## TSTP Solution File: SEV091^5 by Satallax---3.5

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV091^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n009.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
% DateTime : Tue Mar 30 22:04:56 EDT 2021

% Result   : Theorem 0.19s
% Output   : Proof 0.19s
% Verified :
% SZS Type : None (MakeTreeStats fails)
% Syntax   : Number of formulae    : 184

%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: \$i ).

thf(ty_cP,type,
cP: \$i > \$i > \$o ).

thf(ty_eigen__1,type,
eigen__1: \$i ).

thf(ty_eigen__0,type,
eigen__0: \$i ).

thf(ty_eigen__4,type,
eigen__4: \$i ).

thf(ty_eigen__3,type,
eigen__3: \$i ).

thf(ty_cQ,type,
cQ: \$i > \$i > \$o ).

thf(sP1,plain,
( sP1
<=> ( cP @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
( sP2
<=> ( cQ @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
( sP3
<=> ( cQ @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
( sP4
<=> ( ~ ( ( cP @ eigen__0 @ eigen__2 )
=> ~ ( cP @ eigen__2 @ eigen__1 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__0 @ eigen__3 )
=> ~ ( cP @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
( sP6
<=> ( ( cQ @ eigen__4 @ eigen__0 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
( sP7
<=> ( ~ ( ( cQ @ eigen__2 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ eigen__4 ) )
=> ( cQ @ eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
( sP8
<=> ( cQ @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
( sP9
<=> ! [X1: \$i] :
( ~ ( ( cQ @ eigen__3 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ X1 ) )
=> ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
( sP10
<=> ! [X1: \$i,X2: \$i] :
( ~ ( ( cQ @ eigen__3 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
( sP11
<=> ( sP8
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
( sP12
<=> ( ( cQ @ eigen__3 @ eigen__1 )
=> ~ ( cQ @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
( sP13
<=> ( cQ @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
( sP14
<=> ! [X1: \$i,X2: \$i,X3: \$i] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
( sP15
<=> ( ~ ( cP @ eigen__4 @ eigen__1 )
=> ( cQ @ eigen__4 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
( sP16
<=> ( cQ @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
( sP17
<=> ( ~ ( sP8
=> ~ ( cQ @ eigen__0 @ eigen__3 ) )
=> ( cQ @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
( sP18
<=> ( cQ @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
( sP19
<=> ( ~ ( cP @ eigen__0 @ eigen__2 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
( sP20
<=> ( cQ @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
( sP21
<=> ( sP16
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
( sP22
<=> ( cQ @ eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
( sP23
<=> ( cP @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
( sP24
<=> ( cP @ eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
( sP25
<=> ( ~ ( sP16
=> ~ ( cQ @ eigen__1 @ eigen__0 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
( sP26
<=> ( ~ sP24
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
( sP27
<=> ( ~ sP6
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
( sP28
<=> ( ( cQ @ eigen__3 @ eigen__4 )
=> ( cQ @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
( sP29
<=> ( ~ ( cP @ eigen__2 @ eigen__1 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
( sP30
<=> ! [X1: \$i] :
( ~ ( sP8
=> ~ ( cQ @ eigen__0 @ X1 ) )
=> ( cQ @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
( sP31
<=> ! [X1: \$i,X2: \$i,X3: \$i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
( sP32
<=> ( sP22
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
( sP33
<=> ( sP13
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
( sP34
<=> ! [X1: \$i] :
( ~ ( sP23
=> ~ ( cP @ eigen__3 @ X1 ) )
=> ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
( sP35
<=> ( ~ ( sP24
=> ~ ( cP @ eigen__4 @ eigen__1 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
