TSTP Solution File: SYO388^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO388^5 : 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 : n015.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 19:31:47 EDT 2022
% Result : Theorem 0.65s 1.00s
% Output : Proof 0.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_d,type,
d: $i ).
thf(ty_cQ_1,type,
cQ_1: $i > $i > $i > $o ).
thf(ty_b,type,
b: $i ).
thf(ty_cQ_5,type,
cQ_5: $i > $i > $i > $o ).
thf(ty_cQ_2,type,
cQ_2: $i > $i > $i > $o ).
thf(ty_cQ_3,type,
cQ_3: $i > $i > $i > $o ).
thf(ty_cQ_6,type,
cQ_6: $i > $i > $i > $o ).
thf(ty_cQ_4,type,
cQ_4: $i > $i > $i > $o ).
thf(ty_cP_3,type,
cP_3: $i > $i > $o ).
thf(ty_c,type,
c: $i ).
thf(ty_cP_1,type,
cP_1: $i > $i > $o ).
thf(ty_cP_2,type,
cP_2: $i > $i > $o ).
thf(ty_cP_4,type,
cP_4: $i > $i > $o ).
thf(ty_f,type,
f: $i > $i ).
thf(ty_cP_5,type,
cP_5: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_5 @ X1 @ X2 @ X3 )
=> ~ ( cP_5 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_5 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_5 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_6 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ X1 @ X2 @ X3 )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_2 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_3 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP_4 @ c @ c )
=> ( cP_4 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP_1 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ( cQ_3 @ a @ b @ c )
=> ~ ( cP_3 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_3 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_3 @ ( f @ c ) @ X3 ) )
=> ( cQ_4 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cP_5 @ c @ X1 )
=> ( cP_5 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP_5 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cP_5 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP_2 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP_4 @ b @ b )
=> ( cP_4 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cQ_5 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP_4 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cQ_3 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( sP11
=> ~ sP8 )
=> ~ ( cP_5 @ ( f @ b ) @ b ) )
=> ~ ( cP_5 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP14
=> ( cQ_6 @ a @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ sP9 )
=> ~ ( cP_2 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_2 @ ( f @ c ) @ X2 ) )
=> ( cQ_3 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( cP_5 @ a @ X1 )
=> ( cP_5 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( sP13
=> ~ ( cP_3 @ ( f @ a ) @ a ) )
=> ~ ( cP_3 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) )
=> ~ ( cP_1 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X2 ) )
=> ( cQ_2 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( cP_5 @ b @ b )
=> ( cP_5 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( cP_2 @ b @ b )
=> ( cP_2 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cP_5 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP_1 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP11
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cP_5 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( cP_4 @ c @ X1 )
=> ( cP_4 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( cP_4 @ b @ X1 )
=> ( cP_4 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cP_1 @ b @ b )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP27
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( cP_2 @ b @ X1 )
=> ( cP_2 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_5 @ a @ X1 @ X2 )
=> ~ ( cP_5 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_5 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_5 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_6 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( cP_3 @ c @ X1 )
=> ( cP_3 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ a @ b @ c )
=> ~ ( cP_4 @ ( f @ a ) @ a ) )
=> ~ ( cP_4 @ ( f @ b ) @ b ) )
=> ~ ( cP_4 @ ( f @ c ) @ X1 ) )
=> ( cQ_5 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP24
=> ~ ( cP_5 @ ( f @ b ) @ b ) )
=> ~ ( cP_5 @ ( f @ c ) @ X1 ) )
=> ( cQ_6 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( cP_1 @ c @ X1 )
=> ( cP_1 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_3 @ a @ X1 @ X2 )
=> ~ ( cP_3 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_3 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_3 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_4 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ( cQ_4 @ a @ b @ c )
=> ~ ( cP_4 @ ( f @ a ) @ a ) )
=> ~ ( cP_4 @ ( f @ b ) @ b ) )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cP_4 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cP_1 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP25
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( cP_1 @ b @ X1 )
=> ( cP_1 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ a @ X1 @ X2 )
=> ~ ( cP_4 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_4 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_4 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_5 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( cP_3 @ a @ a )
=> ( cP_3 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( cP_5 @ b @ X1 )
=> ( cP_5 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( cP_2 @ c @ c )
=> ( cP_2 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i,X2: $i] :
( ( cP_1 @ X1 @ X2 )
=> ( cP_1 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ~ ( ~ sP30
=> ~ ( cP_1 @ ( f @ c ) @ X1 ) )
=> ( cQ_2 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ a @ b @ c )
=> ~ sP39 )
=> ~ ( cP_4 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_4 @ ( f @ c ) @ X2 ) )
=> ( cQ_5 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ a @ b @ X1 )
=> ~ ( cP_4 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_4 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_4 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_5 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( cP_5 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ( cP_3 @ a @ X1 )
=> ( cP_3 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( cP_2 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( cP_3 @ b @ b )
=> ( cP_3 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( cP_2 @ a @ a )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP7
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( cP_3 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( cQ_6 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( cP_3 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( cQ_1 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( cP_3 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ sP9 )
=> ~ ( cP_2 @ ( f @ b ) @ b ) )
=> ~ sP53 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( cP_4 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( cP_2 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i] :
( ~ ( ~ sP18
=> ~ ( cP_3 @ ( f @ c ) @ X1 ) )
