TSTP Solution File: SYO174^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO174^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : 600s
% DateTime : Thu Jul 21 19:30:39 EDT 2022
% Result : Theorem 2.20s 2.61s
% Output : Proof 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 232
% Syntax : Number of formulae : 254 ( 25 unt; 23 typ; 18 def)
% Number of atoms : 678 ( 87 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 666 ( 219 ~; 182 |; 0 &; 151 @)
% ( 85 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 109 usr; 107 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 18 ^ 52 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_cS,type,
cS: $i > $o ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__26,type,
eigen__26: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__20,type,
eigen__20: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_eigen__36,type,
eigen__36: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_eigen__18,type,
eigen__18: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: $i] :
( ( cR @ eigen__0 )
!= ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cS @ X1 )
= ( cS @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__0 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__0
@ ^ [X1: $i] :
( ( cS @ eigen__7 )
!= ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(eigendef_eigen__20,definition,
( eigen__20
= ( eps__0
@ ^ [X1: $i] :
( ( cS @ eigen__9 )
!= ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__20])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cR @ X1 )
= ( cR @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__36,definition,
( eigen__36
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__9 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__36])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__0
@ ^ [X1: $i] :
( ( cR @ eigen__3 )
!= ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( cQ @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cQ @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( cR @ eigen__9 )
= ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( sP1
= ( cQ @ eigen__12 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( sP1
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cR @ eigen__3 )
= ( cR @ eigen__19 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( sP1
= ( cQ @ eigen__3 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cP @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ~ ! [X1: $i] :
~ ( cP @ X1 ) )
= ( !! @ cQ ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ~ ! [X1: $i] :
~ ( cQ @ X1 ) )
= ( !! @ cR ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cQ @ eigen__0 )
= sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cP @ eigen__4 )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o > $o] :
( ( X1 @ sP8 )
=> ! [X2: $o] :
( ( X2 = sP8 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( cQ @ eigen__12 )
=> ! [X1: $o] :
( ( X1
= ( cQ @ eigen__12 ) )
=> ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( cR @ eigen__0 )
= ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( cR @ eigen__3 )
= ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o > $o] :
( ( X1 @ ( cQ @ eigen__3 ) )
=> ! [X2: $o] :
( ( X2
= ( cQ @ eigen__3 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cP @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( cP @ eigen__4 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( !! @ cQ ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( !! @ cP ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP8
=> ! [X1: $o] :
( ( X1 = sP8 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cR @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cR @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cQ @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cS @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP1
= ( cQ @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( cS @ eigen__8 )
= ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( ~ ! [X1: $i] :
~ ( cS @ X1 ) )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( cS @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP33
= ( cS @ eigen__20 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( cP @ eigen__9 )
= ( cP @ eigen__36 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $o > $o] :
( ( X1 @ sP28 )
=> ! [X2: $o] :
( ( X2 = sP28 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( cR @ eigen__0 )
= ( cR @ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cS @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cS @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( cQ @ eigen__3 )
=> ! [X1: $o] :
( ( X1
= ( cQ @ eigen__3 ) )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( cR @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
~ ( cS @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( cP @ eigen__36 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( cR @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP13
=> ( cP @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ( cP @ eigen__9 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( cS @ eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( cP @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( cR @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cS @ X1 )
= ( cS @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X1 )
= ( cR @ X2 ) ) )
= sP32 )
= ( ( ~ sP52 )
= sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP29 = sP39 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( cR @ eigen__9 )
= sP27 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( ~ sP23 )
= ( ( ~ ! [X1: $i] :
~ ( cR @ X1 ) )
= ( !! @ cS ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i] :
( sP48
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $o] :
( ( X1 = sP28 )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( cP @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ( ~ ! [X1: $i] :
~ ( cR @ X1 ) )
= ( !! @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( cS @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( ( ( ~ sP12 )
= sP10 )
= sP56 )
= sP53 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X1 )
= ( cR @ X2 ) ) )
= sP32 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( cR @ eigen__9 )
= ( cR @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP1 = sP28 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( ( ~ sP12 )
= sP10 )
= sP56 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cR @ X1 )
= ( cR @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP59 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( !! @ cS ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( cR @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( cS @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP40
= ( cS @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( cR @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $o] :
( ( X1
= ( cQ @ eigen__3 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ( ~ sP12 )
= sP10 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i] :
~ ( cR @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i] :
( sP33
= ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $o] :
( ( X1 = sP8 )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ! [X1: $i] :
( sP29
= ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( cQ @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i] :
~ ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( cS @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( !! @ cR ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ( ~ sP52 )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( sP40 = sP71 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(cTHM138,conjecture,
sP62 ).