( sP36
<=> ( sP16
=> ~ ( cQ @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
( sP37
<=> ! [X1: \$i,X2: \$i] :
( ~ ( ( cQ @ eigen__4 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
( sP38
<=> ( cQ @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
( sP39
<=> ( ~ sP5
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
( sP40
<=> ( sP3
=> ( cQ @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
( sP41
<=> ( sP8
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
( sP42
<=> ! [X1: \$i] :
( ~ ( sP24
=> ~ ( cP @ eigen__4 @ X1 ) )
=> ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
( sP43
<=> ! [X1: \$i] :
( ~ ( ( cP @ eigen__0 @ eigen__2 )
=> ~ ( cP @ eigen__2 @ X1 ) )
=> ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
( sP44
<=> ( sP24
=> ~ ( cP @ eigen__4 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
( sP45
<=> ( ~ sP11
=> ( cQ @ eigen__4 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
( sP46
<=> ! [X1: \$i] :
( ~ ( sP13
=> ~ ( cQ @ eigen__1 @ X1 ) )
=> ( cQ @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
( sP47
<=> ! [X1: \$i] :
( ~ ( cP @ eigen__0 @ X1 )
=> ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
( sP48
<=> ( cP @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
( sP49
<=> ( ~ sP23
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
( sP50
<=> ! [X1: \$i] :
( ~ ( cP @ eigen__4 @ X1 )
=> ( cQ @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
( sP51
<=> ! [X1: \$i,X2: \$i] :
( ~ ( ( cP @ eigen__0 @ X1 )
=> ~ ( cP @ X1 @ X2 ) )
=> ( cP @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
( sP52
<=> ( ~ sP12
=> ( cQ @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
( sP53
<=> ( cQ @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
( sP54
<=> ( cP @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
( sP55
<=> ( cQ @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
( sP56
<=> ! [X1: \$i,X2: \$i] :
( ~ ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
( sP57
<=> ( sP53
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
( sP58
<=> ! [X1: \$i] :
( ~ ( cP @ eigen__3 @ X1 )
=> ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
( sP59
<=> ( cQ @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
( sP60
<=> ( cQ @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
( sP61
<=> ( ~ ( cP @ eigen__3 @ eigen__1 )
=> ( cQ @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
( sP62
<=> ( ~ sP57
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
( sP63
<=> ( ( cQ @ eigen__4 @ eigen__2 )
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
( sP64
<=> ( ~ sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
( sP65
<=> ! [X1: \$i] :
( ~ ( sP16
=> ~ ( cQ @ eigen__1 @ X1 ) )
=> ( cQ @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
( sP66
<=> ( cQ @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
( sP67
<=> ! [X1: \$i] :
( ~ ( cP @ eigen__2 @ X1 )
=> ( cQ @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
( sP68
<=> ! [X1: \$i] :
( ~ ( sP53
=> ~ ( cQ @ eigen__4 @ X1 ) )
=> ( cQ @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
( sP69
<=> ! [X1: \$i] :
( ( cQ @ eigen__4 @ X1 )
=> ( cQ @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
( sP70
<=> ! [X1: \$i] :
( ( cQ @ eigen__3 @ X1 )
=> ( cQ @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
( sP71
<=> ( cP @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
( sP72
<=> ! [X1: \$i,X2: \$i] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
( sP73
<=> ( cP @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
( sP74
<=> ! [X1: \$i,X2: \$i] :
( ~ ( ( cQ @ eigen__2 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
( sP75
<=> ( cQ @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
( sP76
<=> ! [X1: \$i] :
( ( cQ @ eigen__0 @ X1 )
=> ( cQ @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
( sP77
<=> ( sP71
=> ~ sP48 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).

