%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO560^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 03:26:01 PM UTC 2025
% Result : Theorem 1.05s 1.28s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 64
% Syntax : Number of formulae : 74 ( 17 unt; 0 typ; 3 def)
% Number of atoms : 220 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 186 ( 54 ~; 46 |; 0 &; 52 @)
% ( 31 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 37 con; 0-2 aty)
% Number of variables : 22 ( 10 ^; 12 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_epso,type,
epso: ( $o > $o ) > $o ).
thf(ty_epsoo,type,
epsoo: ( ( $o > $o ) > $o ) > $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] :
( $false
!= ( epsoo @ epso @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $o] :
( X1
!= ( epsoo @ epso @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o] :
( ( ~ $false )
!= ( epsoo @ epso @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( q
@ ^ [X1: $o] : ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( epso = epso ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: $o] : ~ $false )
= ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ~ $false )
= ( epsoo @ epso @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] :
( $false
= ( epsoo @ epso @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ^ [X1: $o] : X1 )
= ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( epsoo @ epso @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o > $o] :
~ ( epso @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( $false
= ( epsoo @ epso @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
= ( epsoo @ epso @ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( epso
@ ^ [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o] : ~ X1 ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( epsoo @ epso @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( epsoo @ epso @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] :
~ ( epsoo @ epso @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( q
@ ^ [X1: $o] : $false ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP10 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( epso @ ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( q @ ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $o] :
( ( ~ $false )
= ( epsoo @ epso @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP10 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $o] :
( X1
= ( epsoo @ epso @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( ^ [X1: $o] : $false )
= ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP20 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( q
@ ^ [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> $false ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( epsoo @ epso @ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(c,conjecture,
sP21 ).
thf(h1,negated_conjecture,
~ sP21,
inference(assume_negation,[status(cth)],[c]) ).
thf(1,plain,
( ~ sP14
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(choiceaxo,axiom,
! [X1: $o > $o] :
( ~ ! [X2: $o] :
~ ( X1 @ X2 )
=> ( X1 @ ( epso @ X1 ) ) ) ).
thf(2,plain,
( sP13
| sP14 ),
inference(choice_rule,[status(thm)],[choiceaxo]) ).
thf(3,plain,
( sP24
| ~ sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP23
| sP2
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP19
| sP10
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP15
| sP8
| ~ sP3
| ~ sP19 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| sP16
| ~ sP3
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP17
| ~ sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP11
| sP30
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP27
| ~ sP20
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP31
| sP8
| ~ sP3
| ~ sP27 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP16
| sP8
| ~ sP3
| ~ sP23 ),
inference(mating_rule,[status(thm)],[]) ).
thf(14,plain,
~ sP30,
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP5
| sP30
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP22
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(17,plain,
( sP4
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP1
| sP21
| ~ sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(19,plain,
( sP6
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(20,plain,
( sP26
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP18
| sP21
| ~ sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP9
| ~ sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( sP31
| sP17 ),
inference(choice_rule,[status(thm)],[choiceaxo]) ).
thf(choiceaxoo,axiom,
! [X1: ( $o > $o ) > $o] :
( ~ ! [X2: $o > $o] :
~ ( X1 @ X2 )
=> ( X1 @ ( epsoo @ X1 ) ) ) ).
thf(24,plain,
( sP20
| sP9 ),
inference(choice_rule,[status(thm)],[choiceaxoo]) ).
thf(25,plain,
( sP12
| ~ sP2
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP12
| sP2
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP25
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(28,plain,
( sP7
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP29
| sP21
| ~ sP7 ),
inference(mating_rule,[status(thm)],[]) ).
thf(qid,axiom,
sP29 ).
thf(qkf,axiom,
sP18 ).
thf(qkt,axiom,
sP1 ).
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,qid,qkf,qkt,h1]) ).
thf(31,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[30,h0]) ).
thf(0,theorem,
sP21,
inference(contra,[status(thm),contra(discharge,[h1])],[30,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO560^1 : TPTP v9.2.0. Released v5.2.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31 % Computer : n014.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Oct 9 00:47:08 EDT 2025
% 0.10/0.31 % CPUTime :
% 1.05/1.28 % SZS status Theorem
% 1.05/1.28 % Mode: mode506
% 1.05/1.28 % Inferences: 19453
% 1.05/1.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------