%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1.007 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Wed Feb 25 09:54:23 AM UTC 2026
% Result : Theorem 1.62s 1.34s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 156
% Syntax : Number of formulae : 436 ( 35 unt; 0 typ; 112 def)
% Number of atoms : 2812 ( 680 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1106 ( 90 ~; 574 |; 0 &; 357 @)
% ( 85 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 123 ( 120 usr; 115 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
f0: $o > $o ).
thf(func_def_2,type,
f1: $o > $o ).
thf(func_def_3,type,
f2: $o > $o ).
thf(func_def_4,type,
f3: $o > $o ).
thf(func_def_5,type,
f4: $o > $o ).
thf(func_def_6,type,
f5: $o > $o ).
thf(func_def_7,type,
f6: $o > $o ).
thf(f691,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f210,f219,f228,f233,f242,f247,f252,f253,f262,f271,f276,f281,f286,f295,f300,f305,f306,f319,f328,f337,f342,f343,f344,f345,f346,f359,f368,f377,f382,f387,f388,f393,f394,f399,f404,f417,f426,f435,f440,f453,f462,f471,f476,f477,f478,f479,f480,f489,f494,f499,f500,f501,f502,f503,f504,f513,f518,f523,f524,f533,f538,f543,f544,f545,f546,f547,f548,f549,f550,f551,f552,f561,f570,f575,f580,f589,f594,f599,f600,f601,f602,f603,f604,f609,f610,f615,f616,f621,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f640,f641,f642,f643,f644,f645,f646,f647,f648,f649,f650,f651,f652,f653,f654,f655,f656,f657,f658,f659,f660,f661,f662,f663,f664,f665,f666,f667,f668,f669,f670,f671,f672,f673,f674,f675,f676,f677,f678,f679,f680,f681,f682,f683,f684,f685,f686,f687,f688,f689,f690]) ).
thf(f690,plain,
( ( x != $true )
| ( x != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f689,plain,
( ( $true
!= ( f6 @ $false ) )
| ( ( f6 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f688,plain,
( ( sF13 != $false )
| ( sF13 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f687,plain,
( ( ( f6 @ $true )
!= $false )
| ( ( f6 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f686,plain,
( ( $true != sF14 )
| ( sF14 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f685,plain,
( ( $true != sF15 )
| ( sF15 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f684,plain,
( ( sF17 != $false )
| ( sF17 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f683,plain,
( ( ( f4 @ $false )
!= $false )
| ( ( f4 @ $false )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f682,plain,
( ( sF19 != $false )
| ( sF19 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f681,plain,
( ( sF20 != $false )
| ( $true != sF20 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f680,plain,
( ( sF21 != $false )
| ( sF21 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f679,plain,
( ( sF26 != $false )
| ( $true != sF26 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f678,plain,
( ( sF24 != $false )
| ( sF24 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f677,plain,
( ( sF22 != $false )
| ( sF22 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f676,plain,
( ( sF10 != $false )
| ( $true != sF10 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f675,plain,
( ( sF9 != $false )
| ( $true != sF9 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f674,plain,
( ( sF8 != $false )
| ( $true != sF8 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f673,plain,
( ( sF7 != $false )
| ( $true != sF7 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f672,plain,
( ( $false != sF6 )
| ( $true != sF6 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f671,plain,
( ( sF5 != $false )
| ( $true != sF5 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f670,plain,
( ( ( f4 @ $true )
!= $false )
| ( ( f4 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f669,plain,
( ( sF16 != $false )
| ( sF16 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f668,plain,
( ( sF18 != $false )
| ( sF18 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f667,plain,
( ( sF25 != $false )
| ( $true != sF25 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f666,plain,
( ( ( f2 @ $false )
!= $false )
| ( $true
!= ( f2 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f665,plain,
( ( ( f2 @ $true )
!= $false )
| ( ( f2 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f664,plain,
( ( ( f1 @ $false )
!= $false )
| ( ( f1 @ $false )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f663,plain,
( ( ( f1 @ $true )
!= $false )
| ( ( f1 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f662,plain,
( ( sF23 != $false )
| ( sF23 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f661,plain,
( ( ( f3 @ $false )
!= $false )
| ( ( f3 @ $false )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f660,plain,
( ( $false != sF4 )
| ( $true != sF4 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f659,plain,
( ( ( f3 @ $true )
!= $false )
| ( $true
!= ( f3 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f658,plain,
( ( sF11 != $false )
| ( $true != sF11 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f657,plain,
( ( ( f0 @ $false )
!= $false )
| ( $true
!= ( f0 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f656,plain,
( ( sF12 != $false )
| ( sF12 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f655,plain,
( ( ( f0 @ $true )
!= $false )
| ( ( f0 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f654,plain,
( ( sF2 != $false )
| ( $true != sF2 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f653,plain,
( ( sF3 != $false )
| ( sF3 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f652,plain,
( ( $false != sF0 )
| ( $true != sF0 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f651,plain,
( ( sF1 != $false )
| ( sF1 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f650,plain,
( ( ( f5 @ $false )
!= $false )
| ( $true
!= ( f5 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f649,plain,
( ( ( f5 @ $true )
!= $false )
| ( ( f5 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f648,plain,
( spl27_84
| spl27_65
| spl27_76 ),
inference(avatar_split_clause,[status(thm)],[f37,f572,f510,f618]) ).
thf(f618,definition,
( spl27_84
<=> ( sF17 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_84])],[avatar_definition]) ).
thf(f510,definition,
( spl27_65
<=> ( sF18 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_65])],[avatar_definition]) ).
thf(f572,definition,
( spl27_76
<=> ( ( f4 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_76])],[avatar_definition]) ).
thf(f37,plain,
( ( sF17 = $true )
| ( sF18 = $false )
| ( ( f4 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( sF17 = $true )
| ( sF18
= ( f4 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f24,definition,
( sF18
= ( f4 @ sF17 ) ),
introduced(definition,[],[function_definition]) ).
thf(f647,plain,
( spl27_67
| spl27_84
| spl27_77 ),
inference(avatar_split_clause,[status(thm)],[f36,f577,f618,f520]) ).
thf(f520,definition,
( spl27_67
<=> ( sF18 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_67])],[avatar_definition]) ).
thf(f577,definition,
( spl27_77
<=> ( ( f4 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_77])],[avatar_definition]) ).
thf(f36,plain,
( ( sF18 = $true )
| ( ( f4 @ $false )
= $false )
| ( sF17 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f646,plain,
( spl27_75
| spl27_65
| spl27_85 ),
inference(avatar_split_clause,[status(thm)],[f39,f623,f510,f567]) ).
thf(f567,definition,
( spl27_75
<=> ( ( f4 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_75])],[avatar_definition]) ).
thf(f623,definition,
( spl27_85
<=> ( sF17 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_85])],[avatar_definition]) ).
thf(f39,plain,
( ( ( f4 @ $true )
= $true )
| ( sF18 = $false )
| ( sF17 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( sF17 = $false )
| ( sF18
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f645,plain,
( spl27_67
| spl27_73
| spl27_85 ),
inference(avatar_split_clause,[status(thm)],[f38,f623,f558,f520]) ).
thf(f558,definition,
( spl27_73
<=> ( ( f4 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_73])],[avatar_definition]) ).
thf(f38,plain,
( ( ( f4 @ $true )
= $false )
| ( sF18 = $true )
| ( sF17 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f644,plain,
( spl27_22
| spl27_77
| spl27_37 ),
inference(avatar_split_clause,[status(thm)],[f43,f370,f577,f297]) ).
thf(f297,definition,
( spl27_22
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_22])],[avatar_definition]) ).
thf(f370,definition,
( spl27_37
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl27_37])],[avatar_definition]) ).
thf(f43,plain,
( ( sF3 = $true )
| ( ( f4 @ $false )
= $false )
| ( $true = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( sF3 = $true )
| ( ( f4 @ $false )
= sF4 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f10,definition,
( ( f4 @ sF3 )
= sF4 ),
introduced(definition,[],[function_definition]) ).
thf(f643,plain,
( spl27_22
| spl27_76
| spl27_32 ),
inference(avatar_split_clause,[status(thm)],[f42,f348,f572,f297]) ).
thf(f348,definition,
( spl27_32
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl27_32])],[avatar_definition]) ).
thf(f42,plain,
( ( ( f4 @ $false )
= $true )
| ( sF3 = $true )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f642,plain,
( spl27_73
| spl27_20
| spl27_37 ),
inference(avatar_split_clause,[status(thm)],[f45,f370,f288,f558]) ).
thf(f288,definition,
( spl27_20
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_20])],[avatar_definition]) ).
thf(f45,plain,
( ( ( f4 @ $true )
= $false )
| ( $true = sF4 )
| ( sF3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( f4 @ $true )
= sF4 )
| ( sF3 = $false ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f641,plain,
( spl27_20
| spl27_32
| spl27_75 ),
inference(avatar_split_clause,[status(thm)],[f44,f567,f348,f288]) ).
thf(f44,plain,
( ( ( f4 @ $true )
= $true )
| ( $false = sF4 )
| ( sF3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f640,plain,
( spl27_39
| spl27_33
| spl27_81 ),
inference(avatar_split_clause,[status(thm)],[f49,f596,f352,f379]) ).
thf(f379,definition,
( spl27_39
<=> ( ( f3 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_39])],[avatar_definition]) ).
thf(f352,definition,
( spl27_33
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl27_33])],[avatar_definition]) ).
thf(f596,definition,
( spl27_81
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl27_81])],[avatar_definition]) ).
thf(f49,plain,
( ( ( f3 @ $false )
= $false )
| ( $true = sF6 )
| ( $true = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true = sF5 )
| ( ( f3 @ $false )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f12,definition,
( ( f3 @ sF5 )
= sF6 ),
introduced(definition,[],[function_definition]) ).
thf(f639,plain,
( spl27_38
| spl27_78
| spl27_33 ),
inference(avatar_split_clause,[status(thm)],[f48,f352,f582,f374]) ).
thf(f374,definition,
( spl27_38
<=> ( ( f3 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_38])],[avatar_definition]) ).
thf(f582,definition,
( spl27_78
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl27_78])],[avatar_definition]) ).
thf(f48,plain,
( ( $false = sF6 )
| ( $true = sF5 )
| ( ( f3 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f638,plain,
( spl27_35
| spl27_81
| spl27_34 ),
inference(avatar_split_clause,[status(thm)],[f51,f356,f596,f361]) ).
thf(f361,definition,
( spl27_35
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_35])],[avatar_definition]) ).
thf(f356,definition,
( spl27_34
<=> ( ( f3 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_34])],[avatar_definition]) ).
thf(f51,plain,
( ( ( f3 @ $true )
= $false )
| ( $true = sF6 )
| ( sF5 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( sF5 = $false )
| ( ( f3 @ $true )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f637,plain,
( spl27_78
| spl27_35
| spl27_36 ),
inference(avatar_split_clause,[status(thm)],[f50,f365,f361,f582]) ).
thf(f365,definition,
( spl27_36
<=> ( $true
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl27_36])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( f3 @ $true ) )
| ( $false = sF6 )
| ( sF5 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f636,plain,
( spl27_47
| spl27_31
| spl27_61 ),
inference(avatar_split_clause,[status(thm)],[f55,f486,f339,f419]) ).
thf(f419,definition,
( spl27_47
<=> ( sF23 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_47])],[avatar_definition]) ).
thf(f339,definition,
( spl27_31
<=> ( $true
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl27_31])],[avatar_definition]) ).
thf(f486,definition,
( spl27_61
<=> ( sF24 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_61])],[avatar_definition]) ).
thf(f55,plain,
( ( sF23 = $true )
| ( $true
= ( f0 @ $false ) )
| ( sF24 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( sF24
= ( f0 @ $false ) )
| ( sF23 = $true ) ),
inference(cases_simplifying,[status(thm)],[f30]) ).
thf(f30,definition,
( ( f0 @ sF23 )
= sF24 ),
introduced(definition,[],[function_definition]) ).
thf(f635,plain,
( spl27_47
| spl27_30
| spl27_63 ),
inference(avatar_split_clause,[status(thm)],[f54,f496,f334,f419]) ).
thf(f334,definition,
( spl27_30
<=> ( ( f0 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_30])],[avatar_definition]) ).
thf(f496,definition,
( spl27_63
<=> ( sF24 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_63])],[avatar_definition]) ).
thf(f54,plain,
( ( sF23 = $true )
| ( sF24 = $true )
| ( ( f0 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f634,plain,
( spl27_63
| spl27_45
| spl27_24 ),
inference(avatar_split_clause,[status(thm)],[f57,f308,f410,f496]) ).
thf(f410,definition,
( spl27_45
<=> ( sF23 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_45])],[avatar_definition]) ).
thf(f308,definition,
( spl27_24
<=> ( ( f0 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_24])],[avatar_definition]) ).
thf(f57,plain,
( ( sF23 = $false )
| ( ( f0 @ $true )
= $false )
| ( sF24 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( f0 @ $true )
= sF24 )
| ( sF23 = $false ) ),
inference(cases_simplifying,[status(thm)],[f30]) ).
thf(f633,plain,
( spl27_27
| spl27_61
| spl27_45 ),
inference(avatar_split_clause,[status(thm)],[f56,f410,f486,f321]) ).
thf(f321,definition,
( spl27_27
<=> ( ( f0 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_27])],[avatar_definition]) ).
thf(f56,plain,
( ( ( f0 @ $true )
= $true )
| ( sF24 = $false )
| ( sF23 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f632,plain,
( spl27_70
| spl27_83
| spl27_51 ),
inference(avatar_split_clause,[status(thm)],[f61,f437,f612,f535]) ).
thf(f535,definition,
( spl27_70
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl27_70])],[avatar_definition]) ).
thf(f612,definition,
( spl27_83
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl27_83])],[avatar_definition]) ).
thf(f437,definition,
( spl27_51
<=> ( ( f1 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_51])],[avatar_definition]) ).
thf(f61,plain,
( ( $true = sF9 )
| ( ( f1 @ $false )
= $false )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( f1 @ $false )
= sF10 )
| ( $true = sF9 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f16,definition,
( ( f1 @ sF9 )
= sF10 ),
introduced(definition,[],[function_definition]) ).
thf(f631,plain,
( spl27_82
| spl27_49
| spl27_70 ),
inference(avatar_split_clause,[status(thm)],[f60,f535,f428,f606]) ).
thf(f606,definition,
( spl27_82
<=> ( sF10 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_82])],[avatar_definition]) ).
thf(f428,definition,
( spl27_49
<=> ( ( f1 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_49])],[avatar_definition]) ).
thf(f60,plain,
( ( $true = sF9 )
| ( sF10 = $false )
| ( ( f1 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f630,plain,
( spl27_83
| spl27_69
| spl27_48 ),
inference(avatar_split_clause,[status(thm)],[f63,f423,f530,f612]) ).
thf(f530,definition,
( spl27_69
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_69])],[avatar_definition]) ).
thf(f423,definition,
( spl27_48
<=> ( ( f1 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_48])],[avatar_definition]) ).
thf(f63,plain,
( ( sF9 = $false )
| ( ( f1 @ $true )
= $false )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( f1 @ $true )
= sF10 )
| ( sF9 = $false ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f629,plain,
( spl27_82
| spl27_69
| spl27_44 ),
inference(avatar_split_clause,[status(thm)],[f62,f406,f530,f606]) ).
thf(f406,definition,
( spl27_44
<=> ( ( f1 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_44])],[avatar_definition]) ).
thf(f62,plain,
( ( sF10 = $false )
| ( sF9 = $false )
| ( ( f1 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f628,plain,
( spl27_84
| spl27_77
| spl27_72 ),
inference(avatar_split_clause,[status(thm)],[f67,f554,f577,f618]) ).
thf(f554,definition,
( spl27_72
<=> ( sF16 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_72])],[avatar_definition]) ).
