TSTP Solution File: SYN036^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN036^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : Fri Sep 1 03:19:33 EDT 2023
% Result : Theorem 3.33s 3.56s
% Output : Proof 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 232
% Syntax : Number of formulae : 283 ( 85 unt; 32 typ; 17 def)
% Number of atoms : 587 ( 68 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 499 ( 175 ~; 131 |; 0 &; 123 @)
% ( 69 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 104 ( 102 usr; 101 con; 0-2 aty)
% Number of variables : 47 ( 17 ^; 30 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__17,type,
eigen__17: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__176,type,
eigen__176: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__43,type,
eigen__43: $i ).
thf(ty_eigen__39,type,
eigen__39: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__44,type,
eigen__44: $i ).
thf(ty_eigen__188,type,
eigen__188: $i ).
thf(ty_eigen__237,type,
eigen__237: $i ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(ty_eigen__136,type,
eigen__136: $i ).
thf(ty_eigen__45,type,
eigen__45: $i ).
thf(ty_eigen__135,type,
eigen__135: $i ).
thf(ty_eigen__191,type,
eigen__191: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__190,type,
eigen__190: $i ).
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__189,type,
eigen__189: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__67,type,
eigen__67: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_eigen__137,type,
eigen__137: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__138,type,
eigen__138: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__47,type,
eigen__47: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__190,definition,
( eigen__190
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__190])]) ).
thf(eigendef_eigen__137,definition,
( eigen__137
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__137])]) ).
thf(eigendef_eigen__39,definition,
( eigen__39
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__3 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__39])]) ).
thf(eigendef_eigen__45,definition,
( eigen__45
= ( eps__0
@ ^ [X1: $i] :
~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__45])]) ).
thf(eigendef_eigen__47,definition,
( eigen__47
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__19 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__47])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__1 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__191,definition,
( eigen__191
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__67 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__191])]) ).
thf(eigendef_eigen__135,definition,
( eigen__135
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__135])]) ).
thf(eigendef_eigen__43,definition,
( eigen__43
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__43])]) ).
thf(eigendef_eigen__189,definition,
( eigen__189
= ( eps__0
@ ^ [X1: $i] :
~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__189])]) ).
thf(eigendef_eigen__136,definition,
( eigen__136
= ( eps__0
@ ^ [X1: $i] :
~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__136])]) ).
thf(eigendef_eigen__176,definition,
( eigen__176
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__0 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__176])]) ).
thf(eigendef_eigen__188,definition,
( eigen__188
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__188])]) ).
thf(eigendef_eigen__44,definition,
( eigen__44
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__44])]) ).
thf(eigendef_eigen__138,definition,
( eigen__138
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__67 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__138])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__13 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(eigendef_eigen__237,definition,
( eigen__237
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__4 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__237])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ ! [X1: $i] :
~ ( cP @ X1 ) )
= ( ! [X1: $i] : ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( cQ @ eigen__67 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cQ @ eigen__47 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cQ @ eigen__67 )
= ( cQ @ eigen__191 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cQ @ eigen__4 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cQ @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( sP1
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ eigen__135 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ~ ! [X1: $i] :
~ ( cQ @ X1 ) )
= ( ! [X1: $i] : ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cQ @ eigen__1 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] : ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cQ @ eigen__191 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cQ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cQ @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cQ @ eigen__13 )
= sP7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( cQ @ eigen__188 )
= ( cQ @ eigen__189 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( cQ @ eigen__13 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP7 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( cQ @ eigen__188 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cQ @ eigen__237 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cQ @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
~ ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP1
= ( cP @ eigen__39 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cP @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cQ @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( cQ @ eigen__44 )
= sP29 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( cP @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( sP10
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( cQ @ eigen__189 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cQ @ eigen__188 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP9
= ( cP @ eigen__190 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( cP @ eigen__176 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP10 = sP28 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP16 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( cQ @ eigen__44 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP34
= ( cQ @ eigen__137 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( cP @ eigen__138 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( sP7
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( cQ @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i] :
( sP44
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( cQ @ eigen__4 )
= sP24 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( cQ @ eigen__44 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( cP @ eigen__67 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( cQ @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( sP9
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( cQ @ eigen__137 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( cQ @ eigen__67 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP44 = sP50 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( cP @ eigen__136 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( cP @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP44 = sP16 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ~ sP11 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: $i] :
( sP49
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( cP @ eigen__39 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( cQ @ eigen__45 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $i] : ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP10 = sP31 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ sP45 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( cP @ eigen__190 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP10 = sP36 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP48 = sP61 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP49 = sP42 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP9 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(cX2129,conjecture,
sP58 = sP64 ).
