%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO500^1.005 : 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 : n011.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 0.18s 0.40s
% Output : Proof 0.18s
% 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_x,type,
x: $o ).
thf(sP1,plain,
( sP1
<=> ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) )
= sP2 )
=> ( sP2
= ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f2 @ ( f2 @ sP5 ) )
= ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( f1 @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( f2 @ ( f2 @ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( f3 @ ( f4 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f4 @ x )
= ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP2 = sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP2
= ( f1 @ ( f2 @ ( f3 @ ( f3 @ sP9 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP3
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ( f3 @ ( f3 @ sP9 ) )
= ( f2 @ sP5 ) )
=> ( ( f2 @ sP5 )
= ( f3 @ ( f3 @ sP9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( f4 @ ( f4 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( f4 @ x ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( f2 @ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( f3 @ ( f3 @ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP8
= ( f2 @ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> x ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP10 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $o] :
( ( sP8 = X1 )
=> ( X1 = sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP23 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( sP19 = sP23 )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( f2 @ sP21 )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP23 = sP18 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP21 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( f0 @ sP3 )
= sP7 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP18 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( sP19 = sP18 )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( f1 @ ( f2 @ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( f3 @ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP7
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( f2 @ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( f0 @ ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( f4 @ sP18 )
= sP35 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( f4 @ sP18 )
= sP19 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP34 = sP37 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP21 = sP20 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP8 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP9 = sP35 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( f0 @ sP3 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP7 = sP38 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $o] :
( ( sP21 = X1 )
=> ( X1 = sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP5 = sP20 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( f0 @ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP19 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP19 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP21 = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $o] :
( ( sP19 = X1 )
=> ( X1 = sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP37 = sP34 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP34 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP20 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP35
= ( f4 @ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( f0 @ sP3 )
= sP38 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP19 = sP18 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP9 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP20 = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( sP5 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP18 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( sP38
= ( f0 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP35 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $o] :
( ( ( f4 @ sP18 )
= X1 )
=> ( X1
= ( f4 @ sP18 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( f4 @ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP39
=> sP57 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP38 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP7 = sP3 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( f0 @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(kaminski5,conjecture,
sP1 = sP49 ).
thf(h0,negated_conjecture,
sP1 != sP49,
inference(assume_negation,[status(cth)],[kaminski5]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP49,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP49,
introduced(assumption,[]) ).
thf(1,plain,
( sP59
| ~ sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP59
| sP19
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP33
| ~ sP59
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP53
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP51
| ~ sP19
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP51
| sP19
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP27
| ~ sP51
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP53
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP67
| sP18
| ~ sP32 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP19
| sP18
| ~ sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP18
| sP67
| ~ sP59 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP18
| sP19
| ~ sP51 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( sP63
| ~ sP18
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP29
| sP23
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP67
| sP19
| ~ sP63 ),
inference(mating_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP19
| sP67
| ~ sP29 ),
inference(mating_rule,[status(thm)],[]) ).
thf(17,plain,
( sP40
| ~ sP67
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP60
| sP9
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP11
| sP19
| sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP50
| ~ sP19
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP14
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP10
| sP9
| ~ sP40 ),
inference(mating_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP35
| sP9
| ~ sP60 ),
inference(mating_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP9
| sP10
| ~ sP11 ),
inference(mating_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP9
| sP35
| ~ sP50 ),
inference(mating_rule,[status(thm)],[]) ).
thf(26,plain,
( sP65
| sP35
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP44
| ~ sP9
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP21
| sP35
| ~ sP65 ),
inference(mating_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP35
| sP21
| ~ sP44 ),
inference(mating_rule,[status(thm)],[]) ).
thf(30,plain,
( sP39
| ~ sP67
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP39
| sP67
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP68
| ~ sP39
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP66
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP14
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP21
| sP10
| ~ sP57 ),
inference(mating_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP10
| sP21
| ~ sP39 ),
inference(mating_rule,[status(thm)],[]) ).
thf(37,plain,
( sP30
| ~ sP21
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP62
| sP5
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP24
| ~ sP10
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP24
| sP10
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP37
| sP5
| ~ sP30 ),
inference(mating_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP20
| sP5
| ~ sP62 ),
inference(mating_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP5
| sP37
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(44,plain,
( sP61
| sP20
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP52
| ~ sP21
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP48
| ~ sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP8
| sP20
| ~ sP61 ),
inference(mating_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP37
| sP20
| ~ sP52 ),
inference(mating_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP20
| sP8
| ~ sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(50,plain,
( sP42
| ~ sP21
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( sP42
| sP21
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP17
| ~ sP42
| sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP47
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP14
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP8
| sP37
| ~ sP56 ),
inference(mating_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP37
| sP8
| ~ sP42 ),
inference(mating_rule,[status(thm)],[]) ).
thf(57,plain,
( sP22
| ~ sP8
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP41
| sP34
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP28
| ~ sP37
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP28
| sP37
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP3
| sP34
| ~ sP22 ),
inference(mating_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP2
| sP34
| ~ sP41 ),
inference(mating_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP34
| sP3
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(64,plain,
( sP15
| sP2
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( sP6
| ~ sP8
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( sP55
| ~ sP34
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP7
| sP2
| ~ sP15 ),
inference(mating_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP3
| sP2
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP2
| sP7
| ~ sP55 ),
inference(mating_rule,[status(thm)],[]) ).
thf(70,plain,
( sP43
| ~ sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( sP43
| sP8
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP4
| ~ sP43
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP25
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP7
| sP3
| ~ sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP3
| sP7
| ~ sP43 ),
inference(mating_rule,[status(thm)],[]) ).