thf(f67,plain,
( ( ( f4 @ $false )
= $false )
| ( sF17 = $true )
| ( sF16 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( f4 @ $false )
= sF17 )
| ( sF16 = $true ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f23,definition,
( sF17
= ( f4 @ sF16 ) ),
introduced(definition,[],[function_definition]) ).
thf(f627,plain,
( spl27_72
| spl27_76
| spl27_85 ),
inference(avatar_split_clause,[status(thm)],[f66,f623,f572,f554]) ).
thf(f66,plain,
( ( ( f4 @ $false )
= $true )
| ( sF16 = $true )
| ( sF17 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f626,plain,
( spl27_85
| spl27_74
| spl27_75 ),
inference(avatar_split_clause,[status(thm)],[f69,f567,f563,f623]) ).
thf(f563,definition,
( spl27_74
<=> ( sF16 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_74])],[avatar_definition]) ).
thf(f69,plain,
( ( ( f4 @ $true )
= $true )
| ( sF17 = $false )
| ( sF16 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( sF16 = $false )
| ( sF17
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f621,plain,
( spl27_84
| spl27_73
| spl27_74 ),
inference(avatar_split_clause,[status(thm)],[f68,f563,f558,f618]) ).
thf(f68,plain,
( ( ( f4 @ $true )
= $false )
| ( sF17 = $true )
| ( sF16 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f616,plain,
( spl27_29
| spl27_83
| spl27_51 ),
inference(avatar_split_clause,[status(thm)],[f73,f437,f612,f330]) ).
thf(f330,definition,
( spl27_29
<=> ( $true = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl27_29])],[avatar_definition]) ).
thf(f73,plain,
( ( ( f1 @ $false )
= $false )
| ( $true = sF10 )
| ( $true = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true = sF10 )
| ( ( f1 @ $false )
= sF11 ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f17,definition,
( ( f1 @ sF10 )
= sF11 ),
introduced(definition,[],[function_definition]) ).
thf(f615,plain,
( spl27_49
| spl27_25
| spl27_83 ),
inference(avatar_split_clause,[status(thm)],[f72,f612,f312,f428]) ).
thf(f312,definition,
( spl27_25
<=> ( sF11 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_25])],[avatar_definition]) ).
thf(f72,plain,
( ( $true = sF10 )
| ( sF11 = $false )
| ( ( f1 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f610,plain,
( spl27_48
| spl27_29
| spl27_82 ),
inference(avatar_split_clause,[status(thm)],[f75,f606,f330,f423]) ).
thf(f75,plain,
( ( $true = sF11 )
| ( sF10 = $false )
| ( ( f1 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( sF10 = $false )
| ( ( f1 @ $true )
= sF11 ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f609,plain,
( spl27_82
| spl27_44
| spl27_25 ),
inference(avatar_split_clause,[status(thm)],[f74,f312,f406,f606]) ).
thf(f74,plain,
( ( sF10 = $false )
| ( sF11 = $false )
| ( ( f1 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f604,plain,
( spl27_71
| spl27_79
| spl27_58 ),
inference(avatar_split_clause,[status(thm)],[f79,f468,f586,f540]) ).
thf(f540,definition,
( spl27_71
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl27_71])],[avatar_definition]) ).
thf(f586,definition,
( spl27_79
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl27_79])],[avatar_definition]) ).
thf(f468,definition,
( spl27_58
<=> ( ( f2 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_58])],[avatar_definition]) ).
thf(f79,plain,
( ( $true = sF8 )
| ( $true = sF7 )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true = sF7 )
| ( ( f2 @ $false )
= sF8 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f14,definition,
( ( f2 @ sF7 )
= sF8 ),
introduced(definition,[],[function_definition]) ).
thf(f603,plain,
( spl27_59
| spl27_68
| spl27_79 ),
inference(avatar_split_clause,[status(thm)],[f78,f586,f526,f473]) ).
thf(f473,definition,
( spl27_59
<=> ( $true
= ( f2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl27_59])],[avatar_definition]) ).
thf(f526,definition,
( spl27_68
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_68])],[avatar_definition]) ).
thf(f78,plain,
( ( $true = sF7 )
| ( sF8 = $false )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f602,plain,
( spl27_80
| spl27_56
| spl27_71 ),
inference(avatar_split_clause,[status(thm)],[f81,f540,f459,f591]) ).
thf(f591,definition,
( spl27_80
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_80])],[avatar_definition]) ).
thf(f459,definition,
( spl27_56
<=> ( ( f2 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_56])],[avatar_definition]) ).
thf(f81,plain,
( ( ( f2 @ $true )
= $false )
| ( $true = sF8 )
| ( sF7 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( sF7 = $false )
| ( ( f2 @ $true )
= sF8 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f601,plain,
( spl27_68
| spl27_80
| spl27_52 ),
inference(avatar_split_clause,[status(thm)],[f80,f442,f591,f526]) ).
thf(f442,definition,
( spl27_52
<=> ( ( f2 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_52])],[avatar_definition]) ).
thf(f80,plain,
( ( ( f2 @ $true )
= $true )
| ( sF8 = $false )
| ( sF7 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f600,plain,
( spl27_79
| spl27_81
| spl27_39 ),
inference(avatar_split_clause,[status(thm)],[f85,f379,f596,f586]) ).
thf(f85,plain,
( ( $true = sF6 )
| ( $true = sF7 )
| ( ( f3 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( f3 @ $false )
= sF7 )
| ( $true = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f13,definition,
( ( f3 @ sF6 )
= sF7 ),
introduced(definition,[],[function_definition]) ).
thf(f599,plain,
( spl27_38
| spl27_81
| spl27_80 ),
inference(avatar_split_clause,[status(thm)],[f84,f591,f596,f374]) ).
thf(f84,plain,
( ( $true = sF6 )
| ( sF7 = $false )
| ( ( f3 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f594,plain,
( spl27_36
| spl27_80
| spl27_78 ),
inference(avatar_split_clause,[status(thm)],[f87,f582,f591,f365]) ).
thf(f87,plain,
( ( $true
= ( f3 @ $true ) )
| ( sF7 = $false )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( sF7
= ( f3 @ $true ) )
| ( $false = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f589,plain,
( spl27_78
| spl27_79
| spl27_34 ),
inference(avatar_split_clause,[status(thm)],[f86,f356,f586,f582]) ).
thf(f86,plain,
( ( $true = sF7 )
| ( $false = sF6 )
| ( ( f3 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f580,plain,
( spl27_5
| spl27_77
| spl27_72 ),
inference(avatar_split_clause,[status(thm)],[f91,f554,f577,f216]) ).
thf(f216,definition,
( spl27_5
<=> ( $true = sF15 ) ),
introduced(definition,[new_symbols(naming,[spl27_5])],[avatar_definition]) ).
thf(f91,plain,
( ( ( f4 @ $false )
= $false )
| ( $true = sF15 )
| ( sF16 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true = sF15 )
| ( ( f4 @ $false )
= sF16 ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f22,definition,
( sF16
= ( f4 @ sF15 ) ),
introduced(definition,[],[function_definition]) ).
thf(f575,plain,
( spl27_5
| spl27_76
| spl27_74 ),
inference(avatar_split_clause,[status(thm)],[f90,f563,f572,f216]) ).
thf(f90,plain,
( ( sF16 = $false )
| ( ( f4 @ $false )
= $true )
| ( $true = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f570,plain,
( spl27_2
| spl27_74
| spl27_75 ),
inference(avatar_split_clause,[status(thm)],[f93,f567,f563,f203]) ).
thf(f203,definition,
( spl27_2
<=> ( sF15 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_2])],[avatar_definition]) ).
thf(f93,plain,
( ( sF16 = $false )
| ( ( f4 @ $true )
= $true )
| ( sF15 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( sF15 = $false )
| ( sF16
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f561,plain,
( spl27_72
| spl27_73
| spl27_2 ),
inference(avatar_split_clause,[status(thm)],[f92,f203,f558,f554]) ).
thf(f92,plain,
( ( sF16 = $true )
| ( sF15 = $false )
| ( ( f4 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f552,plain,
( spl27_11
| spl27_8
| spl27_21 ),
inference(avatar_split_clause,[status(thm)],[f97,f292,f230,f244]) ).
thf(f244,definition,
( spl27_11
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_11])],[avatar_definition]) ).
thf(f230,definition,
( spl27_8
<=> ( $true
= ( f5 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl27_8])],[avatar_definition]) ).
thf(f292,definition,
( spl27_21
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_21])],[avatar_definition]) ).
thf(f97,plain,
( ( $true
= ( f5 @ $false ) )
| ( sF1 = $true )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( sF1 = $true )
| ( sF2
= ( f5 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f8,definition,
( ( f5 @ sF1 )
= sF2 ),
introduced(definition,[],[function_definition]) ).
thf(f551,plain,
( spl27_7
| spl27_11
| spl27_23 ),
inference(avatar_split_clause,[status(thm)],[f96,f302,f244,f225]) ).
thf(f225,definition,
( spl27_7
<=> ( ( f5 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_7])],[avatar_definition]) ).
thf(f302,definition,
( spl27_23
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(naming,[spl27_23])],[avatar_definition]) ).
thf(f96,plain,
( ( ( f5 @ $false )
= $false )
| ( $true = sF2 )
| ( sF1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f550,plain,
( spl27_23
| spl27_4
| spl27_10 ),
inference(avatar_split_clause,[status(thm)],[f99,f239,f212,f302]) ).
thf(f212,definition,
( spl27_4
<=> ( ( f5 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_4])],[avatar_definition]) ).
thf(f239,definition,
( spl27_10
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_10])],[avatar_definition]) ).
thf(f99,plain,
( ( $true = sF2 )
| ( sF1 = $false )
| ( ( f5 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( f5 @ $true )
= sF2 )
| ( sF1 = $false ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f549,plain,
( spl27_10
| spl27_3
| spl27_21 ),
inference(avatar_split_clause,[status(thm)],[f98,f292,f207,f239]) ).
thf(f207,definition,
( spl27_3
<=> ( ( f5 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_3])],[avatar_definition]) ).
thf(f98,plain,
( ( ( f5 @ $true )
= $true )
| ( sF2 = $false )
| ( sF1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f548,plain,
( spl27_64
| spl27_54
| spl27_59 ),
inference(avatar_split_clause,[status(thm)],[f103,f473,f450,f506]) ).
thf(f506,definition,
( spl27_64
<=> ( sF19 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_64])],[avatar_definition]) ).
thf(f450,definition,
( spl27_54
<=> ( sF20 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_54])],[avatar_definition]) ).
thf(f103,plain,
( ( $true
= ( f2 @ $false ) )
| ( sF20 = $false )
| ( sF19 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( sF20
= ( f2 @ $false ) )
| ( sF19 = $true ) ),
inference(cases_simplifying,[status(thm)],[f26]) ).
thf(f26,definition,
( ( f2 @ sF19 )
= sF20 ),
introduced(definition,[],[function_definition]) ).
thf(f547,plain,
( spl27_57
| spl27_58
| spl27_64 ),
inference(avatar_split_clause,[status(thm)],[f102,f506,f468,f464]) ).
thf(f464,definition,
( spl27_57
<=> ( $true = sF20 ) ),
introduced(definition,[new_symbols(naming,[spl27_57])],[avatar_definition]) ).
thf(f102,plain,
( ( $true = sF20 )
| ( sF19 = $true )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f546,plain,
( spl27_56
| spl27_66
| spl27_57 ),
inference(avatar_split_clause,[status(thm)],[f105,f464,f515,f459]) ).
thf(f515,definition,
( spl27_66
<=> ( sF19 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_66])],[avatar_definition]) ).
thf(f105,plain,
( ( $true = sF20 )
| ( sF19 = $false )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( sF19 = $false )
| ( ( f2 @ $true )
= sF20 ) ),
inference(cases_simplifying,[status(thm)],[f26]) ).
thf(f545,plain,
( spl27_66
| spl27_52
| spl27_54 ),
inference(avatar_split_clause,[status(thm)],[f104,f450,f442,f515]) ).
thf(f104,plain,
( ( sF20 = $false )
| ( sF19 = $false )
| ( ( f2 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f544,plain,
( spl27_51
| spl27_71
| spl27_70 ),
inference(avatar_split_clause,[status(thm)],[f109,f535,f540,f437]) ).
thf(f109,plain,
( ( ( f1 @ $false )
= $false )
| ( $true = sF8 )
| ( $true = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ( f1 @ $false )
= sF9 )
| ( $true = sF8 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f15,definition,
( ( f1 @ sF8 )
= sF9 ),
introduced(definition,[],[function_definition]) ).
thf(f543,plain,
( spl27_69
| spl27_49
| spl27_71 ),
inference(avatar_split_clause,[status(thm)],[f108,f540,f428,f530]) ).
thf(f108,plain,
( ( $true = sF8 )
| ( ( f1 @ $false )
= $true )
| ( sF9 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f538,plain,
( spl27_48
| spl27_68
| spl27_70 ),
inference(avatar_split_clause,[status(thm)],[f111,f535,f526,f423]) ).
thf(f111,plain,
( ( sF8 = $false )
| ( ( f1 @ $true )
= $false )
| ( $true = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( sF8 = $false )
| ( ( f1 @ $true )
= sF9 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f533,plain,
( spl27_68
| spl27_69
| spl27_44 ),
inference(avatar_split_clause,[status(thm)],[f110,f406,f530,f526]) ).
thf(f110,plain,
( ( sF9 = $false )
| ( ( f1 @ $true )
= $true )
| ( sF8 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f524,plain,
( spl27_38
| spl27_67
| spl27_66 ),
inference(avatar_split_clause,[status(thm)],[f115,f515,f520,f374]) ).
thf(f115,plain,
( ( sF18 = $true )
| ( sF19 = $false )
| ( ( f3 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( sF19
= ( f3 @ $false ) )
| ( sF18 = $true ) ),
inference(cases_simplifying,[status(thm)],[f25]) ).
thf(f25,definition,
( sF19
= ( f3 @ sF18 ) ),
introduced(definition,[],[function_definition]) ).
thf(f523,plain,
( spl27_39
| spl27_64
| spl27_67 ),
inference(avatar_split_clause,[status(thm)],[f114,f520,f506,f379]) ).
thf(f114,plain,
( ( ( f3 @ $false )
= $false )
| ( sF18 = $true )
| ( sF19 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f518,plain,
( spl27_65
| spl27_36
| spl27_66 ),
inference(avatar_split_clause,[status(thm)],[f117,f515,f365,f510]) ).
thf(f117,plain,
( ( $true
= ( f3 @ $true ) )
| ( sF18 = $false )
| ( sF19 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( sF19
= ( f3 @ $true ) )
| ( sF18 = $false ) ),
inference(cases_simplifying,[status(thm)],[f25]) ).
thf(f513,plain,
( spl27_34
| spl27_64
| spl27_65 ),
inference(avatar_split_clause,[status(thm)],[f116,f510,f506,f356]) ).
thf(f116,plain,
( ( ( f3 @ $true )
= $false )
| ( sF19 = $true )
| ( sF18 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f504,plain,
( spl27_31
| spl27_43
| spl27_62 ),
inference(avatar_split_clause,[status(thm)],[f121,f491,f401,f339]) ).
thf(f401,definition,
( spl27_43
<=> ( sF26 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_43])],[avatar_definition]) ).
thf(f491,definition,
( spl27_62
<=> ( $true = sF25 ) ),
introduced(definition,[new_symbols(naming,[spl27_62])],[avatar_definition]) ).
thf(f121,plain,
( ( $true = sF25 )
| ( sF26 = $false )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true = sF25 )
| ( sF26
= ( f0 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f32]) ).
thf(f32,definition,
( ( f0 @ sF25 )
= sF26 ),
introduced(definition,[],[function_definition]) ).
thf(f503,plain,
( spl27_30
| spl27_42
| spl27_62 ),
inference(avatar_split_clause,[status(thm)],[f120,f491,f396,f334]) ).
thf(f396,definition,
( spl27_42
<=> ( $true = sF26 ) ),
introduced(definition,[new_symbols(naming,[spl27_42])],[avatar_definition]) ).