thf(h1,negated_conjecture,
sP58 != sP64,
inference(assume_negation,[status(cth)],[cX2129]) ).
thf(h2,assumption,
sP58,
introduced(assumption,[]) ).
thf(h3,assumption,
sP64,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP58,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP64,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
sP32,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h12,assumption,
sP62,
introduced(assumption,[]) ).
thf(h13,assumption,
sP26,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP62,
introduced(assumption,[]) ).
thf(h15,assumption,
sP16,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP45,
introduced(assumption,[]) ).
thf(h17,assumption,
sP2,
introduced(assumption,[]) ).
thf(h18,assumption,
sP45,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h20,assumption,
sP46,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h22,assumption,
sP14,
introduced(assumption,[]) ).
thf(h23,assumption,
sP23,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h25,assumption,
sP1,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP50,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP57
| sP44
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP46
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP54
| ~ sP44
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP46
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h25,h21,h22,h20,h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0])],[1,2,3,4,h15,h20,h26]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h21,h22,h20,h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__4)],[h22,5,h26]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__3)],[h21,6,h25]) ).
thf(8,plain,
( ~ sP62
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP23
| ~ sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h20,h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0])],[8,9,h12,h23]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h20,h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_be(discharge,[h21,h22]),tab_be(discharge,[h23,h24])],[h17,7,10,h21,h22,h23,h24]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__2)],[h16,11,h20]) ).
thf(h27,assumption,
cP @ eigen__5,
introduced(assumption,[]) ).
thf(13,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP38
| ~ sP16
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP13
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(16,plain,
( ~ sP45
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h21,h22,h18,h19,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0])],[13,14,15,16,h15,h18,h22]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h18,h19,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__5)],[h21,17,h27]) ).
thf(h28,assumption,
~ ( cQ @ eigen__12 ),
introduced(assumption,[]) ).
thf(19,plain,
( ~ sP62
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP23
| ~ sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h23,h24,h18,h19,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0])],[19,20,h12,h23]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h18,h19,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__12)],[h24,21,h28]) ).
thf(23,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h18,h19,h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_bq(discharge,[h21,h22]),tab_bq(discharge,[h23,h24])],[h19,18,22,h21,h22,h23,h24]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h15,h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h3,12,23,h16,h17,h18,h19]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__1)],[h11,24,h15]) ).
thf(h29,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h30,assumption,
! [X1: $i] :
( ( cQ @ eigen__14 )
= ( cQ @ X1 ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
sP31,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( cQ @ eigen__16 ),
introduced(assumption,[]) ).
thf(26,plain,
( ~ sP37
| ~ sP10
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP32
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP63
| sP10
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP32
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h32,h31,h21,h22,h30,h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0])],[26,27,28,29,h10,h29,h31]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h21,h22,h30,h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__16)],[h22,30,h32]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h30,h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__15)],[h21,31,h31]) ).
thf(33,plain,
( ~ sP26
| ~ sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h30,h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0])],[33,34,h13,h24]) ).
thf(36,plain,
$false,
inference(tab_be,[status(thm),assumptions([h30,h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_be(discharge,[h21,h22]),tab_be(discharge,[h23,h24])],[h17,32,35,h21,h22,h23,h24]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__14)],[h16,36,h30]) ).
thf(h33,assumption,
cP @ eigen__17,
introduced(assumption,[]) ).
thf(38,plain,
( ~ sP26
| ~ sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h21,h22,h18,h19,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0])],[38,39,h13,h22]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h18,h19,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__17)],[h21,40,h33]) ).
thf(42,plain,
( ~ sP26
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( sP18
| sP25
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP20
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).
thf(45,plain,
( ~ sP45
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP26
| ~ sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h18,h19,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0])],[42,43,44,45,46,h13,h18]) ).
