TSTP Solution File: SYO169^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO169^5 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 19:30:38 EDT 2022
% Result : Theorem 31.39s 31.67s
% Output : Proof 31.39s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_cP,type,
cP: $i > $i > $i > $o ).
thf(ty_b,type,
b: $i ).
thf(ty_cPx,type,
cPx: $i > $i > $o ).
thf(ty_e,type,
e: $i ).
thf(ty_ab,type,
ab: $i ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ! [X1: $i] : ( cP @ e @ X1 @ X1 )
=> ~ ! [X1: $i] : ( cP @ X1 @ e @ X1 ) )
=> ~ ! [X1: $i] : ( cP @ X1 @ X1 @ e ) )
=> ~ ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ( cP @ X1 @ X2 @ X4 )
=> ~ ( cP @ X2 @ X3 @ X5 ) )
=> ( ( cP @ X4 @ X3 @ X6 )
= ( cPx @ X5 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ b @ a @ ab ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ a @ a @ e )
=> ~ ( cP @ a @ b @ X1 ) )
=> ( ( cP @ e @ b @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ a @ a @ X1 )
=> ~ ( cP @ a @ a @ X2 ) )
=> ( ( cP @ X1 @ a @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ e @ X1 )
=> ~ ( cP @ e @ a @ X2 ) )
=> ( ( cP @ X1 @ a @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ e @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ ab @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ b @ b @ X1 )
=> ~ ( cP @ b @ b @ X2 ) )
=> ( ( cP @ X1 @ b @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP6
=> ( ( cP @ ab @ e @ e )
= ( cPx @ e @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP2
= ( cPx @ b @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] : ( cP @ e @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ e @ X1 )
=> ~ ( cP @ e @ e @ X2 ) )
=> ( ( cP @ X1 @ e @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cP @ a @ a @ e )
=> ~ ( cP @ a @ b @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cP @ b @ b @ e )
=> ~ ( cP @ b @ e @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ a @ a @ X2 )
=> ~ ( cP @ a @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cPx @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ b @ b @ X1 )
=> ~ ( cP @ b @ e @ X2 ) )
=> ( ( cP @ X1 @ e @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( ( cP @ a @ b @ ab )
=> ~ ( cP @ b @ e @ b ) )
=> ( ( cP @ ab @ e @ X1 )
= ( cPx @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ e @ e @ e )
= ( cPx @ b @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ( cP @ X1 @ X2 @ X4 )
=> ~ ( cP @ X2 @ X3 @ X5 ) )
=> ( ( cP @ X4 @ X3 @ X6 )
= ( cPx @ X5 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ( cP @ ab @ X1 @ X3 )
=> ~ ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
= ( cPx @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ( cP @ ab @ ab @ b )
=> ~ ( cP @ ab @ a @ b ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cPx @ e @ b ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( cP @ e @ a @ e )
= ( cPx @ e @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cP @ e @ ab @ ab ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ ab @ e @ X2 )
=> ~ ( cP @ e @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cPx @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ~ sP13
=> ( ( cP @ e @ b @ X1 )
= ( cPx @ ab @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cP @ a @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cPx @ ab @ b ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cP @ e @ b @ b )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ a @ b @ X2 )
=> ~ ( cP @ b @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cPx @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ ab @ X1 ) )
=> ( ( cP @ ab @ ab @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( cP @ e @ b @ b )
= sP28 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( ( cP @ a @ b @ ab )
=> ~ ( cP @ b @ e @ b ) )
=> ( ( cP @ ab @ e @ e )
= ( cPx @ b @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cP @ ab @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ a @ X1 ) )
=> ( ( cP @ ab @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP34
= ( cPx @ b @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ b @ b @ X2 )
=> ~ ( cP @ b @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cPx @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ a @ b @ X1 )
=> ~ ( cP @ b @ e @ X2 ) )
=> ( ( cP @ X1 @ e @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( cP @ ab @ e @ ab )
= ( cPx @ b @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ( cP @ b @ X1 @ X3 )
=> ~ ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
= ( cPx @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( cP @ e @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ ab @ ab @ X2 )
=> ~ ( cP @ ab @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cPx @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( cP @ a @ b @ ab ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( cPx @ b @ ab ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( sP27
=> ~ sP27 )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( cPx @ b @ e ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ a @ a @ X1 )
=> ~ ( cP @ a @ b @ X2 ) )
=> ( ( cP @ X1 @ b @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ sP7
=> ( ( cP @ ab @ ab @ b )
= sP28 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ e @ X1 )
=> ~ ( cP @ e @ ab @ X2 ) )
=> ( ( cP @ X1 @ ab @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( cP @ ab @ ab @ b )
= sP28 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ a @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( cP @ ab @ e @ ab ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] : ( cP @ X1 @ X1 @ e ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( cP @ ab @ ab @ b ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i] : ( cP @ X1 @ e @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( cP @ b @ b @ e ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i,X2: $i] :
( ~ ( sP43
=> ~ ( cP @ b @ e @ X1 ) )
=> ( ( cP @ ab @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP43
=> ~ ( cP @ b @ e @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP58
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] :
( ~ ( sP56
=> ~ sP56 )
=> ( ( cP @ e @ b @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP34
= ( cPx @ e @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( cP @ b @ e @ b ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP43
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ~ sP6
=> ( ( cP @ ab @ e @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ( cP @ ab @ a @ b )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP51
=> sP65 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ( cP @ a @ X1 @ X3 )
=> ~ ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
= ( cPx @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i] :
( ~ ( sP27
=> ~ ( cP @ a @ a @ X1 ) )
=> ( ( cP @ e @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ sP1
=> sP63 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( cPx @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ ab @ X1 )
=> ~ ( cP @ ab @ a @ X2 ) )
=> ( ( cP @ X1 @ a @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ! [X1: $i,X2: $i] :
( ~ ( sP52
=> ~ ( cP @ e @ e @ X1 ) )
=> ( ( cP @ ab @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: $i,X2: $i] :
( ~ ( sP54
=> ~ ( cP @ ab @ a @ X1 ) )
=> ( ( cP @ b @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP56
=> ~ sP56 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i,X2: $i] :
( ~ ( sP56