thf(f120,plain,
( ( $true = sF26 )
| ( ( f0 @ $false )
= $false )
| ( $true = sF25 ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f502,plain,
( spl27_60
| spl27_42
| spl27_24 ),
inference(avatar_split_clause,[status(thm)],[f123,f308,f396,f482]) ).
thf(f482,definition,
( spl27_60
<=> ( sF25 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_60])],[avatar_definition]) ).
thf(f123,plain,
( ( ( f0 @ $true )
= $false )
| ( $true = sF26 )
| ( sF25 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( ( f0 @ $true )
= sF26 )
| ( sF25 = $false ) ),
inference(cases_simplifying,[status(thm)],[f32]) ).
thf(f501,plain,
( spl27_27
| spl27_43
| spl27_60 ),
inference(avatar_split_clause,[status(thm)],[f122,f482,f401,f321]) ).
thf(f122,plain,
( ( sF26 = $false )
| ( ( f0 @ $true )
= $true )
| ( sF25 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f500,plain,
( spl27_62
| spl27_30
| spl27_63 ),
inference(avatar_split_clause,[status(thm)],[f127,f496,f334,f491]) ).
thf(f127,plain,
( ( sF24 = $true )
| ( $true = sF25 )
| ( ( f0 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
( ( ( f0 @ $false )
= sF25 )
| ( sF24 = $true ) ),
inference(cases_simplifying,[status(thm)],[f31]) ).
thf(f31,definition,
( ( f0 @ sF24 )
= sF25 ),
introduced(definition,[],[function_definition]) ).
thf(f499,plain,
( spl27_31
| spl27_60
| spl27_63 ),
inference(avatar_split_clause,[status(thm)],[f126,f496,f482,f339]) ).
thf(f126,plain,
( ( sF25 = $false )
| ( sF24 = $true )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f494,plain,
( spl27_62
| spl27_61
| spl27_24 ),
inference(avatar_split_clause,[status(thm)],[f129,f308,f486,f491]) ).
thf(f129,plain,
( ( ( f0 @ $true )
= $false )
| ( sF24 = $false )
| ( $true = sF25 ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( f0 @ $true )
= sF25 )
| ( sF24 = $false ) ),
inference(cases_simplifying,[status(thm)],[f31]) ).
thf(f489,plain,
( spl27_27
| spl27_60
| spl27_61 ),
inference(avatar_split_clause,[status(thm)],[f128,f486,f482,f321]) ).
thf(f128,plain,
( ( sF25 = $false )
| ( ( f0 @ $true )
= $true )
| ( sF24 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f480,plain,
( spl27_46
| spl27_55
| spl27_59 ),
inference(avatar_split_clause,[status(thm)],[f133,f473,f455,f414]) ).
thf(f414,definition,
( spl27_46
<=> ( sF22 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_46])],[avatar_definition]) ).
thf(f455,definition,
( spl27_55
<=> ( sF21 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_55])],[avatar_definition]) ).
thf(f133,plain,
( ( sF21 = $true )
| ( $true
= ( f2 @ $false ) )
| ( sF22 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
( ( sF22
= ( f2 @ $false ) )
| ( sF21 = $true ) ),
inference(cases_simplifying,[status(thm)],[f28]) ).
thf(f28,definition,
( sF22
= ( f2 @ sF21 ) ),
introduced(definition,[],[function_definition]) ).
thf(f479,plain,
( spl27_55
| spl27_58
| spl27_50 ),
inference(avatar_split_clause,[status(thm)],[f132,f432,f468,f455]) ).
thf(f432,definition,
( spl27_50
<=> ( sF22 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_50])],[avatar_definition]) ).
thf(f132,plain,
( ( sF21 = $true )
| ( sF22 = $true )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f478,plain,
( spl27_50
| spl27_53
| spl27_56 ),
inference(avatar_split_clause,[status(thm)],[f135,f459,f446,f432]) ).
thf(f446,definition,
( spl27_53
<=> ( sF21 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_53])],[avatar_definition]) ).
thf(f135,plain,
( ( sF21 = $false )
| ( sF22 = $true )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( sF21 = $false )
| ( ( f2 @ $true )
= sF22 ) ),
inference(cases_simplifying,[status(thm)],[f28]) ).
thf(f477,plain,
( spl27_52
| spl27_46
| spl27_53 ),
inference(avatar_split_clause,[status(thm)],[f134,f446,f414,f442]) ).
thf(f134,plain,
( ( sF22 = $false )
| ( sF21 = $false )
| ( ( f2 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f476,plain,
( spl27_57
| spl27_59
| spl27_53 ),
inference(avatar_split_clause,[status(thm)],[f139,f446,f473,f464]) ).
thf(f139,plain,
( ( $true
= ( f2 @ $false ) )
| ( sF21 = $false )
| ( $true = sF20 ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $true = sF20 )
| ( sF21
= ( f2 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f27]) ).
thf(f27,definition,
( sF21
= ( f2 @ sF20 ) ),
introduced(definition,[],[function_definition]) ).
thf(f471,plain,
( spl27_57
| spl27_58
| spl27_55 ),
inference(avatar_split_clause,[status(thm)],[f138,f455,f468,f464]) ).
thf(f138,plain,
( ( ( f2 @ $false )
= $false )
| ( sF21 = $true )
| ( $true = sF20 ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f462,plain,
( spl27_55
| spl27_56
| spl27_54 ),
inference(avatar_split_clause,[status(thm)],[f141,f450,f459,f455]) ).
thf(f141,plain,
( ( sF20 = $false )
| ( ( f2 @ $true )
= $false )
| ( sF21 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( f2 @ $true )
= sF21 )
| ( sF20 = $false ) ),
inference(cases_simplifying,[status(thm)],[f27]) ).
thf(f453,plain,
( spl27_52
| spl27_53
| spl27_54 ),
inference(avatar_split_clause,[status(thm)],[f140,f450,f446,f442]) ).
thf(f140,plain,
( ( sF20 = $false )
| ( sF21 = $false )
| ( ( f2 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f440,plain,
( spl27_47
| spl27_51
| spl27_50 ),
inference(avatar_split_clause,[status(thm)],[f145,f432,f437,f419]) ).
thf(f145,plain,
( ( sF23 = $true )
| ( ( f1 @ $false )
= $false )
| ( sF22 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( sF22 = $true )
| ( ( f1 @ $false )
= sF23 ) ),
inference(cases_simplifying,[status(thm)],[f29]) ).
thf(f29,definition,
( sF23
= ( f1 @ sF22 ) ),
introduced(definition,[],[function_definition]) ).
thf(f435,plain,
( spl27_49
| spl27_50
| spl27_45 ),
inference(avatar_split_clause,[status(thm)],[f144,f410,f432,f428]) ).
thf(f144,plain,
( ( ( f1 @ $false )
= $true )
| ( sF22 = $true )
| ( sF23 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f426,plain,
( spl27_47
| spl27_46
| spl27_48 ),
inference(avatar_split_clause,[status(thm)],[f147,f423,f414,f419]) ).
thf(f147,plain,
( ( sF23 = $true )
| ( sF22 = $false )
| ( ( f1 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( ( f1 @ $true )
= sF23 )
| ( sF22 = $false ) ),
inference(cases_simplifying,[status(thm)],[f29]) ).
thf(f417,plain,
( spl27_44
| spl27_45
| spl27_46 ),
inference(avatar_split_clause,[status(thm)],[f146,f414,f410,f406]) ).
thf(f146,plain,
( ( ( f1 @ $true )
= $true )
| ( sF22 = $false )
| ( sF23 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f404,plain,
( spl27_43
| spl27_28 ),
inference(avatar_split_clause,[status(thm)],[f149,f325,f401]) ).
thf(f325,definition,
( spl27_28
<=> ( sF12 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_28])],[avatar_definition]) ).
thf(f149,plain,
( ( sF26 = $false )
| ( sF12 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
sF12 != sF26,
inference(definition_folding,[status(thm)],[f5,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f6,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6]) ).
thf(f7,definition,
( sF1
= ( f5 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f9,definition,
( sF3
= ( f5 @ sF2 ) ),
introduced(definition,[],[function_definition]) ).
thf(f11,definition,
( ( f3 @ sF4 )
= sF5 ),
introduced(definition,[],[function_definition]) ).
thf(f18,definition,
( sF12
= ( f0 @ sF11 ) ),
introduced(definition,[],[function_definition]) ).
thf(f6,definition,
( ( f6 @ x )
= sF0 ),
introduced(definition,[],[function_definition]) ).
thf(f19,definition,
( sF13
= ( f6 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f20,definition,
( ( f6 @ sF13 )
= sF14 ),
introduced(definition,[],[function_definition]) ).
thf(f21,definition,
( sF15
= ( f5 @ sF14 ) ),
introduced(definition,[],[function_definition]) ).
thf(f5,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NVo8B1ETwb/DTF2THF_4968.p',kaminski7) ).
thf(f399,plain,
( spl27_26
| spl27_42 ),
inference(avatar_split_clause,[status(thm)],[f148,f396,f316]) ).
thf(f316,definition,
( spl27_26
<=> ( sF12 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_26])],[avatar_definition]) ).
thf(f148,plain,
( ( sF12 = $true )
| ( $true = sF26 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f394,plain,
( spl27_41
| spl27_12
| spl27_17 ),
inference(avatar_split_clause,[status(thm)],[f153,f273,f249,f390]) ).
thf(f390,definition,
( spl27_41
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_41])],[avatar_definition]) ).
thf(f249,definition,
( spl27_12
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl27_12])],[avatar_definition]) ).
thf(f273,definition,
( spl27_17
<=> ( ( f6 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_17])],[avatar_definition]) ).
thf(f153,plain,
( ( ( f6 @ $false )
= $false )
| ( $true = sF0 )
| ( x = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( x = $true )
| ( ( f6 @ $false )
= sF0 ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f393,plain,
( spl27_41
| spl27_9
| spl27_18 ),
inference(avatar_split_clause,[status(thm)],[f152,f278,f235,f390]) ).
thf(f235,definition,
( spl27_9
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl27_9])],[avatar_definition]) ).
thf(f278,definition,
( spl27_18
<=> ( $true
= ( f6 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl27_18])],[avatar_definition]) ).
thf(f152,plain,
( ( x = $true )
| ( $false = sF0 )
| ( $true
= ( f6 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f388,plain,
( spl27_12
| spl27_40
| spl27_14 ),
inference(avatar_split_clause,[status(thm)],[f155,f259,f384,f249]) ).
thf(f384,definition,
( spl27_40
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_40])],[avatar_definition]) ).
thf(f259,definition,
( spl27_14
<=> ( ( f6 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl27_14])],[avatar_definition]) ).
thf(f155,plain,
( ( x = $false )
| ( $true = sF0 )
| ( ( f6 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( ( x = $false )
| ( ( f6 @ $true )
= sF0 ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f387,plain,
( spl27_9
| spl27_15
| spl27_40 ),
inference(avatar_split_clause,[status(thm)],[f154,f384,f264,f235]) ).
thf(f264,definition,
( spl27_15
<=> ( ( f6 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl27_15])],[avatar_definition]) ).
thf(f154,plain,
( ( x = $false )
| ( $false = sF0 )
| ( ( f6 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f382,plain,
( spl27_39
| spl27_37
| spl27_33 ),
inference(avatar_split_clause,[status(thm)],[f159,f352,f370,f379]) ).
thf(f159,plain,
( ( ( f3 @ $false )
= $false )
| ( $true = sF4 )
| ( $true = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
( ( ( f3 @ $false )
= sF5 )
| ( $true = sF4 ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f377,plain,
( spl27_35
| spl27_37
| spl27_38 ),
inference(avatar_split_clause,[status(thm)],[f158,f374,f370,f361]) ).
thf(f158,plain,
( ( ( f3 @ $false )
= $true )
| ( sF5 = $false )
| ( $true = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f368,plain,
( spl27_35
| spl27_36
| spl27_32 ),
inference(avatar_split_clause,[status(thm)],[f161,f348,f365,f361]) ).
thf(f161,plain,
( ( $true
= ( f3 @ $true ) )
| ( $false = sF4 )
| ( sF5 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $false = sF4 )
| ( sF5
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f359,plain,
( spl27_32
| spl27_33
| spl27_34 ),
inference(avatar_split_clause,[status(thm)],[f160,f356,f352,f348]) ).
thf(f160,plain,
( ( $true = sF5 )
| ( $false = sF4 )
| ( ( f3 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f346,plain,
( spl27_13
| spl27_17
| spl27_6 ),
inference(avatar_split_clause,[status(thm)],[f165,f221,f273,f255]) ).
thf(f255,definition,
( spl27_13
<=> ( sF13 = $true ) ),
introduced(definition,[new_symbols(naming,[spl27_13])],[avatar_definition]) ).
thf(f221,definition,
( spl27_6
<=> ( $true = sF14 ) ),
introduced(definition,[new_symbols(naming,[spl27_6])],[avatar_definition]) ).
thf(f165,plain,
( ( $true = sF14 )
| ( ( f6 @ $false )
= $false )
| ( sF13 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( sF13 = $true )
| ( ( f6 @ $false )
= sF14 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f345,plain,
( spl27_18
| spl27_13
| spl27_1 ),
inference(avatar_split_clause,[status(thm)],[f164,f199,f255,f278]) ).
thf(f199,definition,
( spl27_1
<=> ( sF14 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_1])],[avatar_definition]) ).
thf(f164,plain,
( ( sF13 = $true )
| ( sF14 = $false )
| ( $true
= ( f6 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f344,plain,
( spl27_14
| spl27_6
| spl27_16 ),
inference(avatar_split_clause,[status(thm)],[f167,f268,f221,f259]) ).
thf(f268,definition,
( spl27_16
<=> ( sF13 = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_16])],[avatar_definition]) ).
thf(f167,plain,
( ( $true = sF14 )
| ( ( f6 @ $true )
= $false )
| ( sF13 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
( ( ( f6 @ $true )
= sF14 )
| ( sF13 = $false ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f343,plain,
( spl27_16
| spl27_15
| spl27_1 ),
inference(avatar_split_clause,[status(thm)],[f166,f199,f264,f268]) ).
thf(f166,plain,
( ( sF13 = $false )
| ( sF14 = $false )
| ( ( f6 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f342,plain,
( spl27_29
| spl27_31
| spl27_28 ),
inference(avatar_split_clause,[status(thm)],[f171,f325,f339,f330]) ).
thf(f171,plain,
( ( $true = sF11 )
| ( sF12 = $false )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true = sF11 )
| ( sF12
= ( f0 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f337,plain,
( spl27_29
| spl27_30
| spl27_26 ),
inference(avatar_split_clause,[status(thm)],[f170,f316,f334,f330]) ).
thf(f170,plain,
( ( $true = sF11 )
| ( ( f0 @ $false )
= $false )
| ( sF12 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f328,plain,
( spl27_25
| spl27_27
| spl27_28 ),
inference(avatar_split_clause,[status(thm)],[f173,f325,f321,f312]) ).
thf(f173,plain,
( ( sF11 = $false )
| ( sF12 = $false )
| ( ( f0 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( sF11 = $false )
| ( sF12
= ( f0 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f319,plain,
( spl27_24
| spl27_25
| spl27_26 ),
inference(avatar_split_clause,[status(thm)],[f172,f316,f312,f308]) ).
thf(f172,plain,
( ( sF12 = $true )
| ( ( f0 @ $true )
= $false )
| ( sF11 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f306,plain,
( spl27_23
| spl27_8
| spl27_20 ),
inference(avatar_split_clause,[status(thm)],[f177,f288,f230,f302]) ).
thf(f177,plain,
( ( $true = sF2 )
| ( $true
= ( f5 @ $false ) )
| ( sF3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
( ( sF3
= ( f5 @ $false ) )
| ( $true = sF2 ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f305,plain,
( spl27_22
| spl27_7
| spl27_23 ),
inference(avatar_split_clause,[status(thm)],[f176,f302,f225,f297]) ).