thf(48,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h18,h19,h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_bq(discharge,[h21,h22]),tab_bq(discharge,[h23,h24])],[h19,41,47,h21,h22,h23,h24]) ).
thf(49,plain,
$false,
inference(tab_be,[status(thm),assumptions([h29,h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h3,37,48,h16,h17,h18,h19]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h10,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__13)],[h14,49,h29]) ).
thf(51,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h10,h6,h7,h2,h3,h1,h0]),tab_bq(discharge,[h11,h12]),tab_bq(discharge,[h13,h14])],[h7,25,50,h11,h12,h13,h14]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h6,51,h10]) ).
thf(53,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP30
| sP48
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP39
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP67
| ~ sP48
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP39
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP62
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP23
| ~ sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( sP21
| ~ sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP43
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__47]) ).
thf(62,plain,
( sP2
| sP23
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP45
| ~ sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( sP14
| ~ sP61 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__45]) ).
thf(65,plain,
( ~ sP23
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP2
| sP23
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP45
| sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__44]) ).
thf(69,plain,
( sP64
| sP45
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP64
| ~ sP45
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP27
| ~ sP1
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP27
| sP1
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP26
| sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__43]) ).
thf(74,plain,
( sP8
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__39]) ).
thf(75,plain,
( ~ sP62
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( sP12
| ~ sP26
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP11
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h2,h3,h1,h0])],[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,h3,h9,h8]) ).
thf(79,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h2,h3,h1,h0]),tab_bq(discharge,[h6,h7]),tab_bq(discharge,[h8,h9])],[h2,52,78,h6,h7,h8,h9]) ).
thf(80,plain,
( ~ sP35
| sP9
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP51
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP26
| ~ sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
( ~ sP14
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP41
| sP34
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP22
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP19
| ~ sP34
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP22
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP23
| ~ sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP62
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP69
| ~ sP9
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP51
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
( sP47
| sP50
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(93,plain,
( sP5
| ~ sP53
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP6
| ~ sP47 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__237]) ).
thf(95,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__191]) ).
thf(96,plain,
( sP23
| sP65 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__190]) ).
thf(97,plain,
( sP2
| ~ sP23
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP45
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(99,plain,
( ~ sP45
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(100,plain,
( sP14
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__189]) ).
thf(101,plain,
( ~ sP23
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP23
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(103,plain,
( ~ sP14
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(104,plain,
( ~ sP14
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(105,plain,
( ~ sP2
| sP23
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP2
| ~ sP23
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( sP45
| sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__188]) ).
thf(108,plain,
( ~ sP64
| sP45
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(109,plain,
( ~ sP64
| ~ sP45
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( sP66
| sP10
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(111,plain,
( sP68
| ~ sP49
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(112,plain,
( sP32
| ~ sP66 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__176]) ).
thf(113,plain,
( sP59
| ~ sP68 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__138]) ).
thf(114,plain,
( sP26
| sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__137]) ).
thf(115,plain,
( sP12
| sP26
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(116,plain,
( sP12
| ~ sP26
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(117,plain,
( ~ sP11
| ~ sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(118,plain,
( ~ sP11
| ~ sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(119,plain,
( sP62
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__136]) ).
thf(120,plain,
( ~ sP26
| ~ sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(121,plain,
( ~ sP62
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(122,plain,
( ~ sP62
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(123,plain,
( ~ sP12
| sP26
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(124,plain,
( sP11
| sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__135]) ).
thf(125,plain,
( sP58
| sP11
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(126,plain,
( sP58
| ~ sP11
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(127,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h1,h0])],[80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,h5,h4]) ).
thf(128,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,79,127,h2,h3,h4,h5]) ).
thf(129,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[128,h0]) ).
thf(0,theorem,
sP58 = sP64,
inference(contra,[status(thm),contra(discharge,[h1])],[128,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN036^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 20:38:27 EDT 2023
% 0.13/0.36 % CPUTime :
% 3.33/3.56 % SZS status Theorem
% 3.33/3.56 % Mode: cade22grackle2xfee4
% 3.33/3.56 % Steps: 88153
% 3.33/3.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------