%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV028^5 : 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 : n006.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 02:56:08 PM UTC 2025
% Result : Theorem 34.52s 34.59s
% Output : Proof 34.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 145
% Syntax : Number of formulae : 160 ( 18 unt; 0 typ; 10 def)
% Number of atoms : 495 ( 72 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 942 ( 312 ~; 88 |; 0 &; 317 @)
% ( 71 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 84 usr; 80 con; 0-2 aty)
% Number of variables : 154 ( 10 ^; 144 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__11,type,
eigen__11: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__9,type,
eigen__9: a > $o ).
thf(ty_cQ,type,
cQ: a > a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__5 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( cQ @ eigen__0 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__3 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__3 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ( ( cQ @ eigen__0 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ X1 ) )
=> ( cQ @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a] :
~ ( ( cQ @ eigen__3 @ X1 )
=> ( cQ @ X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__0 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a] :
~ ( cQ @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ~ ( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X3 @ X5 )
= ( cQ @ X4 @ X5 ) ) ) )
=> ~ ( X3 @ X1 ) )
=> ( X3 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ~ ( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X3 @ X5 )
= ( cQ @ X4 @ X5 ) ) ) )
=> ~ ( X3 @ X1 ) )
=> ( X3 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( cQ @ eigen__3 @ X1 )
=> ( cQ @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__10 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ~ ( ( cQ @ eigen__0 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ X1 ) )
=> ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__3 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__3 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__7 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__7 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP8
= ( cQ @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cQ @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__11 @ eigen__5 )
=> ! [X1: a] :
( ( eigen__11 @ X1 )
= ( cQ @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__7 @ X1 )
= ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__9 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( eigen__11 @ X1 )
=> ! [X2: a] :
( ( eigen__11 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ~ ! [X1: a] :
~ ( eigen__7 @ X1 )
=> ~ ! [X1: a] :
( ( eigen__7 @ X1 )
=> ! [X2: a] :
( ( eigen__7 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cQ @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP4
= ( cQ @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__11 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__9 @ eigen__1 )
= ( cQ @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__5 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ! [X2: a] :
( ( eigen__10 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a] : ( cQ @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a,X2: a] :
( ~ ( ( cQ @ eigen__0 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
= ( cQ @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP21
= ( cQ @ eigen__5 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP4
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ! [X1: a] :
~ ( eigen__10 @ X1 )
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( eigen__7 @ X1 )
= ( cQ @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cQ @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__10 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP13 = sP18 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eigen__9 @ eigen__1 )
=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( cQ @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( cQ @ eigen__5 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( cQ @ eigen__0 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__7 @ eigen__2 )
= sP10 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cQ @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( ~ sP30
=> ~ sP33 )
=> ~ ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__3 ) )
=> ( X1 = eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP7
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a] :
( ( eigen__11 @ X1 )
= ( cQ @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ! [X1: a] :
~ ( eigen__9 @ X1 )
=> ~ ! [X1: a] :
( ( eigen__9 @ X1 )
=> ! [X2: a] :
( ( eigen__9 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( ~ ! [X1: a] :
~ ( eigen__11 @ X1 )
=> ~ sP14 )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
= ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a] :
( ( eigen__7 @ X1 )
=> ! [X2: a] :
( ( eigen__7 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( cQ @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ ( sP25
=> ~ sP19 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__9 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ sP1
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__7 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP15
=> ~ ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__1 ) )
=> ( X1 = eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP38
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( cQ @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP52 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( cQ @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP33
=> sP46 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ eigen__0 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP13
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP33 = sP32 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ! [X1: a] :
~ ( eigen__11 @ X1 )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ ( ~ sP44
=> ~ sP13 )
=> ~ ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) )
=> ( X1 = eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ sP30
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP57
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP44
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
=> ! [X2: a] :
( ( eigen__9 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP8
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP25
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP45
=> ~ ! [X1: a > $o] :
( ~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__5 ) )
=> ( X1 = eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ ! [X1: a] :
~ ( eigen__7 @ X1 )
=> ~ sP47 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(cTHM558_pme,conjecture,
sP51 ).
thf(h2,negated_conjecture,
~ sP51,
inference(assume_negation,[status(cth)],[cTHM558_pme]) ).
thf(1,plain,
( ~ sP22
| sP50
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP34
| ~ sP13
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP39
| ~ sP52
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| sP8
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP56
| sP52
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP31
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP31
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP12
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP48
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP35
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP60
| ~ sP13
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP36
| ~ sP50
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP68
| ~ sP8
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP42
| ~ sP7
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP47
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP47
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP67
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP67
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP61
| ~ sP33
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP27
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP20
| sP4
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP46
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP58
| ~ sP33
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP29
| ~ sP4
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP24
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP24
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( sP30
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP44
| sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP71
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP15
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP15
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( sP66
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP66
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP64
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP64
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP28
| ~ sP21
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP43
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP11
| ~ sP21
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP14
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( sP62
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP45
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP45
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP70
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP23
| ~ sP70 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(45,plain,
( sP41
| ~ sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP6
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(47,plain,
( sP63
| ~ sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( sP59
| ~ sP63 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(49,plain,
( sP53
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( sP17
| ~ sP53 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(51,plain,
( ~ sP2
| ~ sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP2
| ~ sP59 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP2
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP2
| ~ sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( sP1
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( sP25
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(57,plain,
( sP65
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP65
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP3
| ~ sP65 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(60,plain,
( sP19
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).
thf(61,plain,
( ~ sP69
| ~ sP25
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( sP38
| sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( sP38
| sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( sP54
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( sP54
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( sP5
| ~ sP54 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(67,plain,
( sP26
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(68,plain,
( sP16
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(69,plain,
( ~ sP49
| sP69
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( sP51
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( sP51
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,h2]) ).
thf(73,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[72,h1]) ).
thf(74,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[73,h0]) ).
thf(0,theorem,
sP51,
inference(contra,[status(thm),contra(discharge,[h2])],[72,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV028^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 19:07:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 34.52/34.59 % SZS status Theorem
% 34.52/34.59 % Mode: mode482
% 34.52/34.59 % Inferences: 20406
% 34.52/34.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------