thf(f176,plain,
( ( $true = sF2 )
| ( sF3 = $true )
| ( ( f5 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f300,plain,
( spl27_22
| spl27_21
| spl27_4 ),
inference(avatar_split_clause,[status(thm)],[f179,f212,f292,f297]) ).
thf(f179,plain,
( ( sF2 = $false )
| ( ( f5 @ $true )
= $false )
| ( sF3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
( ( ( f5 @ $true )
= sF3 )
| ( sF2 = $false ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f295,plain,
( spl27_20
| spl27_21
| spl27_3 ),
inference(avatar_split_clause,[status(thm)],[f178,f207,f292,f288]) ).
thf(f178,plain,
( ( sF3 = $false )
| ( ( f5 @ $true )
= $true )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f286,plain,
~ spl27_19,
inference(avatar_split_clause,[status(thm)],[f3,f283]) ).
thf(f283,definition,
( spl27_19
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl27_19])],[avatar_definition]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f281,plain,
( spl27_18
| spl27_12
| spl27_16 ),
inference(avatar_split_clause,[status(thm)],[f183,f268,f249,f278]) ).
thf(f183,plain,
( ( sF13 = $false )
| ( $true
= ( f6 @ $false ) )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
( ( sF13
= ( f6 @ $false ) )
| ( $true = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f276,plain,
( spl27_13
| spl27_12
| spl27_17 ),
inference(avatar_split_clause,[status(thm)],[f182,f273,f249,f255]) ).
thf(f182,plain,
( ( ( f6 @ $false )
= $false )
| ( $true = sF0 )
| ( sF13 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f271,plain,
( spl27_15
| spl27_9
| spl27_16 ),
inference(avatar_split_clause,[status(thm)],[f185,f268,f235,f264]) ).
thf(f185,plain,
( ( $false = sF0 )
| ( ( f6 @ $true )
= $true )
| ( sF13 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( sF13
= ( f6 @ $true ) )
| ( $false = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f262,plain,
( spl27_13
| spl27_14
| spl27_9 ),
inference(avatar_split_clause,[status(thm)],[f184,f235,f259,f255]) ).
thf(f184,plain,
( ( ( f6 @ $true )
= $false )
| ( sF13 = $true )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f253,plain,
( spl27_12
| spl27_8
| spl27_10 ),
inference(avatar_split_clause,[status(thm)],[f189,f239,f230,f249]) ).
thf(f189,plain,
( ( $true = sF0 )
| ( sF1 = $false )
| ( $true
= ( f5 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( sF1
= ( f5 @ $false ) )
| ( $true = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f252,plain,
( spl27_7
| spl27_12
| spl27_11 ),
inference(avatar_split_clause,[status(thm)],[f188,f244,f249,f225]) ).
thf(f188,plain,
( ( ( f5 @ $false )
= $false )
| ( sF1 = $true )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f187]) ).
thf(f247,plain,
( spl27_4
| spl27_11
| spl27_9 ),
inference(avatar_split_clause,[status(thm)],[f191,f235,f244,f212]) ).
thf(f191,plain,
( ( $false = sF0 )
| ( ( f5 @ $true )
= $false )
| ( sF1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
( ( $false = sF0 )
| ( ( f5 @ $true )
= sF1 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f242,plain,
( spl27_3
| spl27_9
| spl27_10 ),
inference(avatar_split_clause,[status(thm)],[f190,f239,f235,f207]) ).
thf(f190,plain,
( ( sF1 = $false )
| ( $false = sF0 )
| ( ( f5 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f233,plain,
( spl27_6
| spl27_2
| spl27_8 ),
inference(avatar_split_clause,[status(thm)],[f195,f230,f203,f221]) ).
thf(f195,plain,
( ( sF15 = $false )
| ( $true
= ( f5 @ $false ) )
| ( $true = sF14 ) ),
inference(binary_proxy_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( sF15
= ( f5 @ $false ) )
| ( $true = sF14 ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f228,plain,
( spl27_6
| spl27_5
| spl27_7 ),
inference(avatar_split_clause,[status(thm)],[f194,f225,f216,f221]) ).
thf(f194,plain,
( ( $true = sF14 )
| ( $true = sF15 )
| ( ( f5 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f193]) ).
thf(f219,plain,
( spl27_4
| spl27_1
| spl27_5 ),
inference(avatar_split_clause,[status(thm)],[f197,f216,f199,f212]) ).
thf(f197,plain,
( ( sF14 = $false )
| ( $true = sF15 )
| ( ( f5 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
( ( ( f5 @ $true )
= sF15 )
| ( sF14 = $false ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f210,plain,
( spl27_1
| spl27_2
| spl27_3 ),
inference(avatar_split_clause,[status(thm)],[f196,f207,f203,f199]) ).
thf(f196,plain,
( ( sF15 = $false )
| ( sF14 = $false )
| ( ( f5 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO500^1.007 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n001.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 14:33:35 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SYO500^1.007 : TPTP v9.2.1. Released v4.1.0.
% 0.29/0.47 % Domain : Syntactic
% 0.29/0.47 % Problem : Seven function variant of the Kaminski equation
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : basic15 [Bro09]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.33 v9.1.0, 0.50 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0
% 0.29/0.47 % Syntax : Number of formulae : 9 ( 1 unt; 8 typ; 0 def)
% 0.29/0.47 % Number of atoms : 31 ( 1 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 1 ( 31 avg)
% 0.29/0.47 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 28 @)
% 0.29/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.29/0.47 % Number of types : 1 ( 0 usr)
% 0.29/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 9 ( 8 usr; 1 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments :
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(x,type,
% 0.29/0.47 x: $o ).
% 0.29/0.47
% 0.29/0.47 thf(f0,type,
% 0.29/0.47 f0: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f1,type,
% 0.29/0.47 f1: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f2,type,
% 0.29/0.47 f2: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f3,type,
% 0.29/0.47 f3: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f4,type,
% 0.29/0.47 f4: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f5,type,
% 0.29/0.47 f5: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f6,type,
% 0.29/0.47 f6: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(kaminski7,conjecture,
% 0.29/0.47 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.47 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 14:33:36 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NVo8B1ETwb/DTF2DTF4968.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(x,type,
% 1.47/1.27 x: $o ).
% 1.47/1.27
% 1.47/1.27 thf(f0,type,
% 1.47/1.27 f0: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f1,type,
% 1.47/1.27 f1: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f2,type,
% 1.47/1.27 f2: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f3,type,
% 1.47/1.27 f3: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f4,type,
% 1.47/1.27 f4: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f5,type,
% 1.47/1.27 f5: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(f6,type,
% 1.47/1.27 f6: $o > $o ).
% 1.47/1.27
% 1.47/1.27 thf(kaminski7,conjecture,
% 1.47/1.27 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) )
% 1.47/1.27 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ ( f6 @ ( f6 @ ( f6 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (5254)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/275Mi)
% 1.47/1.28 % (5252)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/2Mi)
% 1.47/1.29 % (5252)Instruction limit reached!
% 1.47/1.29 % (5252)------------------------------
% 1.47/1.29 % (5252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (5252)Termination reason: Unknown
% 1.47/1.29 % (5252)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (5252)Memory used [KB]: 5373
% 1.47/1.29 % (5252)Time elapsed: 0.002 s
% 1.47/1.29 % (5252)Instructions burned: 2 (million)
% 1.47/1.29 % (5252)------------------------------
% 1.47/1.29 % (5252)------------------------------
% 1.47/1.29 % (5254)Refutation not found, incomplete strategy
% 1.47/1.29 % (5254)------------------------------
% 1.47/1.29 % (5254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (5254)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (5254)Memory used [KB]: 5500
% 1.47/1.29 % (5254)Time elapsed: 0.003 s
% 1.47/1.29 % (5254)Instructions burned: 2 (million)
% 1.47/1.29 % (5254)------------------------------
% 1.47/1.29 % (5254)------------------------------
% 1.47/1.29 % (5249)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/183Mi)
% 1.47/1.29 % (5250)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/4Mi)
% 1.47/1.29 % (5251)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/27Mi)
% 1.47/1.29 % (5253)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/2Mi)
% 1.47/1.29 % (5255)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/18Mi)
% 1.47/1.29 % (5253)Instruction limit reached!
% 1.47/1.29 % (5253)------------------------------
% 1.47/1.29 % (5253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (5253)Termination reason: Unknown
% 1.47/1.29 % (5253)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (5253)Memory used [KB]: 5500
% 1.47/1.29 % (5253)Time elapsed: 0.004 s
% 1.47/1.29 % (5253)Instructions burned: 3 (million)
% 1.47/1.29 % (5253)------------------------------
% 1.47/1.29 % (5253)------------------------------
% 1.47/1.29 % (5250)Instruction limit reached!
% 1.47/1.29 % (5250)------------------------------
% 1.47/1.29 % (5250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (5250)Termination reason: Unknown
% 1.47/1.29 % (5250)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (5250)Memory used [KB]: 5500
% 1.47/1.29 % (5250)Time elapsed: 0.005 s
% 1.47/1.29 % (5250)Instructions burned: 4 (million)
% 1.47/1.29 % (5250)------------------------------
% 1.47/1.29 % (5250)------------------------------
% 1.47/1.29 % (5251)Refutation not found, incomplete strategy
% 1.47/1.29 % (5251)------------------------------
% 1.47/1.29 % (5251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (5251)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (5251)Memory used [KB]: 5500
% 1.47/1.29 % (5251)Time elapsed: 0.005 s
% 1.47/1.29 % (5251)Instructions burned: 4 (million)
% 1.47/1.29 % (5251)------------------------------
% 1.47/1.29 % (5251)------------------------------
% 1.47/1.30 % (5257)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/37Mi)
% 1.62/1.30 % (5256)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/3Mi)
% 1.62/1.30 % (5255)Instruction limit reached!
% 1.62/1.30 % (5255)------------------------------
% 1.62/1.30 % (5255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (5255)Termination reason: Unknown
% 1.62/1.30 % (5255)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (5255)Memory used [KB]: 5628
% 1.62/1.30 % (5255)Time elapsed: 0.014 s
% 1.62/1.30 % (5255)Instructions burned: 19 (million)
% 1.62/1.30 % (5255)------------------------------
% 1.62/1.30 % (5255)------------------------------
% 1.62/1.30 % (5256)Refutation not found, incomplete strategy
% 1.62/1.30 % (5256)------------------------------
% 1.62/1.30 % (5256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (5256)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (5256)Memory used [KB]: 5500
% 1.62/1.30 % (5256)Time elapsed: 0.003 s
% 1.62/1.30 % (5256)Instructions burned: 2 (million)
% 1.62/1.30 % (5256)------------------------------
% 1.62/1.30 % (5256)------------------------------
% 1.62/1.31 % (5257)Instruction limit reached!
% 1.62/1.31 % (5257)------------------------------
% 1.62/1.31 % (5257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (5257)Termination reason: Unknown
% 1.62/1.31 % (5257)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (5257)Memory used [KB]: 5628
% 1.62/1.31 % (5257)Time elapsed: 0.013 s
% 1.62/1.31 % (5257)Instructions burned: 39 (million)
% 1.62/1.31 % (5257)------------------------------
% 1.62/1.31 % (5257)------------------------------
% 1.62/1.31 % (5258)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/15Mi)
% 1.62/1.31 % (5259)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/3Mi)
% 1.62/1.31 % (5260)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/1041Mi)
% 1.62/1.31 % (5259)Refutation not found, incomplete strategy
% 1.62/1.31 % (5259)------------------------------
% 1.62/1.31 % (5259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (5259)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.31
% 1.62/1.31
% 1.62/1.31 % (5259)Memory used [KB]: 5500
% 1.62/1.31 % (5259)Time elapsed: 0.003 s
% 1.62/1.31 % (5259)Instructions burned: 2 (million)
% 1.62/1.31 % (5259)------------------------------
% 1.62/1.31 % (5259)------------------------------
% 1.62/1.32 % (5263)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/3Mi)
% 1.62/1.32 % (5260)Refutation not found, incomplete strategy
% 1.62/1.32 % (5260)------------------------------
% 1.62/1.32 % (5260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (5260)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (5260)Memory used [KB]: 5500
% 1.62/1.32 % (5260)Time elapsed: 0.007 s
% 1.62/1.32 % (5260)Instructions burned: 8 (million)
% 1.62/1.32 % (5260)------------------------------
% 1.62/1.32 % (5260)------------------------------
% 1.62/1.32 % (5263)Instruction limit reached!
% 1.62/1.32 % (5263)------------------------------
% 1.62/1.32 % (5263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (5263)Termination reason: Unknown
% 1.62/1.32 % (5263)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (5263)Memory used [KB]: 5500
% 1.62/1.32 % (5263)Time elapsed: 0.003 s
% 1.62/1.32 % (5263)Instructions burned: 5 (million)
% 1.62/1.32 % (5263)------------------------------
% 1.62/1.32 % (5263)------------------------------
% 1.62/1.32 % (5258)Instruction limit reached!
% 1.62/1.32 % (5258)------------------------------
% 1.62/1.32 % (5258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (5258)Termination reason: Unknown
% 1.62/1.32 % (5258)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (5258)Memory used [KB]: 5756
% 1.62/1.32 % (5258)Time elapsed: 0.011 s
% 1.62/1.32 % (5258)Instructions burned: 15 (million)
% 1.62/1.32 % (5258)------------------------------
% 1.62/1.32 % (5258)------------------------------
% 1.62/1.32 % (5261)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/7Mi)
% 1.62/1.32 % (5262)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/16Mi)
% 1.62/1.33 % (5261)Instruction limit reached!
% 1.62/1.33 % (5261)------------------------------
% 1.62/1.33 % (5261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (5261)Termination reason: Unknown
% 1.62/1.33 % (5261)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (5261)Memory used [KB]: 1023
% 1.62/1.33 % (5261)Time elapsed: 0.006 s
% 1.62/1.33 % (5261)Instructions burned: 7 (million)
% 1.62/1.33 % (5261)------------------------------
% 1.62/1.33 % (5261)------------------------------
% 1.62/1.33 % (5265)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/7Mi)
% 1.62/1.33 % (5264)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/3Mi)
% 1.62/1.33 % (5262)First to succeed.
% 1.62/1.33 % (5265)Instruction limit reached!
% 1.62/1.33 % (5265)------------------------------
% 1.62/1.33 % (5265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (5265)Termination reason: Unknown
% 1.62/1.33 % (5265)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (5265)Memory used [KB]: 5628
% 1.62/1.33 % (5265)Time elapsed: 0.004 s
% 1.62/1.33 % (5265)Instructions burned: 10 (million)
% 1.62/1.33 % (5265)------------------------------
% 1.62/1.33 % (5265)------------------------------
% 1.62/1.33 % (5264)Instruction limit reached!
% 1.62/1.33 % (5264)------------------------------
% 1.62/1.33 % (5264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (5264)Termination reason: Unknown
% 1.62/1.33 % (5264)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (5264)Memory used [KB]: 5500
% 1.62/1.33 % (5264)Time elapsed: 0.003 s
% 1.62/1.33 % (5264)Instructions burned: 4 (million)
% 1.62/1.33 % (5264)------------------------------
% 1.62/1.33 % (5264)------------------------------
% 1.62/1.34 % (5266)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4968 for (2999ds/3Mi)
% 1.62/1.34 % (5262)Refutation found. Thanks to Tanya!
% 1.62/1.34 % SZS status Theorem for DTF2THF_4968
% 1.62/1.34 % SZS output start Proof for DTF2THF_4968
% 1.62/1.34 thf(func_def_1, type, f0: $o > $o).
% 1.62/1.34 thf(func_def_2, type, f1: $o > $o).
% 1.62/1.34 thf(func_def_3, type, f2: $o > $o).
% 1.62/1.34 thf(func_def_4, type, f3: $o > $o).
% 1.62/1.34 thf(func_def_5, type, f4: $o > $o).
% 1.62/1.34 thf(func_def_6, type, f5: $o > $o).
% 1.62/1.34 thf(func_def_7, type, f6: $o > $o).