thf(h1,negated_conjecture,
~ sP62,
inference(assume_negation,[status(cth)],[cTHM138]) ).
thf(1,plain,
( ~ sP24
| ~ sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP22
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP36
| ~ sP50
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP36
| sP50
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP69
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP34
| ~ sP33
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP47
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__36]) ).
thf(8,plain,
( ~ sP21
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP81
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP11
| ~ sP48
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP11
| sP48
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP43
| ~ sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP54
| sP29
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP79
| ~ sP54 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).
thf(15,plain,
( sP77
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20]) ).
thf(16,plain,
( ~ sP83
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( sP38
| ~ sP45
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP76
| ~ sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP6
| sP26
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP17
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).
thf(21,plain,
( sP16
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(22,plain,
( sP57
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(23,plain,
( ~ sP85
| sP40
| ~ sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| sP85 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP68
| ~ sP59
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP20
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP5
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP4
| ~ sP65
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP58
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP15
| sP28
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP37
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP35
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP53
| ~ sP63
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP53
| sP63
| ~ sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP64
| ~ sP73
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP3
| sP64 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP72
| ~ sP40
| sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP31
| sP72 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( sP84
| sP52
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP84
| ~ sP52
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP63
| sP67
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP63
| ~ sP67
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP9
| sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP9
| ~ sP24
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP21
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(46,plain,
( ~ sP52
| ~ sP79 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP43
| ~ sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP20
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP46
| ~ sP13
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP78
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP25
| ~ sP8
| sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP35
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( sP32
| sP43
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP32
| ~ sP43
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP22
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(57,plain,
( sP43
| sP71 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(58,plain,
( ~ sP55
| sP73
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP69
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP12
| ~ sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP52
| ~ sP77 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP24
| ~ sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP22
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP3
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( sP67
| sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(66,plain,
( ~ sP43
| ~ sP61 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP32
| sP43
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP32
| ~ sP43
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP67
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP67
| ~ sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP63
| sP67
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP63
| ~ sP67
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP52
| sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(74,plain,
( sP24
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(75,plain,
( ~ sP21
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP9
| sP24
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP9
| ~ sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP84
| sP52
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP84
| ~ sP52
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP53
| ~ sP63
| ~ sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( sP53
| sP63
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP5
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
( ~ sP7
| ~ sP30
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP74
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP41
| ~ sP80
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP18
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP35
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
( sP69
| ~ sP82 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(89,plain,
( sP83
| ~ sP70 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(90,plain,
( ~ sP76
| ~ sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP69
| sP61 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
sP35,
inference(eq_ind_sym,[status(thm)],]) ).
thf(93,plain,
( sP10
| sP81
| ~ sP83 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP10
| ~ sP81
| sP83 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( sP75
| sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( sP75
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP66
| ~ sP75
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP66
| sP75
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
( sP12
| sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(100,plain,
( sP81
| sP80 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(101,plain,
( ~ sP83
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP81
| ~ sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(103,plain,
( ~ sP10
| sP81
| sP83 ),
inference(prop_rule,[status(thm)],]) ).
thf(104,plain,
( ~ sP10
| ~ sP81
| ~ sP83 ),
inference(prop_rule,[status(thm)],]) ).
thf(105,plain,
( ~ sP75
| sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP75
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( sP60
| sP76
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(108,plain,
( sP60
| ~ sP76
| sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(109,plain,
( ~ sP56
| sP23
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( ~ sP56
| ~ sP23
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(111,plain,
( sP23
| sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(112,plain,
( sP76
| sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(113,plain,
( ~ sP76
| ~ sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(114,plain,
( ~ sP60
| sP76
| sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( ~ sP60
| ~ sP76
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(116,plain,
( ~ sP23
| ~ sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(117,plain,
( sP56
| sP23
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(118,plain,
( sP56
| ~ sP23
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(119,plain,
( sP66
| ~ sP75
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(120,plain,
( sP66
| sP75
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(121,plain,
( sP62
| ~ sP66
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(122,plain,
( sP62
| sP66
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(123,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,h1]) ).
thf(124,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[123,h0]) ).
thf(0,theorem,
sP62,
inference(contra,[status(thm),contra(discharge,[h1])],[123,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO174^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.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 : 600
% 0.12/0.33 % DateTime : Sat Jul 9 09:36:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.20/2.61 % SZS status Theorem
% 2.20/2.61 % Mode: mode506
% 2.20/2.61 % Inferences: 23909
% 2.20/2.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------