TSTP Solution File: NUM016^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 Aug 31 11:37:57 EDT 2023
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_factorial_plus_one,type,
factorial_plus_one: $i > $i ).
thf(ty_prime_divisor,type,
prime_divisor: $i > $i ).
thf(ty_divides,type,
divides: $i > $i > $o ).
thf(ty_less,type,
less: $i > $i > $o ).
thf(ty_a,type,
a: $i ).
thf(ty_prime,type,
prime: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( divides @ ( prime_divisor @ ( factorial_plus_one @ a ) ) @ ( factorial_plus_one @ a ) )
=> ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( prime @ ( factorial_plus_one @ a ) )
=> ~ ( less @ a @ ( factorial_plus_one @ a ) ) )
=> ( less @ ( factorial_plus_one @ a ) @ ( factorial_plus_one @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( divides @ ( prime_divisor @ ( factorial_plus_one @ a ) ) @ ( factorial_plus_one @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( divides @ ( prime_divisor @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( less @ ( factorial_plus_one @ a ) @ ( factorial_plus_one @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( prime @ ( factorial_plus_one @ a ) )
=> ~ ( less @ a @ ( factorial_plus_one @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( prime @ ( factorial_plus_one @ a ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( divides @ ( prime_divisor @ ( factorial_plus_one @ a ) ) @ X1 )
=> ~ ( less @ X1 @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( divides @ ( prime_divisor @ ( factorial_plus_one @ a ) ) @ ( factorial_plus_one @ X1 ) )
=> ( less @ X1 @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
=> ( less @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP4
=> ~ ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( prime @ ( factorial_plus_one @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( ( prime @ X1 )
=> ~ ( less @ a @ X1 ) )
=> ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] :
( ( divides @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
~ ( less @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP8
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( prime @ ( prime_divisor @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP15
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP20
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( less @ a @ ( factorial_plus_one @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(cNUM016_1,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 )
=> ~ ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ) )
=> ~ ( prime @ a ) )
=> ~ sP17 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 )
=> ~ ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ) )
=> ~ ( prime @ a ) )
=> ~ sP17 ),
inference(assume_negation,[status(cth)],[cNUM016_1]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 )
=> ~ ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ) )
=> ~ ( prime @ a ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP17,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 )
=> ~ ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
prime @ a,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP21,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP2,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP18,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: $i] : ( divides @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP19,
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| ~ sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP20
| ~ sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP23
| sP20
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| ~ sP15
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP15
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP22
| sP15
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP21
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP2
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h21,h16,h14,h12,h10,h8,h2]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h19,19,h21,h22]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,20,h19,h20]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,21,h17,h18]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h13,22,h15,h16]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,23,h13,h14]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,24,h11,h12]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,25,h9,h10]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,26,h7,h8]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,28,h3,h4]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,29,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP19
=> ~ ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
=> ~ ( less @ X2 @ X1 ) ) )
=> ~ ! [X1: $i] : ( divides @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( divides @ X1 @ X2 )
=> ~ ( divides @ X2 @ X3 ) )
=> ( divides @ X1 @ X3 ) ) )
=> ~ sP18 )
=> ~ sP2 )
=> ~ sP12 )
=> ~ sP5 )
=> ~ sP21 )
=> ~ ! [X1: $i] :
( ~ ( prime @ X1 )
=> ( less @ ( prime_divisor @ X1 ) @ X1 ) ) )
=> ~ ( prime @ a ) )
=> ~ sP17 ),
inference(contra,[status(thm),contra(discharge,[h0])],[30,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n012.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 : 300
% 0.13/0.33 % DateTime : Fri Aug 25 08:39:41 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % Mode: cade22grackle2xfee4
% 0.19/0.44 % Steps: 654
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------