( ~ ( ~ ( ~ ( sP31
=> ~ sP14 )
=> ~ sP72 )
=> ~ sP56 )
=> ( ~ ! [X1: \$i] : ( !! @ ( cP @ X1 ) )
=> ! [X1: \$i] : ( !! @ ( cQ @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP31
=> ~ sP14 )
=> ~ sP72 )
=> ~ sP56 )
=> ( ~ ! [X1: \$i] : ( !! @ ( cP @ X1 ) )
=> ! [X1: \$i] : ( !! @ ( cQ @ X1 ) ) ) ),

thf(h1,assumption,
~ ( ~ ( ~ ( sP31
=> ~ sP14 )
=> ~ sP72 )
=> ~ sP56 ),
introduced(assumption,[]) ).

thf(h2,assumption,
~ ( ~ ! [X1: \$i] : ( !! @ ( cP @ X1 ) )
=> ! [X1: \$i] : ( !! @ ( cQ @ X1 ) ) ),
introduced(assumption,[]) ).

thf(h3,assumption,
~ ( ~ ( sP31
=> ~ sP14 )
=> ~ sP72 ),
introduced(assumption,[]) ).

thf(h4,assumption,
sP56,
introduced(assumption,[]) ).

thf(h5,assumption,
~ ( sP31
=> ~ sP14 ),
introduced(assumption,[]) ).

thf(h6,assumption,
sP72,
introduced(assumption,[]) ).

thf(h7,assumption,
sP31,
introduced(assumption,[]) ).

thf(h8,assumption,
sP14,
introduced(assumption,[]) ).

thf(h9,assumption,
~ ! [X1: \$i] : ( !! @ ( cP @ X1 ) ),
introduced(assumption,[]) ).

thf(h10,assumption,
~ ! [X1: \$i] : ( !! @ ( cQ @ X1 ) ),
introduced(assumption,[]) ).

thf(h11,assumption,
~ ( !! @ ( cP @ eigen__0 ) ),
introduced(assumption,[]) ).

thf(h12,assumption,
~ sP1,
introduced(assumption,[]) ).

thf(h13,assumption,
~ ( !! @ ( cQ @ eigen__2 ) ),
introduced(assumption,[]) ).

thf(h14,assumption,
~ sP59,
introduced(assumption,[]) ).

thf(1,plain,
( ~ sP43
| sP4 ),
inference(all_rule,[status(thm)],]) ).

thf(2,plain,
( ~ sP4
| sP77
| sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
( ~ sP77
| ~ sP71
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
( ~ sP51
| sP43 ),
inference(all_rule,[status(thm)],]) ).

thf(5,plain,
( ~ sP34
| sP39 ),
inference(all_rule,[status(thm)],]) ).

thf(6,plain,
( ~ sP39
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
( ~ sP5
| ~ sP23
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
( ~ sP51
| sP34 ),
inference(all_rule,[status(thm)],]) ).

thf(9,plain,
( ~ sP47
| sP26 ),
inference(all_rule,[status(thm)],]) ).

thf(10,plain,
( ~ sP26
| sP24
| sP22 ),
inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
( ~ sP31
| sP51 ),
inference(all_rule,[status(thm)],]) ).

thf(12,plain,
( ~ sP51
| sP42 ),
inference(all_rule,[status(thm)],]) ).

thf(13,plain,
( ~ sP42
| sP35 ),
inference(all_rule,[status(thm)],]) ).

thf(14,plain,
( ~ sP35
| sP44
| sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
( ~ sP44
| ~ sP24
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
( ~ sP58
| sP61 ),
inference(all_rule,[status(thm)],]) ).

thf(17,plain,
( ~ sP61
| sP73
| sP75 ),
inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
( ~ sP67
| sP29 ),
inference(all_rule,[status(thm)],]) ).

thf(19,plain,
( ~ sP29
| sP48
| sP13 ),
inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
( ~ sP47
| sP19 ),
inference(all_rule,[status(thm)],]) ).

thf(21,plain,
( ~ sP19
| sP71
| sP2 ),
inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
( ~ sP47
| sP49 ),
inference(all_rule,[status(thm)],]) ).

thf(23,plain,
( ~ sP49
| sP23
| sP20 ),
inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).

thf(25,plain,
( ~ sP9
| sP52 ),
inference(all_rule,[status(thm)],]) ).

thf(26,plain,
( ~ sP52
| sP12
| sP60 ),
inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
( ~ sP12
| ~ sP75
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
( ~ sP74
| sP46 ),
inference(all_rule,[status(thm)],]) ).

thf(29,plain,
( ~ sP46
| sP7 ),
inference(all_rule,[status(thm)],]) ).

thf(30,plain,
( ~ sP7
| sP33
| sP53 ),
inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
( ~ sP33
| ~ sP13
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
( ~ sP76
| sP32 ),
inference(all_rule,[status(thm)],]) ).

thf(33,plain,
( ~ sP32
| ~ sP22
| sP8 ),
inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
( ~ sP50
| sP15 ),
inference(all_rule,[status(thm)],]) ).

thf(35,plain,
( ~ sP15
| sP54
| sP16 ),
inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
( ~ sP30
| sP45 ),
inference(all_rule,[status(thm)],]) ).

thf(37,plain,
( ~ sP45
| sP11
| sP66 ),
inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
( ~ sP11
| ~ sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
( ~ sP30
| sP17 ),
inference(all_rule,[status(thm)],]) ).