thf(77,plain,
( sP70
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( sP45
| sP71
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP1
| sP71
| ~ sP70 ),
inference(mating_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP38
| sP71
| ~ sP45 ),
inference(mating_rule,[status(thm)],[]) ).
thf(81,plain,
( sP36
| ~ sP7
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( sP58
| ~ sP71
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP1
| sP38
| ~ sP36 ),
inference(mating_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP38
| sP49
| ~ sP58 ),
inference(mating_rule,[status(thm)],[]) ).
thf(85,plain,
( sP46
| sP7
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
sP14,
inference(eq_sym,[status(thm)],[]) ).
thf(87,plain,
( ~ sP1
| sP49
| ~ sP46 ),
inference(mating_rule,[status(thm)],[]) ).
thf(88,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,h1,h2]) ).
thf(89,plain,
( sP59
| ~ sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(90,plain,
( sP59
| sP19
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP33
| ~ sP59
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP53
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(93,plain,
( sP51
| ~ sP19
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( sP51
| sP19
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP27
| ~ sP51
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP53
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP67
| sP18
| ~ sP32 ),
inference(mating_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP19
| sP18
| ~ sP26 ),
inference(mating_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP18
| sP67
| ~ sP59 ),
inference(mating_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP18
| sP19
| ~ sP51 ),
inference(mating_rule,[status(thm)],[]) ).
thf(101,plain,
( sP63
| ~ sP18
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(102,plain,
( sP29
| sP23
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP67
| sP19
| ~ sP63 ),
inference(mating_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP19
| sP67
| ~ sP29 ),
inference(mating_rule,[status(thm)],[]) ).
thf(105,plain,
( sP40
| ~ sP67
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( sP60
| sP9
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
( sP11
| sP19
| sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( sP50
| ~ sP19
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP14
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP10
| sP9
| ~ sP40 ),
inference(mating_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP35
| sP9
| ~ sP60 ),
inference(mating_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP9
| sP10
| ~ sP11 ),
inference(mating_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP9
| sP35
| ~ sP50 ),
inference(mating_rule,[status(thm)],[]) ).
thf(114,plain,
( sP65
| sP35
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(115,plain,
( sP44
| ~ sP9
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP21
| sP35
| ~ sP65 ),
inference(mating_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP35
| sP21
| ~ sP44 ),
inference(mating_rule,[status(thm)],[]) ).
thf(118,plain,
( sP39
| ~ sP67
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( sP39
| sP67
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP68
| ~ sP39
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP66
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP14
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP21
| sP10
| ~ sP57 ),
inference(mating_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP10
| sP21
| ~ sP39 ),
inference(mating_rule,[status(thm)],[]) ).
thf(125,plain,
( sP30
| ~ sP21
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( sP62
| sP5
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( sP24
| ~ sP10
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( sP24
| sP10
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP37
| sP5
| ~ sP30 ),
inference(mating_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP20
| sP5
| ~ sP62 ),
inference(mating_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP5
| sP37
| ~ sP24 ),
inference(mating_rule,[status(thm)],[]) ).
thf(132,plain,
( sP61
| sP20
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(133,plain,
( sP52
| ~ sP21
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(134,plain,
( sP48
| ~ sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP8
| sP20
| ~ sP61 ),
inference(mating_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP37
| sP20
| ~ sP52 ),
inference(mating_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP20
| sP8
| ~ sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(138,plain,
( sP42
| ~ sP21
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(139,plain,
( sP42
| sP21
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP17
| ~ sP42
| sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP47
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP14
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP8
| sP37
| ~ sP56 ),
inference(mating_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP37
| sP8
| ~ sP42 ),
inference(mating_rule,[status(thm)],[]) ).
thf(145,plain,
( sP22
| ~ sP8
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(146,plain,
( sP41
| sP34
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( sP28
| sP37
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(148,plain,
( sP54
| ~ sP37
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP3
| sP34
| ~ sP22 ),
inference(mating_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP2
| sP34
| ~ sP41 ),
inference(mating_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP34
| sP3
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP34
| sP2
| ~ sP54 ),
inference(mating_rule,[status(thm)],[]) ).
thf(153,plain,
( sP15
| sP2
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( sP55
| ~ sP34
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP7
| sP2
| ~ sP15 ),
inference(mating_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP2
| sP7
| ~ sP55 ),
inference(mating_rule,[status(thm)],[]) ).
thf(157,plain,
( sP43
| ~ sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( sP43
| sP8
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP4
| ~ sP43
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP25
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP7
| sP3
| ~ sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP3
| sP7
| ~ sP43 ),
inference(mating_rule,[status(thm)],[]) ).
thf(164,plain,
( sP12
| sP3
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( sP16
| ~ sP3
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP71
| sP1
| ~ sP12 ),
inference(mating_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP71
| sP38
| ~ sP16 ),
inference(mating_rule,[status(thm)],[]) ).
thf(168,plain,
( sP64
| sP38
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( sP31
| sP71
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP49
| sP38
| ~ sP64 ),
inference(mating_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP38
| sP1
| ~ sP31 ),
inference(mating_rule,[status(thm)],[]) ).
thf(172,plain,
( sP69
| ~ sP38
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
sP14,
inference(eq_sym,[status(thm)],[]) ).
thf(174,plain,
( ~ sP49
| sP1
| ~ sP69 ),
inference(mating_rule,[status(thm)],[]) ).
thf(175,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,h3,h4]) ).
thf(176,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,88,175,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1 = sP49,
inference(contra,[status(thm),contra(discharge,[h0])],[176,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO500^1.005 : TPTP v9.2.0. Released v4.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.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 : 300
% 0.12/0.33 % DateTime : Thu Oct 9 00:48:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % Mode: mode213
% 0.18/0.40 % Inferences: 556
% 0.18/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------