%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO500^1.006 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 03:25:53 PM UTC 2025
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_f4,type,
f4: $o > $o ).
thf(ty_f0,type,
f0: $o > $o ).
thf(ty_f3,type,
f3: $o > $o ).
thf(ty_f2,type,
f2: $o > $o ).
thf(ty_f1,type,
f1: $o > $o ).
thf(ty_f5,type,
f5: $o > $o ).
thf(ty_x,type,
x: $o ).
thf(sP1,plain,
( sP1
<=> ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( x
= ( f5 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) )
= sP2 )
=> ( sP2
= ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( f4 @ ( f5 @ x ) )
= ( f5 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( f0 @ ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( f2 @ ( f2 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) )
= ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( f5 @ ( f5 @ x ) )
= ( f5 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP2 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( f1 @ ( f2 @ ( f3 @ ( f3 @ sP10 ) ) ) )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP2
= ( f1 @ ( f2 @ ( f3 @ ( f3 @ sP10 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( f5 @ x )
= ( f5 @ ( f5 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP3
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ( f3 @ ( f3 @ sP10 ) )
= ( f2 @ sP6 ) )
=> ( ( f2 @ sP6 )
= ( f3 @ ( f3 @ sP10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( f4 @ ( f4 @ ( f5 @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( f4 @ ( f5 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( f2 @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( f3 @ ( f3 @ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP18
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( f5 @ ( f5 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP9
= ( f2 @ sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> x ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( f5 @ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP11 = sP25 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $o] :
( ( sP9 = X1 )
=> ( X1 = sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( f5 @ sP29 )
= sP30 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP30
= ( f5 @ sP29 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP27 = sP29 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( f5 @ sP29 )
= sP23 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( f4 @ sP21 )
= sP10 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( f2 @ sP25 )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP30 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP25 = sP11 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( f5 @ sP29 )
= sP29 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( f0 @ sP3 )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP21 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( f1 @ ( f2 @ sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( f3 @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP41
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP8
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( f2 @ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP39
=> ( sP21 = sP30 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( f1 @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( f4 @ sP21 )
= sP45 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( f4 @ sP21 )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP25 = sP24 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $o] :
( ( ( f5 @ sP29 )
= X1 )
=> ( X1
= ( f5 @ sP29 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP9 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP6 = sP25 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP10 = sP45 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( f0 @ sP3 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP8 = sP50 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $o] :
( ( sP30 = X1 )
=> ( X1 = sP30 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( f5 @ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $o] :
( ( sP25 = X1 )
=> ( X1 = sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP3 = sP50 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( sP6 = sP24 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( f0 @ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP25 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP44 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP48 = sP44 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP24 = sP25 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP45
= ( f4 @ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ( f0 @ sP3 )
= sP50 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP23 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP10 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP29 = sP27 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( sP24 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( sP21 = sP30 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP50
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( sP45 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ! [X1: $o] :
( ( ( f4 @ sP21 )
= X1 )
=> ( X1
= ( f4 @ sP21 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( f4 @ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( sP50 = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( sP51
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( sP50 = sP8 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( f0 @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(kaminski6,conjecture,
sP1 = sP65 ).
thf(h0,negated_conjecture,
sP1 != sP65,
inference(assume_negation,[status(cth)],[kaminski6]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP65,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP65,
introduced(assumption,[]) ).
thf(1,plain,
( sP18
| ~ sP61
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP18
| sP61
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP26
| ~ sP18
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP54
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP41
| ~ sP61
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP41
| sP61
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP46
| ~ sP41
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP54
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP30
| sP27
| ~ sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP61
| sP27
| ~ sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP27
| sP30
| ~ sP18 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP27
| sP61
| ~ sP41 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( sP35
| ~ sP27
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP74
| sP29
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP30
| sP61
| ~ sP35 ),
inference(mating_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP61
| sP30
| ~ sP74 ),
inference(mating_rule,[status(thm)],[]) ).
thf(17,plain,
( sP34
| ~ sP30
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP7
| sP23
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP33
| sP61
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP36
| ~ sP61
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP15
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP22
| sP23
| ~ sP34 ),
inference(mating_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP21
| sP23
| ~ sP7 ),
inference(mating_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP23
| sP22
| ~ sP33 ),
inference(mating_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP23
| sP21
| ~ sP36 ),
inference(mating_rule,[status(thm)],[]) ).
thf(26,plain,
( sP43
| sP21
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP72
| ~ sP23
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP80
| sP21
| ~ sP43 ),
inference(mating_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP21
| sP80
| ~ sP72 ),
inference(mating_rule,[status(thm)],[]) ).
thf(30,plain,
( sP39
| ~ sP30
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP39
| sP30
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP49
| ~ sP39
| sP76 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP60
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP15
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP80
| sP22
| ~ sP76 ),
inference(mating_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP22
| sP80
| ~ sP39 ),
inference(mating_rule,[status(thm)],[]) ).