=> ~ ( cP @ b @ b @ X1 ) )
=> ( ( cP @ e @ b @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ sP74
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP11
=> ~ sP55 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] :
( ~ sP51
=> ( ( cP @ ab @ a @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( cP @ e @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: $i] :
( ~ ( sP54
=> ~ ( cP @ ab @ a @ b ) )
=> ( ( cP @ b @ a @ X1 )
= ( cPx @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i] :
( ~ ( sP27
=> ~ sP27 )
=> ( ( cP @ e @ a @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ! [X1: $i,X2: $i] :
( ~ ( sP56
=> ~ ( cP @ b @ e @ X1 ) )
=> ( ( cP @ e @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ sP13
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ~ sP7
=> ( ( cP @ ab @ ab @ X1 )
= ( cPx @ ab @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( ~ sP14
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( cP @ ab @ a @ b ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( sP54
=> ~ sP86 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ sP77
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i] :
( ~ sP14
=> ( ( cP @ e @ e @ X1 )
= ( cPx @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( sP27
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( cP @ e @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(cGRP_COMM,conjecture,
sP69 ).
thf(h0,negated_conjecture,
~ sP69,
inference(assume_negation,[status(cth)],[cGRP_COMM]) ).
thf(1,plain,
( ~ sP51
| ~ sP52
| ~ sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP52
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP52
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP87
| ~ sP54
| ~ sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP58
| ~ sP43
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| ~ sP56
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP39
| ~ sP52
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP36
| sP34
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP61
| ~ sP34
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| ~ sP41
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP66
| sP51
| sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP48
| sP7
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP6
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP21
| sP87
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP90
| ~ sP27
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| ~ sP27
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP59
| sP58
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP33
| sP58
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP85
| sP14
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP74
| ~ sP56
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP78
| sP66 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP84
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP64
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP23
| sP79
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP32
| ~ sP91
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP29
| ~ sP91
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP80
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP17
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP17
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP89
| sP85 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP45
| sP90
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP83
| sP13
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP76
| sP74
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP65
| sP86
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP35
| sP78 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP31
| sP84 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP72
| sP64 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP50
| sP54
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP73
| sP80 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP57
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP82
| sP89 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP81
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP26
| sP83 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP60
| sP76 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP5
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP49
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP12
| sP72 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP71
| sP73 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP38
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP16
| sP82 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP68
| sP81 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP3
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP75
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP25
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP25
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP25
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP42
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP10
| sP2
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP53
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP30
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP37
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP4
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP47
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP8
| sP75 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP20
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP20
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP19
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP11
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP55
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP37
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP15
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP15
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP40
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP67
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP67
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP19
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP53
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP11
| sP91 ),
inference(all_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP55
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP19
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP53
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( sP77
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP77
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP88
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( sP88
| ~ sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( sP63
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( sP63
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( sP1
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(89,plain,
( sP1
| ~ sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( sP69
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( sP69
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h0]) ).
thf(0,theorem,
sP69,
inference(contra,[status(thm),contra(discharge,[h0])],[92,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO169^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 17:40:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 31.39/31.67 % SZS status Theorem
% 31.39/31.67 % Mode: mode454
% 31.39/31.67 % Inferences: 22483
% 31.39/31.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------