%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM667^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 02:09:32 PM UTC 2025
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ( ~ ( less @ y @ z )
=> ( y = z ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( less @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( less @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( y = z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( x = z ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( less @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( less @ y @ z )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( ~ sP2
=> ( x = y ) )
=> ( ( less @ y @ X1 )
=> ( less @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ~ sP2
=> ( x = y ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat,X2: nat] :
( ( less @ x @ X1 )
=> ( ( ~ ( less @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( less @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( less @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( ~ ( less @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( less @ X2 @ X3 )
=> ( less @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP2
=> ( x = y ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> $false ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: nat,X2: nat] :
( ( ~ ( less @ x @ X1 )
=> ( x = X1 ) )
=> ( ( less @ X1 @ X2 )
=> ( less @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( less @ X1 @ X2 )
=> ( ( ~ ( less @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( less @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: nat] :
( sP2
=> ( ( ~ ( less @ y @ X1 )
=> ( y = X1 ) )
=> ( less @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(satz17,conjecture,
( ~ sP6
=> sP5 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP6
=> sP5 ),
inference(assume_negation,[status(cth)],[satz17]) ).
thf(h1,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP5
| sP15
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| ~ sP11
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP9
| ~ sP13
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP18
| ~ sP2
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP10
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP17
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
~ sP15,
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP1
| sP11
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP13
| sP2
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz16b,axiom,
sP17 ).
thf(satz16a,axiom,
sP12 ).
thf(k,axiom,
sP1 ).
thf(l,axiom,
sP13 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1,h2,satz16b,satz16a,k,l]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,15,h1,h2]) ).
thf(0,theorem,
( ~ sP6
=> sP5 ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM667^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 22:11:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % Mode: cade22grackle2xfee4
% 0.18/0.40 % Steps: 158
% 0.18/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------