% 1.62/1.34 thf(f691,plain,(
% 1.62/1.34 $false),
% 1.62/1.34 inference(avatar_sat_refutation,[status(thm)],[f210,f219,f228,f233,f242,f247,f252,f253,f262,f271,f276,f281,f286,f295,f300,f305,f306,f319,f328,f337,f342,f343,f344,f345,f346,f359,f368,f377,f382,f387,f388,f393,f394,f399,f404,f417,f426,f435,f440,f453,f462,f471,f476,f477,f478,f479,f480,f489,f494,f499,f500,f501,f502,f503,f504,f513,f518,f523,f524,f533,f538,f543,f544,f545,f546,f547,f548,f549,f550,f551,f552,f561,f570,f575,f580,f589,f594,f599,f600,f601,f602,f603,f604,f609,f610,f615,f616,f621,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f640,f641,f642,f643,f644,f645,f646,f647,f648,f649,f650,f651,f652,f653,f654,f655,f656,f657,f658,f659,f660,f661,f662,f663,f664,f665,f666,f667,f668,f669,f670,f671,f672,f673,f674,f675,f676,f677,f678,f679,f680,f681,f682,f683,f684,f685,f686,f687,f688,f689,f690])).
% 1.62/1.34 thf(f690,plain,(
% 1.62/1.34 (x != $true) | (x != $false) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f689,plain,(
% 1.62/1.34 ($true != (f6 @ $false)) | ((f6 @ $false) != $false) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f688,plain,(
% 1.62/1.34 (sF13 != $false) | (sF13 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f687,plain,(
% 1.62/1.34 ((f6 @ $true) != $false) | ((f6 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f686,plain,(
% 1.62/1.34 ($true != sF14) | (sF14 != $false) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f685,plain,(
% 1.62/1.34 ($true != sF15) | (sF15 != $false) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f684,plain,(
% 1.62/1.34 (sF17 != $false) | (sF17 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f683,plain,(
% 1.62/1.34 ((f4 @ $false) != $false) | ((f4 @ $false) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f682,plain,(
% 1.62/1.34 (sF19 != $false) | (sF19 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f681,plain,(
% 1.62/1.34 (sF20 != $false) | ($true != sF20) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f680,plain,(
% 1.62/1.34 (sF21 != $false) | (sF21 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f679,plain,(
% 1.62/1.34 (sF26 != $false) | ($true != sF26) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f678,plain,(
% 1.62/1.34 (sF24 != $false) | (sF24 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f677,plain,(
% 1.62/1.34 (sF22 != $false) | (sF22 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f676,plain,(
% 1.62/1.34 (sF10 != $false) | ($true != sF10) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f675,plain,(
% 1.62/1.34 (sF9 != $false) | ($true != sF9) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f674,plain,(
% 1.62/1.34 (sF8 != $false) | ($true != sF8) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f673,plain,(
% 1.62/1.34 (sF7 != $false) | ($true != sF7) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f672,plain,(
% 1.62/1.34 ($false != sF6) | ($true != sF6) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f671,plain,(
% 1.62/1.34 (sF5 != $false) | ($true != sF5) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f670,plain,(
% 1.62/1.34 ((f4 @ $true) != $false) | ((f4 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f669,plain,(
% 1.62/1.34 (sF16 != $false) | (sF16 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f668,plain,(
% 1.62/1.34 (sF18 != $false) | (sF18 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f667,plain,(
% 1.62/1.34 (sF25 != $false) | ($true != sF25) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f666,plain,(
% 1.62/1.34 ((f2 @ $false) != $false) | ($true != (f2 @ $false)) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f665,plain,(
% 1.62/1.34 ((f2 @ $true) != $false) | ((f2 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f664,plain,(
% 1.62/1.34 ((f1 @ $false) != $false) | ((f1 @ $false) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f663,plain,(
% 1.62/1.34 ((f1 @ $true) != $false) | ((f1 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f662,plain,(
% 1.62/1.34 (sF23 != $false) | (sF23 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f661,plain,(
% 1.62/1.34 ((f3 @ $false) != $false) | ((f3 @ $false) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f660,plain,(
% 1.62/1.34 ($false != sF4) | ($true != sF4) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f659,plain,(
% 1.62/1.34 ((f3 @ $true) != $false) | ($true != (f3 @ $true)) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f658,plain,(
% 1.62/1.34 (sF11 != $false) | ($true != sF11) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f657,plain,(
% 1.62/1.34 ((f0 @ $false) != $false) | ($true != (f0 @ $false)) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f656,plain,(
% 1.62/1.34 (sF12 != $false) | (sF12 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f655,plain,(
% 1.62/1.34 ((f0 @ $true) != $false) | ((f0 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f654,plain,(
% 1.62/1.34 (sF2 != $false) | ($true != sF2) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f653,plain,(
% 1.62/1.34 (sF3 != $false) | (sF3 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f652,plain,(
% 1.62/1.34 ($false != sF0) | ($true != sF0) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f651,plain,(
% 1.62/1.34 (sF1 != $false) | (sF1 != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f650,plain,(
% 1.62/1.34 ((f5 @ $false) != $false) | ($true != (f5 @ $false)) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f649,plain,(
% 1.62/1.34 ((f5 @ $true) != $false) | ((f5 @ $true) != $true) | ($true = $false)),
% 1.62/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.62/1.34 thf(f648,plain,(
% 1.62/1.34 spl27_84 | spl27_65 | spl27_76),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f37,f572,f510,f618])).
% 1.62/1.34 thf(f618,definition,(
% 1.62/1.34 spl27_84 <=> (sF17 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_84])],[avatar_definition])).
% 1.62/1.34 thf(f510,definition,(
% 1.62/1.34 spl27_65 <=> (sF18 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_65])],[avatar_definition])).
% 1.62/1.34 thf(f572,definition,(
% 1.62/1.34 spl27_76 <=> ((f4 @ $false) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_76])],[avatar_definition])).
% 1.62/1.34 thf(f37,plain,(
% 1.62/1.34 (sF17 = $true) | (sF18 = $false) | ((f4 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.34 thf(f35,plain,(
% 1.62/1.34 (sF17 = $true) | (sF18 = (f4 @ $false))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f24])).
% 1.62/1.34 thf(f24,definition,(
% 1.62/1.34 (sF18 = (f4 @ sF17))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f647,plain,(
% 1.62/1.34 spl27_67 | spl27_84 | spl27_77),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f36,f577,f618,f520])).
% 1.62/1.34 thf(f520,definition,(
% 1.62/1.34 spl27_67 <=> (sF18 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_67])],[avatar_definition])).
% 1.62/1.34 thf(f577,definition,(
% 1.62/1.34 spl27_77 <=> ((f4 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_77])],[avatar_definition])).
% 1.62/1.34 thf(f36,plain,(
% 1.62/1.34 (sF18 = $true) | ((f4 @ $false) = $false) | (sF17 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.34 thf(f646,plain,(
% 1.62/1.34 spl27_75 | spl27_65 | spl27_85),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f39,f623,f510,f567])).
% 1.62/1.34 thf(f567,definition,(
% 1.62/1.34 spl27_75 <=> ((f4 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_75])],[avatar_definition])).
% 1.62/1.34 thf(f623,definition,(
% 1.62/1.34 spl27_85 <=> (sF17 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_85])],[avatar_definition])).
% 1.62/1.34 thf(f39,plain,(
% 1.62/1.34 ((f4 @ $true) = $true) | (sF18 = $false) | (sF17 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.34 thf(f34,plain,(
% 1.62/1.34 (sF17 = $false) | (sF18 = (f4 @ $true))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f24])).
% 1.62/1.34 thf(f645,plain,(
% 1.62/1.34 spl27_67 | spl27_73 | spl27_85),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f38,f623,f558,f520])).
% 1.62/1.34 thf(f558,definition,(
% 1.62/1.34 spl27_73 <=> ((f4 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_73])],[avatar_definition])).
% 1.62/1.34 thf(f38,plain,(
% 1.62/1.34 ((f4 @ $true) = $false) | (sF18 = $true) | (sF17 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.34 thf(f644,plain,(
% 1.62/1.34 spl27_22 | spl27_77 | spl27_37),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f43,f370,f577,f297])).
% 1.62/1.34 thf(f297,definition,(
% 1.62/1.34 spl27_22 <=> (sF3 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_22])],[avatar_definition])).
% 1.62/1.34 thf(f370,definition,(
% 1.62/1.34 spl27_37 <=> ($true = sF4)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_37])],[avatar_definition])).
% 1.62/1.34 thf(f43,plain,(
% 1.62/1.34 (sF3 = $true) | ((f4 @ $false) = $false) | ($true = sF4)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.62/1.34 thf(f41,plain,(
% 1.62/1.34 (sF3 = $true) | ((f4 @ $false) = sF4)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f10])).
% 1.62/1.34 thf(f10,definition,(
% 1.62/1.34 ((f4 @ sF3) = sF4)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f643,plain,(
% 1.62/1.34 spl27_22 | spl27_76 | spl27_32),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f42,f348,f572,f297])).
% 1.62/1.34 thf(f348,definition,(
% 1.62/1.34 spl27_32 <=> ($false = sF4)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_32])],[avatar_definition])).
% 1.62/1.34 thf(f42,plain,(
% 1.62/1.34 ((f4 @ $false) = $true) | (sF3 = $true) | ($false = sF4)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.62/1.34 thf(f642,plain,(
% 1.62/1.34 spl27_73 | spl27_20 | spl27_37),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f45,f370,f288,f558])).
% 1.62/1.34 thf(f288,definition,(
% 1.62/1.34 spl27_20 <=> (sF3 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_20])],[avatar_definition])).
% 1.62/1.34 thf(f45,plain,(
% 1.62/1.34 ((f4 @ $true) = $false) | ($true = sF4) | (sF3 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.34 thf(f40,plain,(
% 1.62/1.34 ((f4 @ $true) = sF4) | (sF3 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f10])).
% 1.62/1.34 thf(f641,plain,(
% 1.62/1.34 spl27_20 | spl27_32 | spl27_75),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f44,f567,f348,f288])).
% 1.62/1.34 thf(f44,plain,(
% 1.62/1.34 ((f4 @ $true) = $true) | ($false = sF4) | (sF3 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.34 thf(f640,plain,(
% 1.62/1.34 spl27_39 | spl27_33 | spl27_81),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f49,f596,f352,f379])).
% 1.62/1.34 thf(f379,definition,(
% 1.62/1.34 spl27_39 <=> ((f3 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_39])],[avatar_definition])).
% 1.62/1.34 thf(f352,definition,(
% 1.62/1.34 spl27_33 <=> ($true = sF5)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_33])],[avatar_definition])).
% 1.62/1.34 thf(f596,definition,(
% 1.62/1.34 spl27_81 <=> ($true = sF6)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_81])],[avatar_definition])).
% 1.62/1.34 thf(f49,plain,(
% 1.62/1.34 ((f3 @ $false) = $false) | ($true = sF6) | ($true = sF5)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.62/1.34 thf(f47,plain,(
% 1.62/1.34 ($true = sF5) | ((f3 @ $false) = sF6)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f12])).
% 1.62/1.34 thf(f12,definition,(
% 1.62/1.34 ((f3 @ sF5) = sF6)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f639,plain,(
% 1.62/1.34 spl27_38 | spl27_78 | spl27_33),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f48,f352,f582,f374])).
% 1.62/1.34 thf(f374,definition,(
% 1.62/1.34 spl27_38 <=> ((f3 @ $false) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_38])],[avatar_definition])).
% 1.62/1.34 thf(f582,definition,(
% 1.62/1.34 spl27_78 <=> ($false = sF6)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_78])],[avatar_definition])).
% 1.62/1.34 thf(f48,plain,(
% 1.62/1.34 ($false = sF6) | ($true = sF5) | ((f3 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.62/1.34 thf(f638,plain,(
% 1.62/1.34 spl27_35 | spl27_81 | spl27_34),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f51,f356,f596,f361])).
% 1.62/1.34 thf(f361,definition,(
% 1.62/1.34 spl27_35 <=> (sF5 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_35])],[avatar_definition])).
% 1.62/1.34 thf(f356,definition,(
% 1.62/1.34 spl27_34 <=> ((f3 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_34])],[avatar_definition])).
% 1.62/1.34 thf(f51,plain,(
% 1.62/1.34 ((f3 @ $true) = $false) | ($true = sF6) | (sF5 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.62/1.34 thf(f46,plain,(
% 1.62/1.34 (sF5 = $false) | ((f3 @ $true) = sF6)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f12])).
% 1.62/1.34 thf(f637,plain,(
% 1.62/1.34 spl27_78 | spl27_35 | spl27_36),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f50,f365,f361,f582])).
% 1.62/1.34 thf(f365,definition,(
% 1.62/1.34 spl27_36 <=> ($true = (f3 @ $true))),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_36])],[avatar_definition])).
% 1.62/1.34 thf(f50,plain,(
% 1.62/1.34 ($true = (f3 @ $true)) | ($false = sF6) | (sF5 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.62/1.34 thf(f636,plain,(
% 1.62/1.34 spl27_47 | spl27_31 | spl27_61),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f55,f486,f339,f419])).
% 1.62/1.34 thf(f419,definition,(
% 1.62/1.34 spl27_47 <=> (sF23 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_47])],[avatar_definition])).
% 1.62/1.34 thf(f339,definition,(
% 1.62/1.34 spl27_31 <=> ($true = (f0 @ $false))),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_31])],[avatar_definition])).
% 1.62/1.34 thf(f486,definition,(
% 1.62/1.34 spl27_61 <=> (sF24 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_61])],[avatar_definition])).
% 1.62/1.34 thf(f55,plain,(
% 1.62/1.34 (sF23 = $true) | ($true = (f0 @ $false)) | (sF24 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.62/1.34 thf(f53,plain,(
% 1.62/1.34 (sF24 = (f0 @ $false)) | (sF23 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f30])).
% 1.62/1.34 thf(f30,definition,(
% 1.62/1.34 ((f0 @ sF23) = sF24)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f635,plain,(
% 1.62/1.34 spl27_47 | spl27_30 | spl27_63),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f54,f496,f334,f419])).
% 1.62/1.34 thf(f334,definition,(
% 1.62/1.34 spl27_30 <=> ((f0 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_30])],[avatar_definition])).
% 1.62/1.34 thf(f496,definition,(
% 1.62/1.34 spl27_63 <=> (sF24 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_63])],[avatar_definition])).
% 1.62/1.34 thf(f54,plain,(
% 1.62/1.34 (sF23 = $true) | (sF24 = $true) | ((f0 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.62/1.34 thf(f634,plain,(
% 1.62/1.34 spl27_63 | spl27_45 | spl27_24),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f57,f308,f410,f496])).
% 1.62/1.34 thf(f410,definition,(
% 1.62/1.34 spl27_45 <=> (sF23 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_45])],[avatar_definition])).
% 1.62/1.34 thf(f308,definition,(
% 1.62/1.34 spl27_24 <=> ((f0 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_24])],[avatar_definition])).
% 1.62/1.34 thf(f57,plain,(
% 1.62/1.34 (sF23 = $false) | ((f0 @ $true) = $false) | (sF24 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.62/1.34 thf(f52,plain,(
% 1.62/1.34 ((f0 @ $true) = sF24) | (sF23 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f30])).
% 1.62/1.34 thf(f633,plain,(
% 1.62/1.34 spl27_27 | spl27_61 | spl27_45),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f56,f410,f486,f321])).
% 1.62/1.34 thf(f321,definition,(
% 1.62/1.34 spl27_27 <=> ((f0 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_27])],[avatar_definition])).
% 1.62/1.34 thf(f56,plain,(
% 1.62/1.34 ((f0 @ $true) = $true) | (sF24 = $false) | (sF23 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.62/1.34 thf(f632,plain,(
% 1.62/1.34 spl27_70 | spl27_83 | spl27_51),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f61,f437,f612,f535])).
% 1.62/1.34 thf(f535,definition,(
% 1.62/1.34 spl27_70 <=> ($true = sF9)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_70])],[avatar_definition])).
