%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP210^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 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 : Sat Feb 28 09:29:46 AM UTC 2026
% Result : Theorem 241.83s 243.08s
% Output : Proof 241.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 59 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 178 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 279 ( 80 ~; 45 |; 0 &; 109 @)
% ( 22 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 27 con; 0-2 aty)
% Number of variables : 18 ( 14 ^; 4 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_assn,type,
assn: $tType ).
thf(ty_produc3658429121746597890et_nat,type,
produc3658429121746597890et_nat: $tType ).
thf(ty_eigen__1,type,
eigen__1: produc3658429121746597890et_nat ).
thf(ty_y,type,
y: assn ).
thf(ty_x,type,
x: assn ).
thf(ty_abs_assn,type,
abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
thf(ty_rep_assn,type,
rep_assn: assn > produc3658429121746597890et_nat > $o ).
thf(h0,assumption,
! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: produc3658429121746597890et_nat] :
( ( ~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
!= ( ~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( ( abs_assn
@ ( rep_assn
@ ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) )
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( x
= ( abs_assn @ ( rep_assn @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( y
= ( abs_assn @ ( rep_assn @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) ) )
=> ( x = y ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) ) )
=> ( y
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( rep_assn @ x @ eigen__1 )
=> ~ ( rep_assn @ y @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ sP7 )
= ( ~ ( ( rep_assn @ y @ eigen__1 )
=> ~ ( rep_assn @ x @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( abs_assn @ ( rep_assn @ x ) )
= y ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( rep_assn @ x @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( rep_assn @ y @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) )
= y ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: assn] :
( ( abs_assn @ ( rep_assn @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ~ sP4 ) = ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( abs_assn @ ( rep_assn @ x ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: produc3658429121746597890et_nat] :
( ( ~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( ~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( y
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) )
= ( abs_assn @ ( rep_assn @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP11
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(conj_0,conjecture,
sP16 ).
thf(h1,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP1
| sP3
| ~ sP12
| ~ sP21 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP15
| sP12
| ~ sP6
| ~ sP13 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP15
| sP21
| ~ sP6
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP17
| sP13
| ~ sP17
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP3
| sP9 ),
inference(symeq,[status(thm)],[]) ).
thf(6,plain,
( ~ sP17
| sP2 ),
inference(symeq,[status(thm)],[]) ).
thf(7,plain,
( sP7
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP7
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP22
| ~ sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| ~ sP10
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP22
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP22
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP8
| sP7
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP8
| ~ sP7
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP18
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(16,plain,
( sP20
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP6
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( sP4
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP4
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP5
| ~ sP15
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP12
| sP19 ),
inference(symeq,[status(thm)],[]) ).
thf(24,plain,
( ~ sP19
| sP12 ),
inference(symeq,[status(thm)],[]) ).
thf(25,plain,
( ~ sP4
| ~ sP15
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP5
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP16
| sP4
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP16
| ~ sP4
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_1_Rep__assn__inverse,axiom,
sP14 ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,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,fact_1_Rep__assn__inverse,h1]) ).
thf(31,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[30,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h1])],[30,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP210^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Feb 26 02:19:44 EST 2026
% 0.17/0.34 % CPUTime :
% 241.83/243.08 % SZS status Theorem
% 241.83/243.08 % Mode: cade22sinegrackle2x2270
% 241.83/243.08 % Steps: 3207
% 241.83/243.08 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------