=> ( cQ_4 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i,X2: $i] :
( ( cP_4 @ X1 @ X2 )
=> ( cP_4 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ X1 )
=> ~ ( cP_2 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_2 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_3 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( cP_4 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ X1 @ X2 @ X3 )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_1 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_2 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( sP60
=> ~ ( cP_1 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X3 ) )
=> ( cQ_2 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
( ( cP_2 @ a @ X1 )
=> ( cP_2 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( cP_3 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ~ sP24
=> ~ ( cP_5 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ( cP_1 @ a @ a )
=> sP40 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( cP_5 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ sP18
=> ~ sP61 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i,X2: $i] :
( ( cP_2 @ X1 @ X2 )
=> ( cP_2 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ a @ b @ c )
=> ~ ( cP_4 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_4 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_4 @ ( f @ c ) @ X3 ) )
=> ( cQ_5 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ sP9 )
=> ~ sP64 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( ~ sP79
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( cP_2 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ! [X1: $i,X2: $i] :
( ( cP_5 @ X1 @ X2 )
=> ( cP_5 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ( cQ_2 @ a @ b @ c )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( sP4
=> ( cP_1 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( sP13
=> ~ sP72 )
=> ~ ( cP_3 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_3 @ ( f @ c ) @ X2 ) )
=> ( cQ_4 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ ( cP_2 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_2 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_2 @ ( f @ c ) @ X3 ) )
=> ( cQ_3 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( cP_2 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ! [X1: $i] :
( ( cP_1 @ a @ X1 )
=> ( cP_1 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( sP11
=> ~ ( cP_5 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_5 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_5 @ ( f @ c ) @ X3 ) )
=> ( cQ_6 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_6 @ X1 @ X2 @ X3 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ~ ( ~ sP30
=> ~ ( cP_1 @ ( f @ c ) @ c ) )
=> ( cQ_2 @ a @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( cP_4 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( cP_3 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $i] :
( ~ ( ~ sP79
=> ~ ( cP_2 @ ( f @ c ) @ X1 ) )
=> ( cQ_3 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP24
=> ~ ( cP_5 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_5 @ ( f @ c ) @ X2 ) )
=> ( cQ_6 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_4 @ X1 @ X2 @ X3 )
=> ~ ( cP_4 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_4 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_4 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_5 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( cP_1 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( cP_4 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( sP13
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( cP_1 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ~ sP76
=> ( cQ_4 @ a @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ~ sP38
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_3 @ a @ b @ X1 )
=> ~ ( cP_3 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_3 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_3 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_4 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( cQ_2 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ! [X1: $i] :
( ( cP_3 @ b @ X1 )
=> ( cP_3 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_5 @ a @ b @ X1 )
=> ~ ( cP_5 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_5 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_5 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_6 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ X1 @ X2 )
=> ~ ( cP_1 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_2 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( ( cQ_4 @ a @ b @ c )
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: $i,X2: $i] :
( ( cP_3 @ X1 @ X2 )
=> ( cP_3 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( cQ_4 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_3 @ X1 @ X2 @ X3 )
=> ~ ( cP_3 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_3 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_3 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_4 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ! [X1: $i] :
( ( cP_2 @ c @ X1 )
=> ( cP_2 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( cP_1 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ X1 @ X2 )
=> ~ ( cP_2 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_3 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ sP30
=> ~ sP97 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ X1 )
=> ~ ( cP_1 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_2 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( sP63
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( sP57
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( cP_2 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ~ sP108
=> ~ sP92 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ! [X1: $i,X2: $i] :
~ ( cQ_6 @ a @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [X1: $i] :
( ( cP_4 @ a @ X1 )
=> ( cP_4 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ! [X1: $i] :
~ ( cQ_6 @ a @ b @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( cP_3 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(cTHM409_5,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) )
=> ~ sP82 )
=> ~ sP1 )
=> ~ sP90 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) )
=> ~ sP82 )
=> ~ sP1 )
=> ~ sP90 ),
inference(assume_negation,[status(cth)],[cTHM409_5]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) )
=> ~ sP82 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP90,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) )
=> ~ sP82 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP82,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h8,assumption,
!! @ ( cP_5 @ d ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP25,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP51,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP7,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP96,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP66,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 ),
introduced(assumption,[]) ).
