%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV084^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 02:56:14 PM UTC 2025
% Result : Theorem 5.03s 5.24s
% Output : Proof 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 66
% Syntax : Number of formulae : 77 ( 15 unt; 0 typ; 6 def)
% Number of atoms : 244 ( 49 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 234 ( 85 ~; 41 |; 0 &; 43 @)
% ( 30 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 36 con; 0-2 aty)
% Number of variables : 40 ( 12 ^; 28 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_cP,type,
cP: $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( X1 = eigen__0 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__5 @ X1 )
!= ( eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( eigen__1 = eigen__0 )
=> ( X1 != eigen__1 ) )
=> ( X1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__2 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i > $o] : ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( ( ^ [X1: $i] :
~ ( cP
=> cP ) )
!= ( ^ [X1: $i] :
( ~ cP
=> ~ cP ) ) )
=> ~ ! [X1: $i > $o] : ( X1 = X1 ) )
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ( cP
=> cP ) )
= ( ~ cP
=> ~ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__2 @ eigen__4 )
= ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( sP2
=> ( eigen__2 != eigen__1 ) )
=> ( eigen__2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] : ( X1 = X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> cP ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__5 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: $i] :
~ ( sP8
=> sP8 ) )
= ( ^ [X1: $i] :
( ~ sP8
=> ~ sP8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__5 @ eigen__6 )
= ( eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__5 @ X1 )
= ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__2 @ eigen__4 )
= ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP11
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP8
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i > $o] :
( ~ ( sP2
=> ( X1 != eigen__1 ) )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP2
=> ( eigen__2 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( ~ ( X1
@ ^ [X2: $i] : sP17
@ ^ [X2: $i] :
~ ( sP8
=> sP8 ) )
=> ~ ! [X2: $i > $o] : ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X1 = eigen__0 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP8
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] : sP4 ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP16 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(cTHM120J_pme,conjecture,
~ sP23 ).
thf(h2,negated_conjecture,
sP23,
inference(assume_negation,[status(cth)],[cTHM120J_pme]) ).
thf(1,plain,
( sP26
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP26
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP17
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP17
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| ~ sP26
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP27
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP11
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP13
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(10,plain,
( sP9
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP7
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(12,plain,
( ~ sP15
| sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP14
| ~ sP30
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP14
| sP30
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP29
| ~ sP16
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP29
| sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP28
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP5
| ~ sP30
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP5
| sP30
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP18
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(22,plain,
( ~ sP2
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP22
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP20
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP20
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP25
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP6
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP6
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP19
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(30,plain,
( sP24
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(31,plain,
( sP3
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(32,plain,
( ~ sP1
| sP15
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP23
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h2]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[34,h1]) ).
thf(36,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[35,h0]) ).
thf(0,theorem,
~ sP23,
inference(contra,[status(thm),contra(discharge,[h2])],[34,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEV084^5 : TPTP v9.2.0. Released v4.0.0.
% 0.13/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 19:12:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 5.03/5.24 % SZS status Theorem
% 5.03/5.24 % Mode: mode495
% 5.03/5.24 % Inferences: 78
% 5.03/5.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------