% 1.62/1.34 thf(f612,definition,(
% 1.62/1.34 spl27_83 <=> ($true = sF10)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_83])],[avatar_definition])).
% 1.62/1.34 thf(f437,definition,(
% 1.62/1.34 spl27_51 <=> ((f1 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_51])],[avatar_definition])).
% 1.62/1.34 thf(f61,plain,(
% 1.62/1.34 ($true = sF9) | ((f1 @ $false) = $false) | ($true = sF10)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.62/1.34 thf(f59,plain,(
% 1.62/1.34 ((f1 @ $false) = sF10) | ($true = sF9)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f16])).
% 1.62/1.34 thf(f16,definition,(
% 1.62/1.34 ((f1 @ sF9) = sF10)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f631,plain,(
% 1.62/1.34 spl27_82 | spl27_49 | spl27_70),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f60,f535,f428,f606])).
% 1.62/1.34 thf(f606,definition,(
% 1.62/1.34 spl27_82 <=> (sF10 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_82])],[avatar_definition])).
% 1.62/1.34 thf(f428,definition,(
% 1.62/1.34 spl27_49 <=> ((f1 @ $false) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_49])],[avatar_definition])).
% 1.62/1.34 thf(f60,plain,(
% 1.62/1.34 ($true = sF9) | (sF10 = $false) | ((f1 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.62/1.34 thf(f630,plain,(
% 1.62/1.34 spl27_83 | spl27_69 | spl27_48),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f63,f423,f530,f612])).
% 1.62/1.34 thf(f530,definition,(
% 1.62/1.34 spl27_69 <=> (sF9 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_69])],[avatar_definition])).
% 1.62/1.34 thf(f423,definition,(
% 1.62/1.34 spl27_48 <=> ((f1 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_48])],[avatar_definition])).
% 1.62/1.34 thf(f63,plain,(
% 1.62/1.34 (sF9 = $false) | ((f1 @ $true) = $false) | ($true = sF10)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.62/1.34 thf(f58,plain,(
% 1.62/1.34 ((f1 @ $true) = sF10) | (sF9 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f16])).
% 1.62/1.34 thf(f629,plain,(
% 1.62/1.34 spl27_82 | spl27_69 | spl27_44),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f62,f406,f530,f606])).
% 1.62/1.34 thf(f406,definition,(
% 1.62/1.34 spl27_44 <=> ((f1 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_44])],[avatar_definition])).
% 1.62/1.34 thf(f62,plain,(
% 1.62/1.34 (sF10 = $false) | (sF9 = $false) | ((f1 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.62/1.34 thf(f628,plain,(
% 1.62/1.34 spl27_84 | spl27_77 | spl27_72),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f67,f554,f577,f618])).
% 1.62/1.34 thf(f554,definition,(
% 1.62/1.34 spl27_72 <=> (sF16 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_72])],[avatar_definition])).
% 1.62/1.34 thf(f67,plain,(
% 1.62/1.34 ((f4 @ $false) = $false) | (sF17 = $true) | (sF16 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.62/1.34 thf(f65,plain,(
% 1.62/1.34 ((f4 @ $false) = sF17) | (sF16 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f23])).
% 1.62/1.34 thf(f23,definition,(
% 1.62/1.34 (sF17 = (f4 @ sF16))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f627,plain,(
% 1.62/1.34 spl27_72 | spl27_76 | spl27_85),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f66,f623,f572,f554])).
% 1.62/1.34 thf(f66,plain,(
% 1.62/1.34 ((f4 @ $false) = $true) | (sF16 = $true) | (sF17 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.62/1.34 thf(f626,plain,(
% 1.62/1.34 spl27_85 | spl27_74 | spl27_75),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f69,f567,f563,f623])).
% 1.62/1.34 thf(f563,definition,(
% 1.62/1.34 spl27_74 <=> (sF16 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_74])],[avatar_definition])).
% 1.62/1.34 thf(f69,plain,(
% 1.62/1.34 ((f4 @ $true) = $true) | (sF17 = $false) | (sF16 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.62/1.34 thf(f64,plain,(
% 1.62/1.34 (sF16 = $false) | (sF17 = (f4 @ $true))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f23])).
% 1.62/1.34 thf(f621,plain,(
% 1.62/1.34 spl27_84 | spl27_73 | spl27_74),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f68,f563,f558,f618])).
% 1.62/1.34 thf(f68,plain,(
% 1.62/1.34 ((f4 @ $true) = $false) | (sF17 = $true) | (sF16 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.62/1.34 thf(f616,plain,(
% 1.62/1.34 spl27_29 | spl27_83 | spl27_51),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f73,f437,f612,f330])).
% 1.62/1.34 thf(f330,definition,(
% 1.62/1.34 spl27_29 <=> ($true = sF11)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_29])],[avatar_definition])).
% 1.62/1.34 thf(f73,plain,(
% 1.62/1.34 ((f1 @ $false) = $false) | ($true = sF10) | ($true = sF11)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.62/1.34 thf(f71,plain,(
% 1.62/1.34 ($true = sF10) | ((f1 @ $false) = sF11)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f17])).
% 1.62/1.34 thf(f17,definition,(
% 1.62/1.34 ((f1 @ sF10) = sF11)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f615,plain,(
% 1.62/1.34 spl27_49 | spl27_25 | spl27_83),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f72,f612,f312,f428])).
% 1.62/1.34 thf(f312,definition,(
% 1.62/1.34 spl27_25 <=> (sF11 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_25])],[avatar_definition])).
% 1.62/1.34 thf(f72,plain,(
% 1.62/1.34 ($true = sF10) | (sF11 = $false) | ((f1 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.62/1.34 thf(f610,plain,(
% 1.62/1.34 spl27_48 | spl27_29 | spl27_82),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f75,f606,f330,f423])).
% 1.62/1.34 thf(f75,plain,(
% 1.62/1.34 ($true = sF11) | (sF10 = $false) | ((f1 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.62/1.34 thf(f70,plain,(
% 1.62/1.34 (sF10 = $false) | ((f1 @ $true) = sF11)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f17])).
% 1.62/1.34 thf(f609,plain,(
% 1.62/1.34 spl27_82 | spl27_44 | spl27_25),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f74,f312,f406,f606])).
% 1.62/1.34 thf(f74,plain,(
% 1.62/1.34 (sF10 = $false) | (sF11 = $false) | ((f1 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.62/1.34 thf(f604,plain,(
% 1.62/1.34 spl27_71 | spl27_79 | spl27_58),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f79,f468,f586,f540])).
% 1.62/1.34 thf(f540,definition,(
% 1.62/1.34 spl27_71 <=> ($true = sF8)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_71])],[avatar_definition])).
% 1.62/1.34 thf(f586,definition,(
% 1.62/1.34 spl27_79 <=> ($true = sF7)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_79])],[avatar_definition])).
% 1.62/1.34 thf(f468,definition,(
% 1.62/1.34 spl27_58 <=> ((f2 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_58])],[avatar_definition])).
% 1.62/1.34 thf(f79,plain,(
% 1.62/1.34 ($true = sF8) | ($true = sF7) | ((f2 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.62/1.34 thf(f77,plain,(
% 1.62/1.34 ($true = sF7) | ((f2 @ $false) = sF8)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f14])).
% 1.62/1.34 thf(f14,definition,(
% 1.62/1.34 ((f2 @ sF7) = sF8)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f603,plain,(
% 1.62/1.34 spl27_59 | spl27_68 | spl27_79),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f78,f586,f526,f473])).
% 1.62/1.34 thf(f473,definition,(
% 1.62/1.34 spl27_59 <=> ($true = (f2 @ $false))),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_59])],[avatar_definition])).
% 1.62/1.34 thf(f526,definition,(
% 1.62/1.34 spl27_68 <=> (sF8 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_68])],[avatar_definition])).
% 1.62/1.34 thf(f78,plain,(
% 1.62/1.34 ($true = sF7) | (sF8 = $false) | ($true = (f2 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.62/1.34 thf(f602,plain,(
% 1.62/1.34 spl27_80 | spl27_56 | spl27_71),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f81,f540,f459,f591])).
% 1.62/1.34 thf(f591,definition,(
% 1.62/1.34 spl27_80 <=> (sF7 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_80])],[avatar_definition])).
% 1.62/1.34 thf(f459,definition,(
% 1.62/1.34 spl27_56 <=> ((f2 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_56])],[avatar_definition])).
% 1.62/1.34 thf(f81,plain,(
% 1.62/1.34 ((f2 @ $true) = $false) | ($true = sF8) | (sF7 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.62/1.34 thf(f76,plain,(
% 1.62/1.34 (sF7 = $false) | ((f2 @ $true) = sF8)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f14])).
% 1.62/1.34 thf(f601,plain,(
% 1.62/1.34 spl27_68 | spl27_80 | spl27_52),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f80,f442,f591,f526])).
% 1.62/1.34 thf(f442,definition,(
% 1.62/1.34 spl27_52 <=> ((f2 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_52])],[avatar_definition])).
% 1.62/1.34 thf(f80,plain,(
% 1.62/1.34 ((f2 @ $true) = $true) | (sF8 = $false) | (sF7 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.62/1.34 thf(f600,plain,(
% 1.62/1.34 spl27_79 | spl27_81 | spl27_39),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f85,f379,f596,f586])).
% 1.62/1.34 thf(f85,plain,(
% 1.62/1.34 ($true = sF6) | ($true = sF7) | ((f3 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.62/1.34 thf(f83,plain,(
% 1.62/1.34 ((f3 @ $false) = sF7) | ($true = sF6)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f13])).
% 1.62/1.34 thf(f13,definition,(
% 1.62/1.34 ((f3 @ sF6) = sF7)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f599,plain,(
% 1.62/1.34 spl27_38 | spl27_81 | spl27_80),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f84,f591,f596,f374])).
% 1.62/1.34 thf(f84,plain,(
% 1.62/1.34 ($true = sF6) | (sF7 = $false) | ((f3 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.62/1.34 thf(f594,plain,(
% 1.62/1.34 spl27_36 | spl27_80 | spl27_78),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f87,f582,f591,f365])).
% 1.62/1.34 thf(f87,plain,(
% 1.62/1.34 ($true = (f3 @ $true)) | (sF7 = $false) | ($false = sF6)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.62/1.34 thf(f82,plain,(
% 1.62/1.34 (sF7 = (f3 @ $true)) | ($false = sF6)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f13])).
% 1.62/1.34 thf(f589,plain,(
% 1.62/1.34 spl27_78 | spl27_79 | spl27_34),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f86,f356,f586,f582])).
% 1.62/1.34 thf(f86,plain,(
% 1.62/1.34 ($true = sF7) | ($false = sF6) | ((f3 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.62/1.34 thf(f580,plain,(
% 1.62/1.34 spl27_5 | spl27_77 | spl27_72),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f91,f554,f577,f216])).
% 1.62/1.34 thf(f216,definition,(
% 1.62/1.34 spl27_5 <=> ($true = sF15)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_5])],[avatar_definition])).
% 1.62/1.34 thf(f91,plain,(
% 1.62/1.34 ((f4 @ $false) = $false) | ($true = sF15) | (sF16 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.62/1.34 thf(f89,plain,(
% 1.62/1.34 ($true = sF15) | ((f4 @ $false) = sF16)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f22])).
% 1.62/1.34 thf(f22,definition,(
% 1.62/1.34 (sF16 = (f4 @ sF15))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f575,plain,(
% 1.62/1.34 spl27_5 | spl27_76 | spl27_74),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f90,f563,f572,f216])).
% 1.62/1.34 thf(f90,plain,(
% 1.62/1.34 (sF16 = $false) | ((f4 @ $false) = $true) | ($true = sF15)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.62/1.34 thf(f570,plain,(
% 1.62/1.34 spl27_2 | spl27_74 | spl27_75),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f93,f567,f563,f203])).
% 1.62/1.34 thf(f203,definition,(
% 1.62/1.34 spl27_2 <=> (sF15 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_2])],[avatar_definition])).
% 1.62/1.34 thf(f93,plain,(
% 1.62/1.34 (sF16 = $false) | ((f4 @ $true) = $true) | (sF15 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.62/1.34 thf(f88,plain,(
% 1.62/1.34 (sF15 = $false) | (sF16 = (f4 @ $true))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f22])).
% 1.62/1.34 thf(f561,plain,(
% 1.62/1.34 spl27_72 | spl27_73 | spl27_2),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f92,f203,f558,f554])).
% 1.62/1.34 thf(f92,plain,(
% 1.62/1.34 (sF16 = $true) | (sF15 = $false) | ((f4 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.62/1.34 thf(f552,plain,(
% 1.62/1.34 spl27_11 | spl27_8 | spl27_21),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f97,f292,f230,f244])).
% 1.62/1.34 thf(f244,definition,(
% 1.62/1.34 spl27_11 <=> (sF1 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_11])],[avatar_definition])).
% 1.62/1.34 thf(f230,definition,(
% 1.62/1.34 spl27_8 <=> ($true = (f5 @ $false))),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_8])],[avatar_definition])).
% 1.62/1.34 thf(f292,definition,(
% 1.62/1.34 spl27_21 <=> (sF2 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_21])],[avatar_definition])).
% 1.62/1.34 thf(f97,plain,(
% 1.62/1.34 ($true = (f5 @ $false)) | (sF1 = $true) | (sF2 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.62/1.34 thf(f95,plain,(
% 1.62/1.34 (sF1 = $true) | (sF2 = (f5 @ $false))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f8])).
% 1.62/1.34 thf(f8,definition,(
% 1.62/1.34 ((f5 @ sF1) = sF2)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f551,plain,(
% 1.62/1.34 spl27_7 | spl27_11 | spl27_23),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f96,f302,f244,f225])).
% 1.62/1.34 thf(f225,definition,(
% 1.62/1.34 spl27_7 <=> ((f5 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_7])],[avatar_definition])).
% 1.62/1.34 thf(f302,definition,(
% 1.62/1.34 spl27_23 <=> ($true = sF2)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_23])],[avatar_definition])).
% 1.62/1.34 thf(f96,plain,(
% 1.62/1.34 ((f5 @ $false) = $false) | ($true = sF2) | (sF1 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.62/1.34 thf(f550,plain,(
% 1.62/1.34 spl27_23 | spl27_4 | spl27_10),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f99,f239,f212,f302])).
% 1.62/1.34 thf(f212,definition,(
% 1.62/1.34 spl27_4 <=> ((f5 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_4])],[avatar_definition])).
% 1.62/1.34 thf(f239,definition,(
% 1.62/1.34 spl27_10 <=> (sF1 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_10])],[avatar_definition])).
% 1.62/1.34 thf(f99,plain,(
% 1.62/1.34 ($true = sF2) | (sF1 = $false) | ((f5 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.62/1.34 thf(f94,plain,(
% 1.62/1.34 ((f5 @ $true) = sF2) | (sF1 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f8])).
% 1.62/1.34 thf(f549,plain,(
% 1.62/1.34 spl27_10 | spl27_3 | spl27_21),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f98,f292,f207,f239])).
% 1.62/1.34 thf(f207,definition,(
% 1.62/1.34 spl27_3 <=> ((f5 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_3])],[avatar_definition])).
% 1.62/1.34 thf(f98,plain,(
% 1.62/1.34 ((f5 @ $true) = $true) | (sF2 = $false) | (sF1 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.62/1.34 thf(f548,plain,(
% 1.62/1.34 spl27_64 | spl27_54 | spl27_59),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f103,f473,f450,f506])).
% 1.62/1.34 thf(f506,definition,(
% 1.62/1.34 spl27_64 <=> (sF19 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_64])],[avatar_definition])).
% 1.62/1.34 thf(f450,definition,(
% 1.62/1.34 spl27_54 <=> (sF20 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_54])],[avatar_definition])).
% 1.62/1.34 thf(f103,plain,(
% 1.62/1.34 ($true = (f2 @ $false)) | (sF20 = $false) | (sF19 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.62/1.34 thf(f101,plain,(
% 1.62/1.34 (sF20 = (f2 @ $false)) | (sF19 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f26])).
