%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUN025^2 : TPTP v9.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 02:12:59 PM UTC 2025
% Result : Theorem 21.37s 20.76s
% Output : Proof 21.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_ite,type,
ite: $o > $i > $i > $i ).
thf(ty_zero,type,
zero: $i ).
thf(ty_h,type,
h: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( h @ X1 )
= ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( ite @ ~ $false @ X1 @ X2 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( h @ zero )
= ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ite @ ~ $false @ zero @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( h @ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( ite @ $false @ zero @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ite @ $false @ zero @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ite @ $false @ zero @ ( s @ zero ) )
= ( ite
@ ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( h @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( zero
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ite @ sP13 @ zero @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP12
=> ( ( h @ ( s @ zero ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ite @ $false @ zero @ ( s @ zero ) )
= ( ite @ sP13 @ zero @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( ite
@ ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( s @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( h @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( s @ X1 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( h @ ( s @ zero ) )
= ( ite @ ~ $false @ zero @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( s @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ite @ sP24 @ zero @ ( s @ zero ) )
= ( h @ ( s @ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> $false ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i] :
( ( ite @ sP26 @ X1 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( ite @ ~ sP26 @ zero @ X1 )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(n10,conjecture,
( ~ ( ~ ( ~ ( sP10
=> ~ sP28 )
=> ~ sP20 )
=> ~ sP1 )
=> ~ sP21 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP10
=> ~ sP28 )
=> ~ sP20 )
=> ~ sP1 )
=> ~ sP21 ),
inference(assume_negation,[status(cth)],[n10]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP10
=> ~ sP28 )
=> ~ sP20 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP21,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP10
=> ~ sP28 )
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP10
=> ~ sP28 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP20,
introduced(assumption,[]) ).
thf(h7,assumption,
sP10,
introduced(assumption,[]) ).
thf(h8,assumption,
sP28,
introduced(assumption,[]) ).
thf(1,plain,
( sP11
| sP26
| sP26
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP16
| sP26
| sP26
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP9
| sP22
| ~ sP11
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| sP14
| ~ sP16
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
~ sP26,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP23
| sP19
| sP26
| ~ sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP12
| ~ sP3
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP17
| sP8
| ~ sP25
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP29
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP15
| ~ sP12
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP2
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP27
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP13
| sP18 ),
inference(symeq,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| sP15
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP17
| sP25 ),
inference(symeq,[status(thm)],[]) ).
thf(17,plain,
( ~ sP4
| sP3 ),
inference(symeq,[status(thm)],[]) ).
thf(18,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP28
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP20
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP20
| ~ sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP21
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP1
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h7,h8,h6,h4,h2]) ).
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,
( ~ ( ~ ( ~ ( sP10
=> ~ sP28 )
=> ~ sP20 )
=> ~ sP1 )
=> ~ sP21 ),
inference(contra,[status(thm),contra(discharge,[h0])],[30,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN025^2 : TPTP v9.2.0. Released v6.4.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n016.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 : 300
% 0.12/0.34 % DateTime : Wed Oct 8 13:37:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 21.37/20.76 % SZS status Theorem
% 21.37/20.76 % Mode: cade22grackle2x798d
% 21.37/20.76 % Steps: 1687
% 21.37/20.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------