TSTP Solution File: NUM682^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 11:40:25 EDT 2023
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
~ ( ( ( X1 = X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ( X1 != X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( y = x )
=> ( ( pl @ y @ z )
= ( pl @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat,X2: nat] :
( ( more @ x @ X1 )
=> ( more @ ( pl @ x @ X2 ) @ ( pl @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( x != y )
=> ( ~ ( more @ x @ y )
=> ( less @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( y != x )
=> ( ~ ( more @ y @ x )
=> ( less @ y @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ~ ( more @ X1 @ X2 )
=> ( less @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( more @ ( pl @ x @ z ) @ ( pl @ x @ z ) )
=> ~ ( less @ ( pl @ x @ z ) @ ( pl @ x @ z ) ) )
=> ( less @ ( pl @ x @ z ) @ ( pl @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( more @ y @ y )
=> ( ( ( more @ y @ y )
=> ~ ( less @ y @ y ) )
=> ( less @ y @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( less @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat] :
~ ( ( ( ( pl @ x @ z )
= X1 )
=> ~ ( more @ ( pl @ x @ z ) @ X1 ) )
=> ( ( ( more @ ( pl @ x @ z ) @ X1 )
=> ~ ( less @ ( pl @ x @ z ) @ X1 ) )
=> ~ ( ( less @ ( pl @ x @ z ) @ X1 )
=> ( ( pl @ x @ z )
!= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( more @ y @ y ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( ( pl @ x @ z )
= ( pl @ y @ z ) )
=> ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
=> ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
=> ~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
=> ~ ( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
=> ( ( pl @ x @ z )
!= ( pl @ y @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( more @ x @ y )
=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
=> ~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
=> ~ ( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
=> ( ( pl @ x @ z )
!= ( pl @ y @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( y = x ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( pl @ y @ z )
= ( pl @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( less @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( more @ y @ x )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( more @ x @ y )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( sP11
=> ~ ( less @ y @ y ) )
=> ( less @ y @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
=> ~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> $false ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: nat] :
( ( x != X1 )
=> ( ~ ( more @ x @ X1 )
=> ( less @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: nat] :
( ( more @ x @ y )
=> ( more @ ( pl @ x @ X1 ) @ ( pl @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: nat] :
( sP16
=> ( ( pl @ y @ X1 )
= ( pl @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ z ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( more @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( less @ y @ y ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: nat] :
( ( y != X1 )
=> ( ~ ( more @ y @ X1 )
=> ( less @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( more @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( less @ ( pl @ x @ z ) @ ( pl @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: nat] :
~ ( ( ( y = X1 )
=> ~ ( more @ y @ X1 ) )
=> ( ( ( more @ y @ X1 )
=> ~ ( less @ y @ X1 ) )
=> ~ ( ( less @ y @ X1 )
=> ( y != X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( X1 = X2 )
=> ( ( pl @ X1 @ X3 )
= ( pl @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: nat,X2: nat] :
( ( y = X1 )
=> ( ( pl @ y @ X2 )
= ( pl @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(satz20c,conjecture,
sP18 ).
thf(h0,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[satz20c]) ).
thf(1,plain,
( ~ sP22
| ~ sP31
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP14
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP12
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP30
| sP35
| ~ sP17
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( sP7
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP28
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| ~ sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP32
| ~ sP15
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP34
| sP11
| ~ sP15
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( sP21
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP8
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP8
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP36
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| sP34
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| sP16
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP33
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| ~ sP29
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP25
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| ~ sP16
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP26
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP20
| sP29
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP38
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP4
| sP15
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP37
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP1
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP6
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP3
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
~ sP23,
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP27
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP6
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(satz10a,axiom,
sP6 ).
thf(satz19b,axiom,
sP37 ).
thf(satz19a,axiom,
sP27 ).
thf(satz10b,axiom,
sP1 ).
thf(l,axiom,
sP30 ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h0,satz10a,satz19b,satz19a,satz10b,l]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:55:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % Mode: cade22grackle2xfee4
% 0.19/0.52 % Steps: 1056
% 0.19/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------