thf(h20,assumption,
!! @ ( cP_4 @ d ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP68,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP98,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP63,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 ),
introduced(assumption,[]) ).
thf(h28,assumption,
sP111,
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
sP109,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 ),
introduced(assumption,[]) ).
thf(h32,assumption,
!! @ ( cP_3 @ d ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 ),
introduced(assumption,[]) ).
thf(h34,assumption,
sP57,
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 ),
introduced(assumption,[]) ).
thf(h36,assumption,
sP124,
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP59,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 ),
introduced(assumption,[]) ).
thf(h40,assumption,
sP2,
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
sP77,
introduced(assumption,[]) ).
thf(h43,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 ),
introduced(assumption,[]) ).
thf(h44,assumption,
!! @ ( cP_2 @ d ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 ),
introduced(assumption,[]) ).
thf(h46,assumption,
sP87,
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 ),
introduced(assumption,[]) ).
thf(h48,assumption,
sP81,
introduced(assumption,[]) ).
thf(h49,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 ),
introduced(assumption,[]) ).
thf(h50,assumption,
sP119,
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 ),
introduced(assumption,[]) ).
thf(h52,assumption,
sP69,
introduced(assumption,[]) ).
thf(h53,assumption,
~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
sP47,
introduced(assumption,[]) ).
thf(h55,assumption,
~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h56,assumption,
!! @ ( cP_1 @ d ),
introduced(assumption,[]) ).
thf(h57,assumption,
~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 ),
introduced(assumption,[]) ).
thf(h58,assumption,
sP4,
introduced(assumption,[]) ).
thf(h59,assumption,
~ ( sP60
=> ~ sP100 ),
introduced(assumption,[]) ).
thf(h60,assumption,
sP113,
introduced(assumption,[]) ).
thf(h61,assumption,
sP60,
introduced(assumption,[]) ).
thf(h62,assumption,
sP100,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP123
| ~ sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP90
| sP121 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP121
| sP123 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP116
| sP70 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP70
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP19
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP48
| sP91 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP91
| sP115
| sP104 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP115
| sP30
| ~ sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP30
| sP27
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP27
| ~ sP60
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP69
| sP107 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP107
| sP116 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP67
| sP86 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP86
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP94 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP94
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP62
| sP80
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP80
| sP79
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP79
| sP83
| ~ sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP83
| ~ sP104
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP2
| sP114 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP114
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP103
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP5
| sP85 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP85
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP65
| sP101 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP101
| sP76
| sP110 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP76
| sP18
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP18
| sP99
| ~ sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP99
| ~ sP13
| ~ sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP111
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP37
| sP103 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP50
| sP78 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP78
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP49
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP34
| sP102 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP102
| sP38
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP38
| sP120
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP120
| sP108
| ~ sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP108
| ~ sP110
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP96
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP43
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP106
| sP89 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP89
| sP95 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP95
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP35
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP15
| sP14
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP14
| sP73
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP73
| sP24
| ~ sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP24
| ~ sP11
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP1
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP32
| sP106 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP47
| sP88 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP88
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP74
| ~ sP100
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP47
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP42
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP29
| ~ sP113
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP47
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP36
| sP84 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP84
| ~ sP4
| sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP77
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP71
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP55
| ~ sP119
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP77
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP31
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP21
| ~ sP81
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP77
| sP112 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP112
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP46
| ~ sP87
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP109
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP52
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP44
| ~ sP59
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP109
| sP105 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP105
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP54
| ~ sP124
| sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP109
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP33
| sP118 ),
inference(all_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP118
| ~ sP57
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP66
| sP122 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP122
| sP117 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
( ~ sP117
| ~ sP63
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP66
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP28
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP10
| ~ sP98
| sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP66
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP26
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP3
| ~ sP68
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP82
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP17
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP56
| ~ sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(93,plain,
( ~ sP82
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(94,plain,
( ~ sP45
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP20
| ~ sP51
| sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP82
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP6
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP41
| ~ sP25
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,h61,h62,h60,h58,h54,h52,h50,h48,h46,h42,h40,h38,h36,h34,h30,h28,h26,h24,h22,h18,h16,h14,h12,h10,h6,h4,h2]) ).