thf(40,plain,
( ~ sP17
| sP41
| sP38 ),
inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
( ~ sP41
| ~ sP8
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
( ~ sP69
| sP21 ),
inference(all_rule,[status(thm)],]) ).

thf(43,plain,
( ~ sP21
| ~ sP16
| sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
( ~ sP37
| sP30 ),
inference(all_rule,[status(thm)],]) ).

thf(45,plain,
( ~ sP30
| sP27 ),
inference(all_rule,[status(thm)],]) ).

thf(46,plain,
( ~ sP27
| sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
( ~ sP6
| ~ sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
( ~ sP37
| sP65 ),
inference(all_rule,[status(thm)],]) ).

thf(49,plain,
( ~ sP65
| sP25 ),
inference(all_rule,[status(thm)],]) ).

thf(50,plain,
( ~ sP25
| sP36
| sP8 ),
inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
( ~ sP36
| ~ sP16
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
( ~ sP70
| sP28 ),
inference(all_rule,[status(thm)],]) ).

thf(53,plain,
( ~ sP28
| ~ sP60
| sP38 ),
inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
( ~ sP69
| sP63 ),
inference(all_rule,[status(thm)],]) ).

thf(55,plain,
( ~ sP63
| ~ sP66
| sP53 ),
inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],]) ).

thf(57,plain,
( ~ sP14
| sP74 ),
inference(all_rule,[status(thm)],]) ).

thf(58,plain,
( ~ sP74
| sP68 ),
inference(all_rule,[status(thm)],]) ).

thf(59,plain,
( ~ sP68
| sP62 ),
inference(all_rule,[status(thm)],]) ).

thf(60,plain,
( ~ sP62
| sP57
| sP59 ),
inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
( ~ sP57
| ~ sP53
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
( ~ sP56
| sP50 ),
inference(all_rule,[status(thm)],]) ).

thf(63,plain,
( ~ sP72
| sP69 ),
inference(all_rule,[status(thm)],]) ).

thf(64,plain,
( ~ sP14
| sP37 ),
inference(all_rule,[status(thm)],]) ).

thf(65,plain,
( ~ sP56
| sP58 ),
inference(all_rule,[status(thm)],]) ).

thf(66,plain,
( ~ sP72
| sP76 ),
inference(all_rule,[status(thm)],]) ).

thf(67,plain,
( ~ sP76
| sP40 ),
inference(all_rule,[status(thm)],]) ).

thf(68,plain,
( ~ sP40
| ~ sP3
| sP55 ),
inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
( ~ sP72
| sP70 ),
inference(all_rule,[status(thm)],]) ).

thf(70,plain,
( ~ sP56
| sP67 ),
inference(all_rule,[status(thm)],]) ).

thf(71,plain,
( ~ sP56
| sP47 ),
inference(all_rule,[status(thm)],]) ).

thf(72,plain,
( ~ sP47
| sP64 ),
inference(all_rule,[status(thm)],]) ).

thf(73,plain,
( ~ sP64
| sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
\$false,
inference(prop_unsat,[status(thm),assumptions([h14,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,h7,h8,h6,h4,h12,h14]) ).

thf(75,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,74,h14]) ).

thf(76,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h10,75,h13]) ).

thf(77,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,76,h12]) ).

thf(78,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h9,77,h11]) ).

thf(79,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,78,h9,h10]) ).

thf(80,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,79,h7,h8]) ).

thf(81,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,80,h5,h6]) ).

thf(82,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,81,h3,h4]) ).

thf(83,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,82,h1,h2]) ).

thf(0,theorem,
( ~ ( ~ ( ~ ( sP31
=> ~ sP14 )
=> ~ sP72 )
=> ~ sP56 )
=> ( ~ ! [X1: \$i] : ( !! @ ( cP @ X1 ) )
=> ! [X1: \$i] : ( !! @ ( cQ @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[83,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV091^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n009.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  : 600
% 0.12/0.34  % DateTime : Fri Mar 26 14:17:38 EDT 2021
% 0.12/0.34  % CPUTime  :
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: mode213
% 0.19/0.45  % Inferences: 595
% 0.19/0.45  % SZS output start Proof
% See solution above
% 0.19/0.45  % SZS output end Proof
%------------------------------------------------------------------------------
```