% 1.62/1.34 thf(f26,definition,(
% 1.62/1.34 ((f2 @ sF19) = sF20)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f547,plain,(
% 1.62/1.34 spl27_57 | spl27_58 | spl27_64),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f102,f506,f468,f464])).
% 1.62/1.34 thf(f464,definition,(
% 1.62/1.34 spl27_57 <=> ($true = sF20)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_57])],[avatar_definition])).
% 1.62/1.34 thf(f102,plain,(
% 1.62/1.34 ($true = sF20) | (sF19 = $true) | ((f2 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.62/1.34 thf(f546,plain,(
% 1.62/1.34 spl27_56 | spl27_66 | spl27_57),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f105,f464,f515,f459])).
% 1.62/1.34 thf(f515,definition,(
% 1.62/1.34 spl27_66 <=> (sF19 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_66])],[avatar_definition])).
% 1.62/1.34 thf(f105,plain,(
% 1.62/1.34 ($true = sF20) | (sF19 = $false) | ((f2 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.62/1.34 thf(f100,plain,(
% 1.62/1.34 (sF19 = $false) | ((f2 @ $true) = sF20)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f26])).
% 1.62/1.34 thf(f545,plain,(
% 1.62/1.34 spl27_66 | spl27_52 | spl27_54),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f104,f450,f442,f515])).
% 1.62/1.34 thf(f104,plain,(
% 1.62/1.34 (sF20 = $false) | (sF19 = $false) | ((f2 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.62/1.34 thf(f544,plain,(
% 1.62/1.34 spl27_51 | spl27_71 | spl27_70),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f109,f535,f540,f437])).
% 1.62/1.34 thf(f109,plain,(
% 1.62/1.34 ((f1 @ $false) = $false) | ($true = sF8) | ($true = sF9)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.62/1.34 thf(f107,plain,(
% 1.62/1.34 ((f1 @ $false) = sF9) | ($true = sF8)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f15])).
% 1.62/1.34 thf(f15,definition,(
% 1.62/1.34 ((f1 @ sF8) = sF9)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f543,plain,(
% 1.62/1.34 spl27_69 | spl27_49 | spl27_71),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f108,f540,f428,f530])).
% 1.62/1.34 thf(f108,plain,(
% 1.62/1.34 ($true = sF8) | ((f1 @ $false) = $true) | (sF9 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.62/1.34 thf(f538,plain,(
% 1.62/1.34 spl27_48 | spl27_68 | spl27_70),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f111,f535,f526,f423])).
% 1.62/1.34 thf(f111,plain,(
% 1.62/1.34 (sF8 = $false) | ((f1 @ $true) = $false) | ($true = sF9)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.62/1.34 thf(f106,plain,(
% 1.62/1.34 (sF8 = $false) | ((f1 @ $true) = sF9)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f15])).
% 1.62/1.34 thf(f533,plain,(
% 1.62/1.34 spl27_68 | spl27_69 | spl27_44),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f110,f406,f530,f526])).
% 1.62/1.34 thf(f110,plain,(
% 1.62/1.34 (sF9 = $false) | ((f1 @ $true) = $true) | (sF8 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.62/1.34 thf(f524,plain,(
% 1.62/1.34 spl27_38 | spl27_67 | spl27_66),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f115,f515,f520,f374])).
% 1.62/1.34 thf(f115,plain,(
% 1.62/1.34 (sF18 = $true) | (sF19 = $false) | ((f3 @ $false) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.62/1.34 thf(f113,plain,(
% 1.62/1.34 (sF19 = (f3 @ $false)) | (sF18 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f25])).
% 1.62/1.34 thf(f25,definition,(
% 1.62/1.34 (sF19 = (f3 @ sF18))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f523,plain,(
% 1.62/1.34 spl27_39 | spl27_64 | spl27_67),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f114,f520,f506,f379])).
% 1.62/1.34 thf(f114,plain,(
% 1.62/1.34 ((f3 @ $false) = $false) | (sF18 = $true) | (sF19 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.62/1.34 thf(f518,plain,(
% 1.62/1.34 spl27_65 | spl27_36 | spl27_66),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f117,f515,f365,f510])).
% 1.62/1.34 thf(f117,plain,(
% 1.62/1.34 ($true = (f3 @ $true)) | (sF18 = $false) | (sF19 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.62/1.34 thf(f112,plain,(
% 1.62/1.34 (sF19 = (f3 @ $true)) | (sF18 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f25])).
% 1.62/1.34 thf(f513,plain,(
% 1.62/1.34 spl27_34 | spl27_64 | spl27_65),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f116,f510,f506,f356])).
% 1.62/1.34 thf(f116,plain,(
% 1.62/1.34 ((f3 @ $true) = $false) | (sF19 = $true) | (sF18 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.62/1.34 thf(f504,plain,(
% 1.62/1.34 spl27_31 | spl27_43 | spl27_62),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f121,f491,f401,f339])).
% 1.62/1.34 thf(f401,definition,(
% 1.62/1.34 spl27_43 <=> (sF26 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_43])],[avatar_definition])).
% 1.62/1.34 thf(f491,definition,(
% 1.62/1.34 spl27_62 <=> ($true = sF25)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_62])],[avatar_definition])).
% 1.62/1.34 thf(f121,plain,(
% 1.62/1.34 ($true = sF25) | (sF26 = $false) | ($true = (f0 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.62/1.34 thf(f119,plain,(
% 1.62/1.34 ($true = sF25) | (sF26 = (f0 @ $false))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f32])).
% 1.62/1.34 thf(f32,definition,(
% 1.62/1.34 ((f0 @ sF25) = sF26)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f503,plain,(
% 1.62/1.34 spl27_30 | spl27_42 | spl27_62),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f120,f491,f396,f334])).
% 1.62/1.34 thf(f396,definition,(
% 1.62/1.34 spl27_42 <=> ($true = sF26)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_42])],[avatar_definition])).
% 1.62/1.34 thf(f120,plain,(
% 1.62/1.34 ($true = sF26) | ((f0 @ $false) = $false) | ($true = sF25)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.62/1.34 thf(f502,plain,(
% 1.62/1.34 spl27_60 | spl27_42 | spl27_24),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f123,f308,f396,f482])).
% 1.62/1.34 thf(f482,definition,(
% 1.62/1.34 spl27_60 <=> (sF25 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_60])],[avatar_definition])).
% 1.62/1.34 thf(f123,plain,(
% 1.62/1.34 ((f0 @ $true) = $false) | ($true = sF26) | (sF25 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.62/1.34 thf(f118,plain,(
% 1.62/1.34 ((f0 @ $true) = sF26) | (sF25 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f32])).
% 1.62/1.34 thf(f501,plain,(
% 1.62/1.34 spl27_27 | spl27_43 | spl27_60),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f122,f482,f401,f321])).
% 1.62/1.34 thf(f122,plain,(
% 1.62/1.34 (sF26 = $false) | ((f0 @ $true) = $true) | (sF25 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.62/1.34 thf(f500,plain,(
% 1.62/1.34 spl27_62 | spl27_30 | spl27_63),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f127,f496,f334,f491])).
% 1.62/1.34 thf(f127,plain,(
% 1.62/1.34 (sF24 = $true) | ($true = sF25) | ((f0 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.62/1.34 thf(f125,plain,(
% 1.62/1.34 ((f0 @ $false) = sF25) | (sF24 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f31])).
% 1.62/1.34 thf(f31,definition,(
% 1.62/1.34 ((f0 @ sF24) = sF25)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f499,plain,(
% 1.62/1.34 spl27_31 | spl27_60 | spl27_63),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f126,f496,f482,f339])).
% 1.62/1.34 thf(f126,plain,(
% 1.62/1.34 (sF25 = $false) | (sF24 = $true) | ($true = (f0 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.62/1.34 thf(f494,plain,(
% 1.62/1.34 spl27_62 | spl27_61 | spl27_24),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f129,f308,f486,f491])).
% 1.62/1.34 thf(f129,plain,(
% 1.62/1.34 ((f0 @ $true) = $false) | (sF24 = $false) | ($true = sF25)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.62/1.34 thf(f124,plain,(
% 1.62/1.34 ((f0 @ $true) = sF25) | (sF24 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f31])).
% 1.62/1.34 thf(f489,plain,(
% 1.62/1.34 spl27_27 | spl27_60 | spl27_61),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f128,f486,f482,f321])).
% 1.62/1.34 thf(f128,plain,(
% 1.62/1.34 (sF25 = $false) | ((f0 @ $true) = $true) | (sF24 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.62/1.34 thf(f480,plain,(
% 1.62/1.34 spl27_46 | spl27_55 | spl27_59),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f133,f473,f455,f414])).
% 1.62/1.34 thf(f414,definition,(
% 1.62/1.34 spl27_46 <=> (sF22 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_46])],[avatar_definition])).
% 1.62/1.34 thf(f455,definition,(
% 1.62/1.34 spl27_55 <=> (sF21 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_55])],[avatar_definition])).
% 1.62/1.34 thf(f133,plain,(
% 1.62/1.34 (sF21 = $true) | ($true = (f2 @ $false)) | (sF22 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.62/1.34 thf(f131,plain,(
% 1.62/1.34 (sF22 = (f2 @ $false)) | (sF21 = $true)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f28])).
% 1.62/1.34 thf(f28,definition,(
% 1.62/1.34 (sF22 = (f2 @ sF21))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f479,plain,(
% 1.62/1.34 spl27_55 | spl27_58 | spl27_50),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f132,f432,f468,f455])).
% 1.62/1.34 thf(f432,definition,(
% 1.62/1.34 spl27_50 <=> (sF22 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_50])],[avatar_definition])).
% 1.62/1.34 thf(f132,plain,(
% 1.62/1.34 (sF21 = $true) | (sF22 = $true) | ((f2 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.62/1.34 thf(f478,plain,(
% 1.62/1.34 spl27_50 | spl27_53 | spl27_56),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f135,f459,f446,f432])).
% 1.62/1.34 thf(f446,definition,(
% 1.62/1.34 spl27_53 <=> (sF21 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_53])],[avatar_definition])).
% 1.62/1.34 thf(f135,plain,(
% 1.62/1.34 (sF21 = $false) | (sF22 = $true) | ((f2 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.62/1.34 thf(f130,plain,(
% 1.62/1.34 (sF21 = $false) | ((f2 @ $true) = sF22)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f28])).
% 1.62/1.34 thf(f477,plain,(
% 1.62/1.34 spl27_52 | spl27_46 | spl27_53),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f134,f446,f414,f442])).
% 1.62/1.34 thf(f134,plain,(
% 1.62/1.34 (sF22 = $false) | (sF21 = $false) | ((f2 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.62/1.34 thf(f476,plain,(
% 1.62/1.34 spl27_57 | spl27_59 | spl27_53),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f139,f446,f473,f464])).
% 1.62/1.34 thf(f139,plain,(
% 1.62/1.34 ($true = (f2 @ $false)) | (sF21 = $false) | ($true = sF20)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.62/1.34 thf(f137,plain,(
% 1.62/1.34 ($true = sF20) | (sF21 = (f2 @ $false))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f27])).
% 1.62/1.34 thf(f27,definition,(
% 1.62/1.34 (sF21 = (f2 @ sF20))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f471,plain,(
% 1.62/1.34 spl27_57 | spl27_58 | spl27_55),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f138,f455,f468,f464])).
% 1.62/1.34 thf(f138,plain,(
% 1.62/1.34 ((f2 @ $false) = $false) | (sF21 = $true) | ($true = sF20)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.62/1.34 thf(f462,plain,(
% 1.62/1.34 spl27_55 | spl27_56 | spl27_54),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f141,f450,f459,f455])).
% 1.62/1.34 thf(f141,plain,(
% 1.62/1.34 (sF20 = $false) | ((f2 @ $true) = $false) | (sF21 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.62/1.34 thf(f136,plain,(
% 1.62/1.34 ((f2 @ $true) = sF21) | (sF20 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f27])).
% 1.62/1.34 thf(f453,plain,(
% 1.62/1.34 spl27_52 | spl27_53 | spl27_54),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f140,f450,f446,f442])).
% 1.62/1.34 thf(f140,plain,(
% 1.62/1.34 (sF20 = $false) | (sF21 = $false) | ((f2 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.62/1.34 thf(f440,plain,(
% 1.62/1.34 spl27_47 | spl27_51 | spl27_50),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f145,f432,f437,f419])).
% 1.62/1.34 thf(f145,plain,(
% 1.62/1.34 (sF23 = $true) | ((f1 @ $false) = $false) | (sF22 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.62/1.34 thf(f143,plain,(
% 1.62/1.34 (sF22 = $true) | ((f1 @ $false) = sF23)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f29])).
% 1.62/1.34 thf(f29,definition,(
% 1.62/1.34 (sF23 = (f1 @ sF22))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f435,plain,(
% 1.62/1.34 spl27_49 | spl27_50 | spl27_45),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f144,f410,f432,f428])).
% 1.62/1.34 thf(f144,plain,(
% 1.62/1.34 ((f1 @ $false) = $true) | (sF22 = $true) | (sF23 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.62/1.34 thf(f426,plain,(
% 1.62/1.34 spl27_47 | spl27_46 | spl27_48),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f147,f423,f414,f419])).
% 1.62/1.34 thf(f147,plain,(
% 1.62/1.34 (sF23 = $true) | (sF22 = $false) | ((f1 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.62/1.34 thf(f142,plain,(
% 1.62/1.34 ((f1 @ $true) = sF23) | (sF22 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f29])).
% 1.62/1.34 thf(f417,plain,(
% 1.62/1.34 spl27_44 | spl27_45 | spl27_46),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f146,f414,f410,f406])).
% 1.62/1.34 thf(f146,plain,(
% 1.62/1.34 ((f1 @ $true) = $true) | (sF22 = $false) | (sF23 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.62/1.34 thf(f404,plain,(
% 1.62/1.34 spl27_43 | spl27_28),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f149,f325,f401])).
% 1.62/1.34 thf(f325,definition,(
% 1.62/1.34 spl27_28 <=> (sF12 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_28])],[avatar_definition])).
% 1.62/1.34 thf(f149,plain,(
% 1.62/1.34 (sF26 = $false) | (sF12 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.34 thf(f33,plain,(
% 1.62/1.34 (sF12 != sF26)),
% 1.62/1.34 inference(definition_folding,[status(thm)],[f5,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f6,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6])).
% 1.62/1.34 thf(f7,definition,(
% 1.62/1.34 (sF1 = (f5 @ sF0))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f9,definition,(
% 1.62/1.34 (sF3 = (f5 @ sF2))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f11,definition,(
% 1.62/1.34 ((f3 @ sF4) = sF5)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f18,definition,(
% 1.62/1.34 (sF12 = (f0 @ sF11))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f6,definition,(
% 1.62/1.34 ((f6 @ x) = sF0)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f19,definition,(
% 1.62/1.34 (sF13 = (f6 @ sF0))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f20,definition,(
% 1.62/1.34 ((f6 @ sF13) = sF14)),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f21,definition,(
% 1.62/1.34 (sF15 = (f5 @ sF14))),
% 1.62/1.34 introduced(definition,[],[function_definition])).
% 1.62/1.34 thf(f5,plain,(
% 1.62/1.34 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ (f6 @ x))))))))))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ (f6 @ (f6 @ (f6 @ x))))))))))))))))),
% 1.62/1.34 inference(cnf_transformation,[status(thm)],[f4])).
% 1.62/1.34 thf(f4,plain,(
% 1.62/1.34 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ (f6 @ x))))))))))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ (f6 @ (f6 @ (f6 @ x))))))))))))))))),
% 1.62/1.34 inference(flattening,[status(thm)],[f2])).
