%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP138^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 01:47:04 PM UTC 2025
% Result : Theorem 92.31s 92.42s
% Output : Proof 92.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 65
% Syntax : Number of formulae : 71 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 198 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 301 ( 68 ~; 34 |; 0 &; 140 @)
% ( 31 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 36 con; 0-2 aty)
% Number of variables : 46 ( 22 ^; 24 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_Pa1764573435lle_tv,type,
set_Pa1764573435lle_tv: $tType ).
thf(ty_paraco1605129243lle_tv,type,
paraco1605129243lle_tv: $tType ).
thf(ty_list_char,type,
list_char: $tType ).
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_set_list_char,type,
set_list_char: $tType ).
thf(ty_paraco1604210848lle_fm,type,
paraco1604210848lle_fm: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_p,type,
p: paraco1604210848lle_fm ).
thf(ty_paraco1933902578domain,type,
paraco1933902578domain: set_nat > set_Pa1764573435lle_tv ).
thf(ty_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(ty_eigen__4,type,
eigen__4: list_char > paraco1605129243lle_tv ).
thf(ty_top_to748628679t_char,type,
top_to748628679t_char: set_list_char ).
thf(ty_paraco1344940915le_Det,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(ty_eigen__3,type,
eigen__3: list_char > paraco1605129243lle_tv ).
thf(ty_ord_le241064091lle_tv,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(ty_image_1187894195lle_tv,type,
image_1187894195lle_tv: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv ).
thf(ty_top_to1057771083lle_tv,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(ty_paraco1325918602e_eval,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(ty_collec1111687558lle_tv,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(h0,assumption,
! [X1: ( list_char > paraco1605129243lle_tv ) > $o,X2: list_char > paraco1605129243lle_tv] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: list_char > paraco1605129243lle_tv] :
~ ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X1 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X2: nat] : ~ $false ) ) )
=> ( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
!= ( paraco1344940915le_Det @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv,X3: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ X1 @ X2 )
=> ( ( ord_le241064091lle_tv @ X3 @ X1 )
=> ( ord_le241064091lle_tv @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : ~ $false )
= ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ X1 )
=> ( ( ord_le241064091lle_tv @ X2 @ top_to1057771083lle_tv )
=> ( ord_le241064091lle_tv @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__4 @ top_to748628679t_char ) @ top_to1057771083lle_tv )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__4 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
( ( X1 = X2 )
=> ( ord_le241064091lle_tv @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__3 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) )
=> ( ( paraco1325918602e_eval @ eigen__3 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ X1 @ top_to1057771083lle_tv ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) )
= ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__4 @ top_to748628679t_char ) @ top_to1057771083lle_tv ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__4 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) )
=> ( ( paraco1325918602e_eval @ eigen__4 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ X1 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X2: nat] : ~ $false ) ) )
=> ( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv
@ ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : ~ $false ) )
=> ( sP2
=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( paraco1325918602e_eval @ eigen__4 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: set_Pa1764573435lle_tv] :
( ( top_to1057771083lle_tv = X1 )
=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv
@ ( collec1111687558lle_tv
@ ^ [X1: paraco1605129243lle_tv] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP5
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: set_Pa1764573435lle_tv] :
( sP17
=> ( ( ( collec1111687558lle_tv
@ ^ [X2: paraco1605129243lle_tv] : ~ $false )
= X1 )
=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ! [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) )
= ( ~ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv,X3: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ X1 @ X2 )
=> ( ( X2 = X3 )
=> ( ord_le241064091lle_tv @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: set_Pa1764573435lle_tv] :
( sP20
=> ( ( ord_le241064091lle_tv @ X1 @ top_to1057771083lle_tv )
=> ( ord_le241064091lle_tv @ X1
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X2: nat] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ X1 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP20
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ eigen__4 @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [X1: nat] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: set_Pa1764573435lle_tv] :
( ( ( paraco1933902578domain
@ ( collect_nat
@ ^ [X2: nat] : ~ $false ) )
= X1 )
=> ( X1
= ( paraco1933902578domain
@ ( collect_nat
@ ^ [X2: nat] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( paraco1325918602e_eval @ eigen__3 @ p )
= ( paraco1344940915le_Det @ ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: set_Pa1764573435lle_tv,X2: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ X1 )
=> ( ( X1 = X2 )
=> ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(conj_0,conjecture,
~ sP22 ).
thf(h1,negated_conjecture,
sP22,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP31
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP14
| ~ sP17
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP18
| ~ sP2
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP24
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP26
| ~ sP20
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| ~ sP10
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP23
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP25
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| ~ sP28
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP7
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP25
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(17,plain,
( sP13
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(18,plain,
( ~ sP11
| ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP29
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP27
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP16
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP19
| ~ sP5
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
sP27,
inference(eq_sym,[status(thm)],[]) ).
thf(25,plain,
( ~ sP22
| ~ sP25
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP22
| sP25
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_0_universal__domain,axiom,
sP9 ).
thf(fact_56_dual__order_Otrans,axiom,
sP1 ).
thf(fact_64_ord__le__eq__trans,axiom,
sP23 ).
thf(fact_74_eq__refl,axiom,
sP6 ).
thf(fact_203_UNIV__def,axiom,
sP5 ).
thf(fact_213_top__greatest,axiom,
sP8 ).
thf(27,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,fact_0_universal__domain,fact_56_dual__order_Otrans,fact_64_ord__le__eq__trans,fact_74_eq__refl,fact_203_UNIV__def,fact_213_top__greatest,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
~ sP22,
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP138^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n004.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 18:14:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 92.31/92.42 % SZS status Theorem
% 92.31/92.42 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 92.31/92.42 % Inferences: 1471
% 92.31/92.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------