TSTP Solution File: SEV034^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV034^5 : 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 : n029.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 Aug 31 19:32:23 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__2,type,
eigen__2: a > b ).
thf(ty_eigen__3,type,
eigen__3: a > b ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__1,type,
eigen__1: a > b > b > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( eigen__0 @ eigen__5 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__5 @ ( eigen__2 @ eigen__5 ) @ ( eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
= ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) @ ( eigen__3 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__4 @ eigen__4 )
=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__4 ) )
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__2 @ eigen__5 ) ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__5 @ eigen__5 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) )
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__3 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( sP1
=> ~ ( eigen__0 @ eigen__5 @ eigen__4 ) )
=> ( eigen__0 @ eigen__4 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ~ ( sP1
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__0 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: b,X2: b] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__4 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__4 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: b] :
( ~ ( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) )
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ X1 ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__0 @ eigen__5 @ eigen__4 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__5 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__5 ) )
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) @ ( eigen__3 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP14
=> ( ( eigen__1 @ eigen__4 )
!= ( eigen__1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) @ ( eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP18
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__3 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__5 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP22
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP1
=> ~ ( eigen__0 @ eigen__5 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( eigen__1 @ eigen__5 @ ( eigen__2 @ eigen__5 ) )
= ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ X1 )
=> ~ ( eigen__1 @ eigen__4 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__0 @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP1
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: b] :
( ~ ( sP22
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ! [X1: b,X2: b] :
( ( eigen__1 @ eigen__5 @ X1 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__1 @ eigen__5 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__5 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__5 @ X1 @ X3 ) ) )
=> ( ( eigen__1 @ eigen__5 )
!= ( eigen__1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__0 @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__4 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__4 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( ~ ( ! [X3: b,X4: b] :
( ( eigen__1 @ X1 @ X3 @ X4 )
=> ( eigen__1 @ X1 @ X4 @ X3 ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ( eigen__1 @ X1 @ X3 @ X4 )
=> ~ ( eigen__1 @ X1 @ X4 @ X5 ) )
=> ( eigen__1 @ X1 @ X3 @ X5 ) ) )
=> ( ( eigen__1 @ X1 )
!= ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: b] :
( ( eigen__1 @ eigen__5 @ X1 )
= ( eigen__1 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: b,X2: b] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: b] :
( ~ ( sP20
=> ~ ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) @ X1 ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: b] :
( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 )
=> ( eigen__1 @ eigen__4 @ X1 @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP16
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( ~ sP14
=> ( ( eigen__1 @ eigen__4 )
!= ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP10
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( eigen__1 @ eigen__5 )
= ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__0 @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( ~ ( ! [X2: b,X3: b] :
( ( eigen__1 @ eigen__5 @ X2 @ X3 )
=> ( eigen__1 @ eigen__5 @ X3 @ X2 ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ( eigen__1 @ eigen__5 @ X2 @ X3 )
=> ~ ( eigen__1 @ eigen__5 @ X3 @ X4 ) )
=> ( eigen__1 @ eigen__5 @ X2 @ X4 ) ) )
=> ( ( eigen__1 @ eigen__5 )
!= ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP1
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP37
=> ~ sP36 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a] :
( ~ ( sP37
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 )
=> ~ ( eigen__1 @ eigen__4 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: b] :
( ( eigen__1 @ eigen__5 @ ( eigen__2 @ eigen__5 ) @ X1 )
= ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__5 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(cTHM518_pme,conjecture,
! [X1: a > a > $o,X2: a > b > b > $o,X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) ) )
=> ( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X1 @ X6 @ X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X1 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X1 @ X5 @ X7 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ~ ( ~ ( ! [X7: b,X8: b] :
( ( X2 @ X5 @ X7 @ X8 )
=> ( X2 @ X5 @ X8 @ X7 ) )
=> ~ ! [X7: b,X8: b,X9: b] :
( ~ ( ( X2 @ X5 @ X7 @ X8 )
=> ~ ( X2 @ X5 @ X8 @ X9 ) )
=> ( X2 @ X5 @ X7 @ X9 ) ) )
=> ( ( X2 @ X5 )
!= ( X2 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > b > b > $o,X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) ) )
=> ( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X1 @ X6 @ X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X1 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X1 @ X5 @ X7 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ~ ( ~ ( ! [X7: b,X8: b] :
( ( X2 @ X5 @ X7 @ X8 )
=> ( X2 @ X5 @ X8 @ X7 ) )
=> ~ ! [X7: b,X8: b,X9: b] :
( ~ ( ( X2 @ X5 @ X7 @ X8 )
=> ~ ( X2 @ X5 @ X8 @ X9 ) )
=> ( X2 @ X5 @ X7 @ X9 ) ) )
=> ( ( X2 @ X5 )
!= ( X2 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM518_pme]) ).