% 1.62/1.34 thf(f2,negated_conjecture,(
% 1.62/1.34 ~((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ (f6 @ x))))))))))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ (f6 @ (f6 @ (f6 @ x))))))))))))))))),
% 1.62/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.34 thf(f1,conjecture,(
% 1.62/1.34 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ (f6 @ x))))))))))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ (f6 @ (f6 @ (f6 @ x))))))))))))))))),
% 1.62/1.34 file('/export/starexec/sandbox/tmp/tmp.NVo8B1ETwb/DTF2THF_4968.p',kaminski7)).
% 1.62/1.34 thf(f399,plain,(
% 1.62/1.34 spl27_26 | spl27_42),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f148,f396,f316])).
% 1.62/1.34 thf(f316,definition,(
% 1.62/1.34 spl27_26 <=> (sF12 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_26])],[avatar_definition])).
% 1.62/1.34 thf(f148,plain,(
% 1.62/1.34 (sF12 = $true) | ($true = sF26)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.34 thf(f394,plain,(
% 1.62/1.34 spl27_41 | spl27_12 | spl27_17),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f153,f273,f249,f390])).
% 1.62/1.34 thf(f390,definition,(
% 1.62/1.34 spl27_41 <=> (x = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_41])],[avatar_definition])).
% 1.62/1.34 thf(f249,definition,(
% 1.62/1.34 spl27_12 <=> ($true = sF0)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_12])],[avatar_definition])).
% 1.62/1.34 thf(f273,definition,(
% 1.62/1.34 spl27_17 <=> ((f6 @ $false) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_17])],[avatar_definition])).
% 1.62/1.34 thf(f153,plain,(
% 1.62/1.34 ((f6 @ $false) = $false) | ($true = sF0) | (x = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.62/1.34 thf(f151,plain,(
% 1.62/1.34 (x = $true) | ((f6 @ $false) = sF0)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f6])).
% 1.62/1.34 thf(f393,plain,(
% 1.62/1.34 spl27_41 | spl27_9 | spl27_18),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f152,f278,f235,f390])).
% 1.62/1.34 thf(f235,definition,(
% 1.62/1.34 spl27_9 <=> ($false = sF0)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_9])],[avatar_definition])).
% 1.62/1.34 thf(f278,definition,(
% 1.62/1.34 spl27_18 <=> ($true = (f6 @ $false))),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_18])],[avatar_definition])).
% 1.62/1.34 thf(f152,plain,(
% 1.62/1.34 (x = $true) | ($false = sF0) | ($true = (f6 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.62/1.34 thf(f388,plain,(
% 1.62/1.34 spl27_12 | spl27_40 | spl27_14),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f155,f259,f384,f249])).
% 1.62/1.34 thf(f384,definition,(
% 1.62/1.34 spl27_40 <=> (x = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_40])],[avatar_definition])).
% 1.62/1.34 thf(f259,definition,(
% 1.62/1.34 spl27_14 <=> ((f6 @ $true) = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_14])],[avatar_definition])).
% 1.62/1.34 thf(f155,plain,(
% 1.62/1.34 (x = $false) | ($true = sF0) | ((f6 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.62/1.34 thf(f150,plain,(
% 1.62/1.34 (x = $false) | ((f6 @ $true) = sF0)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f6])).
% 1.62/1.34 thf(f387,plain,(
% 1.62/1.34 spl27_9 | spl27_15 | spl27_40),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f154,f384,f264,f235])).
% 1.62/1.34 thf(f264,definition,(
% 1.62/1.34 spl27_15 <=> ((f6 @ $true) = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_15])],[avatar_definition])).
% 1.62/1.34 thf(f154,plain,(
% 1.62/1.34 (x = $false) | ($false = sF0) | ((f6 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.62/1.34 thf(f382,plain,(
% 1.62/1.34 spl27_39 | spl27_37 | spl27_33),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f159,f352,f370,f379])).
% 1.62/1.34 thf(f159,plain,(
% 1.62/1.34 ((f3 @ $false) = $false) | ($true = sF4) | ($true = sF5)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.62/1.34 thf(f157,plain,(
% 1.62/1.34 ((f3 @ $false) = sF5) | ($true = sF4)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f11])).
% 1.62/1.34 thf(f377,plain,(
% 1.62/1.34 spl27_35 | spl27_37 | spl27_38),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f158,f374,f370,f361])).
% 1.62/1.34 thf(f158,plain,(
% 1.62/1.34 ((f3 @ $false) = $true) | (sF5 = $false) | ($true = sF4)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.62/1.34 thf(f368,plain,(
% 1.62/1.34 spl27_35 | spl27_36 | spl27_32),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f161,f348,f365,f361])).
% 1.62/1.34 thf(f161,plain,(
% 1.62/1.34 ($true = (f3 @ $true)) | ($false = sF4) | (sF5 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.62/1.34 thf(f156,plain,(
% 1.62/1.34 ($false = sF4) | (sF5 = (f3 @ $true))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f11])).
% 1.62/1.34 thf(f359,plain,(
% 1.62/1.34 spl27_32 | spl27_33 | spl27_34),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f160,f356,f352,f348])).
% 1.62/1.34 thf(f160,plain,(
% 1.62/1.34 ($true = sF5) | ($false = sF4) | ((f3 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.62/1.34 thf(f346,plain,(
% 1.62/1.34 spl27_13 | spl27_17 | spl27_6),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f165,f221,f273,f255])).
% 1.62/1.34 thf(f255,definition,(
% 1.62/1.34 spl27_13 <=> (sF13 = $true)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_13])],[avatar_definition])).
% 1.62/1.34 thf(f221,definition,(
% 1.62/1.34 spl27_6 <=> ($true = sF14)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_6])],[avatar_definition])).
% 1.62/1.34 thf(f165,plain,(
% 1.62/1.34 ($true = sF14) | ((f6 @ $false) = $false) | (sF13 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.62/1.34 thf(f163,plain,(
% 1.62/1.34 (sF13 = $true) | ((f6 @ $false) = sF14)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f20])).
% 1.62/1.34 thf(f345,plain,(
% 1.62/1.34 spl27_18 | spl27_13 | spl27_1),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f164,f199,f255,f278])).
% 1.62/1.34 thf(f199,definition,(
% 1.62/1.34 spl27_1 <=> (sF14 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_1])],[avatar_definition])).
% 1.62/1.34 thf(f164,plain,(
% 1.62/1.34 (sF13 = $true) | (sF14 = $false) | ($true = (f6 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.62/1.34 thf(f344,plain,(
% 1.62/1.34 spl27_14 | spl27_6 | spl27_16),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f167,f268,f221,f259])).
% 1.62/1.34 thf(f268,definition,(
% 1.62/1.34 spl27_16 <=> (sF13 = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_16])],[avatar_definition])).
% 1.62/1.34 thf(f167,plain,(
% 1.62/1.34 ($true = sF14) | ((f6 @ $true) = $false) | (sF13 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.62/1.34 thf(f162,plain,(
% 1.62/1.34 ((f6 @ $true) = sF14) | (sF13 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f20])).
% 1.62/1.34 thf(f343,plain,(
% 1.62/1.34 spl27_16 | spl27_15 | spl27_1),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f166,f199,f264,f268])).
% 1.62/1.34 thf(f166,plain,(
% 1.62/1.34 (sF13 = $false) | (sF14 = $false) | ((f6 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.62/1.34 thf(f342,plain,(
% 1.62/1.34 spl27_29 | spl27_31 | spl27_28),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f171,f325,f339,f330])).
% 1.62/1.34 thf(f171,plain,(
% 1.62/1.34 ($true = sF11) | (sF12 = $false) | ($true = (f0 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 1.62/1.34 thf(f169,plain,(
% 1.62/1.34 ($true = sF11) | (sF12 = (f0 @ $false))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f18])).
% 1.62/1.34 thf(f337,plain,(
% 1.62/1.34 spl27_29 | spl27_30 | spl27_26),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f170,f316,f334,f330])).
% 1.62/1.34 thf(f170,plain,(
% 1.62/1.34 ($true = sF11) | ((f0 @ $false) = $false) | (sF12 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 1.62/1.34 thf(f328,plain,(
% 1.62/1.34 spl27_25 | spl27_27 | spl27_28),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f173,f325,f321,f312])).
% 1.62/1.34 thf(f173,plain,(
% 1.62/1.34 (sF11 = $false) | (sF12 = $false) | ((f0 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 1.62/1.34 thf(f168,plain,(
% 1.62/1.34 (sF11 = $false) | (sF12 = (f0 @ $true))),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f18])).
% 1.62/1.34 thf(f319,plain,(
% 1.62/1.34 spl27_24 | spl27_25 | spl27_26),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f172,f316,f312,f308])).
% 1.62/1.34 thf(f172,plain,(
% 1.62/1.34 (sF12 = $true) | ((f0 @ $true) = $false) | (sF11 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 1.62/1.34 thf(f306,plain,(
% 1.62/1.34 spl27_23 | spl27_8 | spl27_20),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f177,f288,f230,f302])).
% 1.62/1.34 thf(f177,plain,(
% 1.62/1.34 ($true = sF2) | ($true = (f5 @ $false)) | (sF3 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.62/1.34 thf(f175,plain,(
% 1.62/1.34 (sF3 = (f5 @ $false)) | ($true = sF2)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f9])).
% 1.62/1.34 thf(f305,plain,(
% 1.62/1.34 spl27_22 | spl27_7 | spl27_23),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f176,f302,f225,f297])).
% 1.62/1.34 thf(f176,plain,(
% 1.62/1.34 ($true = sF2) | (sF3 = $true) | ((f5 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.62/1.34 thf(f300,plain,(
% 1.62/1.34 spl27_22 | spl27_21 | spl27_4),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f179,f212,f292,f297])).
% 1.62/1.34 thf(f179,plain,(
% 1.62/1.34 (sF2 = $false) | ((f5 @ $true) = $false) | (sF3 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.62/1.34 thf(f174,plain,(
% 1.62/1.34 ((f5 @ $true) = sF3) | (sF2 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f9])).
% 1.62/1.34 thf(f295,plain,(
% 1.62/1.34 spl27_20 | spl27_21 | spl27_3),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f178,f207,f292,f288])).
% 1.62/1.34 thf(f178,plain,(
% 1.62/1.34 (sF3 = $false) | ((f5 @ $true) = $true) | (sF2 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.62/1.34 thf(f286,plain,(
% 1.62/1.34 ~spl27_19),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f3,f283])).
% 1.62/1.34 thf(f283,definition,(
% 1.62/1.34 spl27_19 <=> ($true = $false)),
% 1.62/1.34 introduced(definition,[new_symbols(naming,[spl27_19])],[avatar_definition])).
% 1.62/1.34 thf(f3,plain,(
% 1.62/1.34 ($true != $false)),
% 1.62/1.34 introduced(definition,[],[fool_axiom])).
% 1.62/1.34 thf(f281,plain,(
% 1.62/1.34 spl27_18 | spl27_12 | spl27_16),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f183,f268,f249,f278])).
% 1.62/1.34 thf(f183,plain,(
% 1.62/1.34 (sF13 = $false) | ($true = (f6 @ $false)) | ($true = sF0)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.62/1.34 thf(f181,plain,(
% 1.62/1.34 (sF13 = (f6 @ $false)) | ($true = sF0)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f19])).
% 1.62/1.34 thf(f276,plain,(
% 1.62/1.34 spl27_13 | spl27_12 | spl27_17),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f182,f273,f249,f255])).
% 1.62/1.34 thf(f182,plain,(
% 1.62/1.34 ((f6 @ $false) = $false) | ($true = sF0) | (sF13 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.62/1.34 thf(f271,plain,(
% 1.62/1.34 spl27_15 | spl27_9 | spl27_16),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f185,f268,f235,f264])).
% 1.62/1.34 thf(f185,plain,(
% 1.62/1.34 ($false = sF0) | ((f6 @ $true) = $true) | (sF13 = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.62/1.34 thf(f180,plain,(
% 1.62/1.34 (sF13 = (f6 @ $true)) | ($false = sF0)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f19])).
% 1.62/1.34 thf(f262,plain,(
% 1.62/1.34 spl27_13 | spl27_14 | spl27_9),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f184,f235,f259,f255])).
% 1.62/1.34 thf(f184,plain,(
% 1.62/1.34 ((f6 @ $true) = $false) | (sF13 = $true) | ($false = sF0)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.62/1.34 thf(f253,plain,(
% 1.62/1.34 spl27_12 | spl27_8 | spl27_10),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f189,f239,f230,f249])).
% 1.62/1.34 thf(f189,plain,(
% 1.62/1.34 ($true = sF0) | (sF1 = $false) | ($true = (f5 @ $false))),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.62/1.34 thf(f187,plain,(
% 1.62/1.34 (sF1 = (f5 @ $false)) | ($true = sF0)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f7])).
% 1.62/1.34 thf(f252,plain,(
% 1.62/1.34 spl27_7 | spl27_12 | spl27_11),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f188,f244,f249,f225])).
% 1.62/1.34 thf(f188,plain,(
% 1.62/1.34 ((f5 @ $false) = $false) | (sF1 = $true) | ($true = sF0)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.62/1.34 thf(f247,plain,(
% 1.62/1.34 spl27_4 | spl27_11 | spl27_9),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f191,f235,f244,f212])).
% 1.62/1.34 thf(f191,plain,(
% 1.62/1.34 ($false = sF0) | ((f5 @ $true) = $false) | (sF1 = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.62/1.34 thf(f186,plain,(
% 1.62/1.34 ($false = sF0) | ((f5 @ $true) = sF1)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f7])).
% 1.62/1.34 thf(f242,plain,(
% 1.62/1.34 spl27_3 | spl27_9 | spl27_10),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f190,f239,f235,f207])).
% 1.62/1.34 thf(f190,plain,(
% 1.62/1.34 (sF1 = $false) | ($false = sF0) | ((f5 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.62/1.34 thf(f233,plain,(
% 1.62/1.34 spl27_6 | spl27_2 | spl27_8),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f195,f230,f203,f221])).
% 1.62/1.34 thf(f195,plain,(
% 1.62/1.34 (sF15 = $false) | ($true = (f5 @ $false)) | ($true = sF14)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f193])).
% 1.62/1.34 thf(f193,plain,(
% 1.62/1.34 (sF15 = (f5 @ $false)) | ($true = sF14)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f21])).
% 1.62/1.34 thf(f228,plain,(
% 1.62/1.34 spl27_6 | spl27_5 | spl27_7),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f194,f225,f216,f221])).
% 1.62/1.34 thf(f194,plain,(
% 1.62/1.34 ($true = sF14) | ($true = sF15) | ((f5 @ $false) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f193])).
% 1.62/1.34 thf(f219,plain,(
% 1.62/1.34 spl27_4 | spl27_1 | spl27_5),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f197,f216,f199,f212])).
% 1.62/1.34 thf(f197,plain,(
% 1.62/1.34 (sF14 = $false) | ($true = sF15) | ((f5 @ $true) = $false)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.62/1.34 thf(f192,plain,(
% 1.62/1.34 ((f5 @ $true) = sF15) | (sF14 = $false)),
% 1.62/1.34 inference(cases_simplifying,[status(thm)],[f21])).
% 1.62/1.34 thf(f210,plain,(
% 1.62/1.34 spl27_1 | spl27_2 | spl27_3),
% 1.62/1.34 inference(avatar_split_clause,[status(thm)],[f196,f207,f203,f199])).
% 1.62/1.34 thf(f196,plain,(
% 1.62/1.34 (sF15 = $false) | (sF14 = $false) | ((f5 @ $true) = $true)),
% 1.62/1.34 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.62/1.34 % SZS output end Proof for DTF2THF_4968
% 1.62/1.34 % (5262)------------------------------
% 1.62/1.34 % (5262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (5262)Termination reason: Refutation
% 1.62/1.34
% 1.62/1.34 % (5262)Memory used [KB]: 5884
% 1.62/1.34 % (5262)Time elapsed: 0.015 s
% 1.62/1.34 % (5262)Instructions burned: 12 (million)
% 1.62/1.34 % (5262)------------------------------
% 1.62/1.34 % (5262)------------------------------
% 1.62/1.34 % (5248)Success in time 0.055 s
%------------------------------------------------------------------------------