600
% 0.12/0.34 % DateTime : Thu Jul 7 18:28:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 124.45/119.95 slave returned with unknown status
% 185.54/181.33 % SZS status Theorem
% 185.54/181.33 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 185.54/181.33 % Inferences: 649
% 185.54/181.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------