thf(h1,assumption,
~ ! [X1: a > b > b > $o,X2: a > b,X3: a > b] :
( ! [X4: a] :
( ( eigen__0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ~ ( sP11
=> ~ sP55 )
=> ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ~ ( ~ ( ! [X6: b,X7: b] :
( ( X1 @ X4 @ X6 @ X7 )
=> ( X1 @ X4 @ X7 @ X6 ) )
=> ~ ! [X6: b,X7: b,X8: b] :
( ~ ( ( X1 @ X4 @ X6 @ X7 )
=> ~ ( X1 @ X4 @ X7 @ X8 ) )
=> ( X1 @ X4 @ X6 @ X8 ) ) )
=> ( ( X1 @ X4 )
!= ( X1 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) )
=> ( ~ ( sP11
=> ~ sP55 )
=> ( sP39
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a > b] :
( ! [X2: a] :
( ( eigen__0 @ X2 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__2 @ X2 ) @ ( X1 @ X2 ) ) )
=> ( sP19
=> ( ~ ( sP11
=> ~ sP55 )
=> ( sP39
=> ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ ( eigen__2 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP3
=> ( sP19
=> ( ~ ( sP11
=> ~ sP55 )
=> ( sP39
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP19
=> ( ~ ( sP11
=> ~ sP55 )
=> ( sP39
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP19,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP11
=> ~ sP55 )
=> ( sP39
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP11
=> ~ sP55 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP39
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP11,
introduced(assumption,[]) ).
thf(h12,assumption,
sP55,
introduced(assumption,[]) ).
thf(h13,assumption,
sP39,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> sP44 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP44,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP18
| ~ sP20
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP4
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP24
| sP18
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP26
| ~ sP22
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP58
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP42
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP26
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP28
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP40
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP29
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP35
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| ~ sP52
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP47
| sP10
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP29
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP49
| ~ sP52
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP38
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP57
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP43
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP41
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP38
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP48
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP36
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP54
| ~ sP37
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP21
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP51
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP34
| ~ sP1
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP16
| ~ sP37
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP45
| sP16
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP56
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP27
| ~ sP1
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP12
| sP27
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP25
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP8
| ~ sP17
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP53
| ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP2
| ~ sP1
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP55
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP39
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP33
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP50
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP32
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP46
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( sP14
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP14
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP6
| ~ sP31
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP11
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP19
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP55
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP39
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,h5,h7,h11,h12,h13,h17,h18]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,53,h17,h18]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,54,h16]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,55,h15]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h10,56,h13,h14]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,57,h11,h12]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,58,h9,h10]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,59,h7,h8]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,60,h5,h6]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,61,h4]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,62,h3]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,63,h2]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,64,h1]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > b > b > $o,X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) ) )
=> ( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X1 @ X6 @ X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X1 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X1 @ X5 @ X7 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ~ ( ~ ( ! [X7: b,X8: b] :
( ( X2 @ X5 @ X7 @ X8 )
=> ( X2 @ X5 @ X8 @ X7 ) )
=> ~ ! [X7: b,X8: b,X9: b] :
( ~ ( ( X2 @ X5 @ X7 @ X8 )
=> ~ ( X2 @ X5 @ X8 @ X9 ) )
=> ( X2 @ X5 @ X7 @ X9 ) ) )
=> ( ( X2 @ X5 )
!= ( X2 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[65,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV034^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:45:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % Mode: cade22grackle2xfee4
% 0.20/0.45 % Steps: 504
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------