thf(37,plain,
( sP52
| ~ sP80
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP73
| sP10
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP12
| ~ sP22
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP12
| sP22
| sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP11
| sP10
| ~ sP52 ),
inference(mating_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP45
| sP10
| ~ sP73 ),
inference(mating_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP10
| sP11
| ~ sP12 ),
inference(mating_rule,[status(thm)],[]) ).
thf(44,plain,
( sP78
| sP45
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP37
| ~ sP80
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP57
| ~ sP10
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP25
| sP45
| ~ sP78 ),
inference(mating_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP11
| sP45
| ~ sP37 ),
inference(mating_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP45
| sP25
| ~ sP57 ),
inference(mating_rule,[status(thm)],[]) ).
thf(50,plain,
( sP51
| ~ sP80
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( sP51
| sP80
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP82
| ~ sP51
| sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP79
| sP82 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP15
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP25
| sP11
| ~ sP70 ),
inference(mating_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP11
| sP25
| ~ sP51 ),
inference(mating_rule,[status(thm)],[]) ).
thf(57,plain,
( sP40
| ~ sP25
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP40
| sP25
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP31
| ~ sP11
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP31
| sP11
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP48
| sP6
| ~ sP40 ),
inference(mating_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP6
| sP48
| ~ sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(63,plain,
( sP75
| sP24
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( sP66
| ~ sP25
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( sP64
| ~ sP6
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( sP56
| sP6
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP9
| sP24
| ~ sP75 ),
inference(mating_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP48
| sP24
| ~ sP66 ),
inference(mating_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP24
| sP9
| ~ sP64 ),
inference(mating_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP24
| sP48
| ~ sP56 ),
inference(mating_rule,[status(thm)],[]) ).
thf(71,plain,
( sP53
| ~ sP25
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( sP53
| sP25
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP20
| ~ sP53
| sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP62
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP15
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP9
| sP48
| ~ sP69 ),
inference(mating_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP48
| sP9
| ~ sP53 ),
inference(mating_rule,[status(thm)],[]) ).
thf(78,plain,
( sP28
| ~ sP9
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( sP28
| sP9
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( sP38
| sP48
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( sP68
| ~ sP48
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP3
| sP44
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP44
| sP3
| ~ sP38 ),
inference(mating_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP44
| sP2
| ~ sP68 ),
inference(mating_rule,[status(thm)],[]) ).
thf(85,plain,
( sP17
| sP2
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( sP67
| ~ sP44
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( sP16
| sP44
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP50
| sP2
| ~ sP17 ),
inference(mating_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP2
| sP50
| ~ sP67 ),
inference(mating_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP2
| sP3
| ~ sP16 ),
inference(mating_rule,[status(thm)],[]) ).
thf(91,plain,
( sP55
| ~ sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( sP55
| sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP5
| ~ sP55
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP32
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP15
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP50
| sP3
| ~ sP14 ),
inference(mating_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP3
| sP50
| ~ sP55 ),
inference(mating_rule,[status(thm)],[]) ).
thf(98,plain,
( sP63
| sP3
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( sP19
| ~ sP3
| ~ sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP84
| sP65
| ~ sP63 ),
inference(mating_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP84
| sP8
| ~ sP19 ),
inference(mating_rule,[status(thm)],[]) ).
thf(102,plain,
( sP47
| sP8
| sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(103,plain,
( sP71
| sP84
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP1
| sP8
| ~ sP47 ),
inference(mating_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP8
| sP65
| ~ sP71 ),
inference(mating_rule,[status(thm)],[]) ).
thf(106,plain,
( sP59
| ~ sP8
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
sP15,
inference(eq_sym,[status(thm)],[]) ).
thf(108,plain,
( ~ sP1
| sP65
| ~ sP59 ),
inference(mating_rule,[status(thm)],[]) ).
thf(109,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,h1,h2]) ).
thf(110,plain,
( sP18
| ~ sP61
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( sP18
| sP61
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP26
| ~ sP18
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP54
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( sP41
| ~ sP61
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(115,plain,
( sP41
| sP61
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP46
| ~ sP41
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP54
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP30
| sP27
| ~ sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP61
| sP27
| ~ sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP27
| sP30
| ~ sP18 ),
inference(mating_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP27
| sP61
| ~ sP41 ),
inference(mating_rule,[status(thm)],[]) ).
thf(122,plain,
( sP35
| ~ sP27
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(123,plain,
( sP74
| sP29
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP30
| sP61
| ~ sP35 ),
inference(mating_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP61
| sP30
| ~ sP74 ),
inference(mating_rule,[status(thm)],[]) ).
thf(126,plain,
( sP34
| ~ sP30
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( sP7
| sP23
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( sP33
| sP61
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(129,plain,
( sP36
| ~ sP61
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP15
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP22
| sP23
| ~ sP34 ),
inference(mating_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP21
| sP23
| ~ sP7 ),
inference(mating_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP23
| sP22
| ~ sP33 ),
inference(mating_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP23
| sP21
| ~ sP36 ),
inference(mating_rule,[status(thm)],[]) ).
