TSTP Solution File: SYO169^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO169^5 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 04:45:42 EDT 2023
% Result : Theorem 0.55s 0.81s
% Output : Proof 0.55s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_cPx,type,
cPx: $i > $i > $o ).
thf(ty_e,type,
e: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_ab,type,
ab: $i ).
thf(ty_cP,type,
cP: $i > $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ a @ b @ ab ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ e @ e ) )
=> ( ( cP @ ab @ e @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ b @ b @ e )
=> ~ ( cP @ b @ e @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ a @ a @ e )
=> ~ ( cP @ a @ a @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ e @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ( cP @ ab @ ab @ b )
=> ~ ( cP @ ab @ a @ e ) )
=> ( ( cP @ b @ a @ ab )
= ( cPx @ e @ ab ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP @ ab @ ab @ b )
=> ~ ( cP @ ab @ a @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP5
=> ( sP7
= ( cPx @ b @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ a @ a @ e )
=> ~ ( cP @ a @ b @ X1 ) )
=> ( ( cP @ e @ b @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cP @ b @ b @ e ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ ab @ ab ) )
=> ( ( cP @ ab @ ab @ b )
= ( cPx @ ab @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [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,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cP @ ab @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( cP @ ab @ ab @ e )
=> ~ ( cP @ ab @ ab @ e ) )
=> ( ( cP @ e @ ab @ ab )
= ( cPx @ e @ ab ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ e @ ab @ ab )
= ( cPx @ e @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] : ( cP @ X1 @ e @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ~ ( sP13
=> ~ ( cP @ b @ e @ X1 ) )
=> ( ( cP @ e @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [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,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ( cP @ ab @ e @ ab )
=> ~ sP7 )
=> ( ( cP @ ab @ e @ e )
= ( cPx @ e @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [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,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ ab @ X1 ) )
=> ( ( cP @ ab @ ab @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ~ ( ( cP @ a @ a @ e )
=> ~ sP2 )
=> ( ( cP @ e @ b @ X1 )
= ( cPx @ ab @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ~ sP5
=> ( ( cP @ e @ e @ X1 )
= ( cPx @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( cP @ ab @ e @ e )
= ( cPx @ b @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( cP @ b @ a @ ab )
= ( cPx @ e @ ab ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cP @ ab @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [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,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ( cP @ a @ a @ e )
=> ~ sP2 )
=> ( ( cP @ e @ b @ b )
= ( cPx @ ab @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ a @ e ) )
=> ( sP16
= ( cPx @ e @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( cP @ e @ a @ e )
= ( cPx @ e @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP7
= ( cPx @ b @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] : ( cP @ e @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( cPx @ ab @ b ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [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,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( cP @ ab @ ab @ b ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cP @ e @ ab @ ab ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i] :
( ~ ( sP38
=> ~ ( cP @ ab @ a @ X1 ) )
=> ( ( cP @ b @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [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,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( cPx @ e @ ab ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( cP @ a @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ ab @ e )
=> ~ ( cP @ ab @ ab @ X1 ) )
=> ( ( cP @ e @ ab @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( cP @ e @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( cP @ ab @ ab @ e ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP38 = sP36 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ~ ( sP46
=> ~ sP46 )
=> ( ( cP @ e @ ab @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP6
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [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,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [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,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ sP39 )
=> ( ( cP @ ab @ ab @ X1 )
= ( cPx @ ab @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( cPx @ e @ e ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( cP @ b @ e @ b ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [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,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [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,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( cP @ ab @ e @ ab )
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP2
=> ~ sP54 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [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,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ( cP @ ab @ e @ ab )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i,X2: $i] :
( ~ ( sP2
=> ~ ( cP @ b @ e @ X1 ) )
=> ( ( cP @ ab @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [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,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( cP @ e @ b @ b )
= sP36 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ~ sP10
=> ( ( cP @ b @ a @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ e @ ab )
=> ~ ( cP @ e @ a @ X1 ) )
=> ( ( cP @ ab @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( cP @ b @ a @ ab ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i] :
( ~ sP58
=> ( ( cP @ ab @ e @ X1 )
= ( cPx @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i] :
( ~ ( sP43
=> ~ ( cP @ a @ a @ X1 ) )
=> ( ( cP @ e @ a @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [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,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [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,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
( ~ sP6
=> ( ( cP @ e @ a @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP29 = sP53 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( cP @ e @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( cPx @ b @ e ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( cP @ ab @ e @ ab ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ ab @ X1 )
=> ~ ( cP @ ab @ ab @ X2 ) )
=> ( ( cP @ X1 @ ab @ X3 )
= ( cPx @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP46
=> ~ sP46 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] : ( cP @ X1 @ X1 @ e ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ! [X1: $i] :