thf(100,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[h59,99,h61,h62]) ).
thf(101,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h59,h60])],[h57,100,h59,h60]) ).
thf(102,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h57,h58])],[h55,101,h57,h58]) ).
thf(103,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h55,h56])],[h53,102,h55,h56]) ).
thf(104,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h53,h54])],[h51,103,h53,h54]) ).
thf(105,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h51,h52])],[h49,104,h51,h52]) ).
thf(106,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h49,h50])],[h47,105,h49,h50]) ).
thf(107,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h47,h48])],[h45,106,h47,h48]) ).
thf(108,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h45,h46])],[h43,107,h45,h46]) ).
thf(109,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h43,h44])],[h41,108,h43,h44]) ).
thf(110,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h39,109,h41,h42]) ).
thf(111,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h37,110,h39,h40]) ).
thf(112,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h35,111,h37,h38]) ).
thf(113,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h33,112,h35,h36]) ).
thf(114,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h33,h34])],[h31,113,h33,h34]) ).
thf(115,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h31,h32])],[h29,114,h31,h32]) ).
thf(116,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h27,115,h29,h30]) ).
thf(117,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h25,116,h27,h28]) ).
thf(118,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h23,117,h25,h26]) ).
thf(119,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h21,118,h23,h24]) ).
thf(120,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h19,119,h21,h22]) ).
thf(121,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,120,h19,h20]) ).
thf(122,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,121,h17,h18]) ).
thf(123,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h13,122,h15,h16]) ).
thf(124,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,123,h13,h14]) ).
thf(125,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,124,h11,h12]) ).
thf(126,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,125,h9,h10]) ).
thf(127,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,126,h7,h8]) ).
thf(128,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,127,h5,h6]) ).
thf(129,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,128,h3,h4]) ).
thf(130,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,129,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP60
=> ~ sP100 )
=> ~ sP113 )
=> ~ sP4 )
=> ~ ( !! @ ( cP_1 @ d ) ) )
=> ~ sP47 )
=> ~ sP69 )
=> ~ sP119 )
=> ~ sP81 )
=> ~ sP87 )
=> ~ ( !! @ ( cP_2 @ d ) ) )
=> ~ sP77 )
=> ~ sP2 )
=> ~ sP59 )
=> ~ sP124 )
=> ~ sP57 )
=> ~ ( !! @ ( cP_3 @ d ) ) )
=> ~ sP109 )
=> ~ sP111 )
=> ~ sP63 )
=> ~ sP98 )
=> ~ sP68 )
=> ~ ( !! @ ( cP_4 @ d ) ) )
=> ~ sP66 )
=> ~ sP96 )
=> ~ sP7 )
=> ~ sP51 )
=> ~ sP25 )
=> ~ ( !! @ ( cP_5 @ d ) ) )
=> ~ sP82 )
=> ~ sP1 )
=> ~ sP90 ),
inference(contra,[status(thm),contra(discharge,[h0])],[130,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO388^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 16:45:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.65/1.00 % SZS status Theorem
% 0.65/1.00 % Mode: mode213
% 0.65/1.00 % Inferences: 186
% 0.65/1.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------