thf(135,plain,
( sP43
| sP21
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(136,plain,
( sP72
| ~ sP23
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP80
| sP21
| ~ sP43 ),
inference(mating_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP21
| sP80
| ~ sP72 ),
inference(mating_rule,[status(thm)],[]) ).
thf(139,plain,
( sP39
| ~ sP30
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( sP39
| sP30
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP49
| ~ sP39
| sP76 ),
inference(prop_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP60
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP15
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP80
| sP22
| ~ sP76 ),
inference(mating_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP22
| sP80
| ~ sP39 ),
inference(mating_rule,[status(thm)],[]) ).
thf(146,plain,
( sP52
| ~ sP80
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( sP73
| sP10
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(148,plain,
( sP12
| ~ sP22
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(149,plain,
( sP12
| sP22
| sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP11
| sP10
| ~ sP52 ),
inference(mating_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP45
| sP10
| ~ sP73 ),
inference(mating_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP10
| sP11
| ~ sP12 ),
inference(mating_rule,[status(thm)],[]) ).
thf(153,plain,
( sP78
| sP45
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( sP37
| ~ sP80
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( sP57
| ~ sP10
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP25
| sP45
| ~ sP78 ),
inference(mating_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP11
| sP45
| ~ sP37 ),
inference(mating_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP45
| sP25
| ~ sP57 ),
inference(mating_rule,[status(thm)],[]) ).
thf(159,plain,
( sP51
| ~ sP80
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( sP51
| sP80
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP82
| ~ sP51
| sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP79
| sP82 ),
inference(all_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP15
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP25
| sP11
| ~ sP70 ),
inference(mating_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP11
| sP25
| ~ sP51 ),
inference(mating_rule,[status(thm)],[]) ).
thf(166,plain,
( sP40
| ~ sP25
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(167,plain,
( sP40
| sP25
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(168,plain,
( sP31
| ~ sP11
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( sP31
| sP11
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP48
| sP6
| ~ sP40 ),
inference(mating_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP6
| sP48
| ~ sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(172,plain,
( sP75
| sP24
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( sP66
| ~ sP25
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(174,plain,
( sP64
| ~ sP6
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(175,plain,
( sP56
| sP6
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP9
| sP24
| ~ sP75 ),
inference(mating_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP48
| sP24
| ~ sP66 ),
inference(mating_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP24
| sP9
| ~ sP64 ),
inference(mating_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP24
| sP48
| ~ sP56 ),
inference(mating_rule,[status(thm)],[]) ).
thf(180,plain,
( sP53
| ~ sP25
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(181,plain,
( sP53
| sP25
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP20
| ~ sP53
| sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP62
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP15
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP9
| sP48
| ~ sP69 ),
inference(mating_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP48
| sP9
| ~ sP53 ),
inference(mating_rule,[status(thm)],[]) ).
thf(187,plain,
( sP28
| ~ sP9
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(188,plain,
( sP28
| sP9
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( sP38
| sP48
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( sP68
| ~ sP48
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP3
| sP44
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP44
| sP3
| ~ sP38 ),
inference(mating_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP44
| sP2
| ~ sP68 ),
inference(mating_rule,[status(thm)],[]) ).
thf(194,plain,
( sP17
| sP2
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(195,plain,
( sP67
| ~ sP44
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(196,plain,
( sP16
| sP44
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP50
| sP2
| ~ sP17 ),
inference(mating_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP2
| sP50
| ~ sP67 ),
inference(mating_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP2
| sP3
| ~ sP16 ),
inference(mating_rule,[status(thm)],[]) ).
thf(200,plain,
( sP55
| ~ sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(201,plain,
( sP55
| sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP5
| ~ sP55
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP32
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP15
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP50
| sP3
| ~ sP14 ),
inference(mating_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP3
| sP50
| ~ sP55 ),
inference(mating_rule,[status(thm)],[]) ).
thf(207,plain,
( sP81
| ~ sP50
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(208,plain,
( sP58
| sP84
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP65
| sP84
| ~ sP81 ),
inference(mating_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP8
| sP84
| ~ sP58 ),
inference(mating_rule,[status(thm)],[]) ).
thf(211,plain,
( sP77
| ~ sP50
| ~ sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(212,plain,
( sP42
| ~ sP84
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP65
| sP8
| ~ sP77 ),
inference(mating_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP8
| sP1
| ~ sP42 ),
inference(mating_rule,[status(thm)],[]) ).
thf(215,plain,
( sP83
| sP50
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(216,plain,
sP15,
inference(eq_sym,[status(thm)],[]) ).
thf(217,plain,
( ~ sP65
| sP1
| ~ sP83 ),
inference(mating_rule,[status(thm)],[]) ).
thf(218,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,h3,h4]) ).
thf(219,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,109,218,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1 = sP65,
inference(contra,[status(thm),contra(discharge,[h0])],[219,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYO500^1.006 : TPTP v9.2.0. Released v4.1.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 00:34:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % Mode: mode213
% 0.20/0.45 % Inferences: 700
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------