( ~ sP57
=> ( ( cP @ ab @ a @ X1 )
= ( cPx @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP75
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( sP43
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( sP16 = sP53 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $i,X2: $i] :
( ~ ( sP75
=> ~ ( cP @ e @ e @ X1 ) )
=> ( ( cP @ ab @ e @ X2 )
= ( cPx @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ~ sP58
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(cGRP_COMM,conjecture,
( ~ ( ~ ( ~ ( sP35
=> ~ sP19 )
=> ~ sP78 )
=> ~ sP62 )
=> ( sP2
=> sP66 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP35
=> ~ sP19 )
=> ~ sP78 )
=> ~ sP62 )
=> ( sP2
=> sP66 ) ),
inference(assume_negation,[status(cth)],[cGRP_COMM]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP35
=> ~ sP19 )
=> ~ sP78 )
=> ~ sP62 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP2
=> sP66 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP35
=> ~ sP19 )
=> ~ sP78 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP62,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP35
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP78,
introduced(assumption,[]) ).
thf(h7,assumption,
sP35,
introduced(assumption,[]) ).
thf(h8,assumption,
sP19,
introduced(assumption,[]) ).
thf(h9,assumption,
sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP66,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP57
| ~ sP75
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP32
| sP57
| sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP80
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP80
| ~ sP75
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP60
| ~ sP75
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP22
| sP60
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| ~ sP13
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP5
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP58
| ~ sP2
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP84
| sP58
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP79
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP52
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP27
| sP29
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP72
| ~ sP29
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP34
| ~ sP7
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP26
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP67
| sP84 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| ~ sP43
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP49
| sP6
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP31
| sP81
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP81
| ~ sP43
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP65
| sP79 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP24
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP83
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP17
| sP77
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP77
| ~ sP46
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP18
| ~ sP39
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP33
| sP45
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP63
| ~ sP73
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP20
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP61
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP71
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP25
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP37
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP51
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP59
| sP83 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP48
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP8
| sP10
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP10
| ~ sP38
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP82
| sP16
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP28
| sP66
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP70
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP23
| sP61 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP68
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP12
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP1
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP1
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP1
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP44
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP64
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP35
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP56
| sP70 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP69
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP50
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP15
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP41
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP76
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP40
| sP64 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP47
| sP38
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP55
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP30
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP30
| sP76 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP41
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP78
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP19
| sP75 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP35
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP62
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP21
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP3
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP3
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP78
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP62
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP9
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP78
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP19
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP35
| sP73 ),
inference(all_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP62
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(80,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h7,h8,h6,h4,h9,h10]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,80,h9,h10]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,81,h7,h8]) ).
thf(83,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,82,h5,h6]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,83,h3,h4]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,84,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP35
=> ~ sP19 )
=> ~ sP78 )
=> ~ sP62 )
=> ( sP2
=> sP66 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[85,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO169^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n001.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 : 300
% 0.13/0.33 % DateTime : Sat Aug 26 00:45:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.55/0.81 % SZS status Theorem
% 0.55/0.81 % Mode: cade22grackle2xfee4
% 0.55/0.81 % Steps: 4667
% 0.55/0.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------