%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM926^2 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 02:12:28 PM UTC 2025
% Result : Theorem 274.23s 272.30s
% Output : Proof 274.23s
% 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
<=> ( ord_less_eq_int @ one_one_int @ t ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ord_less_int @ one_one_int @ t )
=> ! [X1: $o] :
( ( ( ord_less_int @ one_one_int @ t )
= X1 )
=> ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: int,X2: int] :
( ( ord_less_int @ X1 @ X2 )
= ( ~ ( ( ord_less_eq_int @ X1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: int] :
( ( ord_less_int @ one_one_int @ X1 )
= ( ~ ( ( ord_less_eq_int @ one_one_int @ X1 )
=> ( one_one_int = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( one_one_int = t )
=> ( t = one_one_int ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: int,X2: int] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( ord_less_int @ one_one_int @ t )
= ( ~ ( sP1
=> ( one_one_int = t ) ) ) )
=> ( sP1
=> ( one_one_int = t ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( t = one_one_int ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o > $o] :
( ( X1 @ ( ord_less_int @ one_one_int @ t ) )
=> ! [X2: $o] :
( ( ( ord_less_int @ one_one_int @ t )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: int] :
( ( one_one_int = X1 )
=> ( X1 = one_one_int ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> ( one_one_int = t ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> ~ ! [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,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( one_one_int = t ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [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,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ord_less_int @ one_one_int @ t )
= ( ~ sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ord_less_int @ one_one_int @ t ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o] :
( ( sP16 = X1 )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP16
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(conj_0,conjecture,
~ sP14 ).
thf(h0,negated_conjecture,
sP14,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP11
| ~ sP1
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| ~ sP15
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP18
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP16
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP17
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
sP17,
inference(eq_ind,[status(thm)],[]) ).
thf(10,plain,
( ~ sP19
| ~ sP16
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP5
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
sP6,
inference(eq_sym,[status(thm)],[]) ).
thf(15,plain,
( ~ sP12
| ~ sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_37_zless__le,axiom,
sP3 ).
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,
sP19 ).
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,
sP12 ).
thf(fact_0_tpos,axiom,
sP1 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,fact_37_zless__le,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_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_0_tpos,h0]) ).
thf(0,theorem,
~ sP14,
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM926^2 : TPTP v9.2.0. Released v5.3.0.
% 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 22:16:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 274.23/272.30 % SZS status Theorem
% 274.23/272.30 % Mode: mode472:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=2.:SINE_DEPTH=2
% 274.23/272.30 % Inferences: 3626
% 274.23/272.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------