%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV128^5 : 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 : n019.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 02:56:19 PM UTC 2025
% Result : Theorem 22.06s 22.31s
% Output : Proof 22.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 84
% Syntax : Number of formulae : 100 ( 20 unt; 0 typ; 10 def)
% Number of atoms : 281 ( 33 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1301 ( 311 ~; 47 |; 0 &; 620 @)
% ( 40 <=>; 283 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 187 ( 187 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 50 con; 0-2 aty)
% Number of variables : 369 ( 50 ^; 319 !; 0 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a > a > $o ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a > a > $o ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(h0,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ~ ! [X7: a > a > $o] :
( ( eigen__0 @ X7 )
=> ( X6
!= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ~ ( ! [X11: a,X12: a] :
( ( X7 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
=> ~ ! [X11: a,X12: a,X13: a] :
( ~ ( ( X10 @ X11 @ X12 )
=> ~ ( X10 @ X12 @ X13 ) )
=> ( X10 @ X11 @ X13 ) ) )
=> ( X10 @ X8 @ X9 ) ) ) ) )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__5 @ X1 ) )
=> ( eigen__3 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h2,assumption,
! [X1: ( ( a > a > $o ) > $o ) > $o,X2: ( a > a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__2
@ ^ [X1: ( a > a > $o ) > $o] :
~ ! [X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ! [X12: a,X13: a,X14: a] :
( ~ ( ( X11 @ X12 @ X13 )
=> ~ ( X11 @ X13 @ X14 ) )
=> ( X11 @ X12 @ X14 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__8 @ eigen__9 @ X1 )
=> ( eigen__3 @ eigen__9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__7
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
~ ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ( X5
!= ( ^ [X7: a,X8: a] :
! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X6 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ! [X10: a,X11: a,X12: a] :
( ~ ( ( X9 @ X10 @ X11 )
=> ~ ( X9 @ X11 @ X12 ) )
=> ( X9 @ X10 @ X12 ) ) )
=> ( X9 @ X7 @ X8 ) ) ) ) )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ( eigen__0 @ X5 )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__5 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ~ ! [X7: a > a > $o] :
( ( eigen__0 @ X7 )
=> ( X6
!= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ~ ( ! [X11: a,X12: a] :
( ( X7 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
=> ~ ! [X11: a,X12: a,X13: a] :
( ~ ( ( X10 @ X11 @ X12 )
=> ~ ( X10 @ X12 @ X13 ) )
=> ( X10 @ X11 @ X13 ) ) )
=> ( X10 @ X8 @ X9 ) ) ) ) )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__5 @ X1 ) )
=> ( eigen__3 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__7 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) )
=> ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__9 @ X1 ) )
=> ( eigen__3 @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__7 @ eigen__5 )
= ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__8 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__7 @ eigen__5 @ X1 )
= ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__8 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ~ ! [X5: a > a > $o] :
( ( eigen__0 @ X5 )
=> ( X4
!= ( ^ [X6: a,X7: a] :
! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X5 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) ) ) )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__3 @ eigen__9 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__7
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > a > $o] :
( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ eigen__8 )
=> ~ ( eigen__8 @ eigen__9 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3
= ( ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__8 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) )
=> ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__0 @ eigen__8 )
=> ( eigen__7
!= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__7
= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__8 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__3 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__9 @ eigen__10 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ( eigen__8 @ eigen__9 @ X1 )
=> ( eigen__3 @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP12
=> ( eigen__3 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__8 @ eigen__9 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP11
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ( X5
!= ( ^ [X7: a,X8: a] :
! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X6 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ! [X10: a,X11: a,X12: a] :
( ~ ( ( X9 @ X10 @ X11 )
=> ~ ( X9 @ X11 @ X12 ) )
=> ( X9 @ X10 @ X12 ) ) )
=> ( X9 @ X7 @ X8 ) ) ) ) )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ( eigen__0 @ X5 )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__3 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ! [X12: a,X13: a,X14: a] :
( ~ ( ( X11 @ X12 @ X13 )
=> ~ ( X11 @ X13 @ X14 ) )
=> ( X11 @ X12 @ X14 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a,X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__9 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP5
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP31
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP25
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( eigen__7 @ X1 )
= ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP9
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP34
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(cTHM253_B_pme,conjecture,
sP30 ).
thf(h3,negated_conjecture,
~ sP30,
inference(assume_negation,[status(cth)],[cTHM253_B_pme]) ).
thf(1,plain,
( ~ sP32
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP13
| ~ sP40
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP21
| sP32
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP35
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP35
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP14
| ~ sP3
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP23
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10]) ).
thf(10,plain,
( ~ sP8
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( sP31
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(12,plain,
( ~ sP7
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP19
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP39
| sP34
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP34
| ~ sP31
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP37
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP18
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP17
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP17
| sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP11
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(21,plain,
( sP27
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP27
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP12
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(24,plain,
( sP24
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP24
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP2
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(27,plain,
( sP36
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(28,plain,
( ~ sP9
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP16
| sP26
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP26
| ~ sP36
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP33
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( sP33
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP4
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP4
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP15
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(36,plain,
( sP38
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP38
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP28
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(39,plain,
( sP1
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(40,plain,
( sP30
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__0]) ).
thf(41,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,h3]) ).
thf(42,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[41,h2]) ).
thf(43,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[42,h1]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[43,h0]) ).
thf(0,theorem,
sP30,
inference(contra,[status(thm),contra(discharge,[h3])],[41,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV128^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 19:44:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 22.06/22.31 % SZS status Theorem
% 22.06/22.31 % Mode: mode459
% 22.06/22.31 % Inferences: 193
% 22.06/22.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------