%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1.005 : 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 : n003.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 1.89s 1.62s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 112
% Syntax : Number of formulae : 312 ( 27 unt; 0 typ; 80 def)
% Number of atoms : 2000 ( 484 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 786 ( 66 ~; 406 |; 0 &; 253 @)
% ( 61 <=>; 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 : 89 ( 86 usr; 83 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(f495,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f154,f163,f172,f177,f190,f199,f208,f213,f218,f223,f224,f225,f234,f243,f248,f253,f262,f267,f272,f273,f286,f295,f304,f309,f314,f323,f328,f333,f334,f335,f336,f337,f338,f347,f352,f357,f358,f367,f372,f377,f378,f383,f388,f389,f390,f399,f404,f413,f418,f419,f420,f421,f422,f423,f424,f425,f426,f431,f436,f437,f438,f439,f440,f441,f442,f447,f448,f453,f454,f455,f456,f457,f458,f459,f460,f461,f462,f463,f464,f465,f466,f467,f468,f469,f470,f471,f472,f473,f474,f475,f476,f477,f478,f479,f480,f481,f482,f483,f484,f485,f486,f487,f488,f489,f490,f491,f492,f493,f494]) ).
thf(f494,plain,
( ( $true != sF5 )
| ( sF5 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f493,plain,
( ( $true != sF17 )
| ( sF17 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f492,plain,
( ( x != $false )
| ( x != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f491,plain,
( ( $false != sF12 )
| ( $true != sF12 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f490,plain,
( ( $true != sF13 )
| ( sF13 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f489,plain,
( ( sF15 != $false )
| ( $true != sF15 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f488,plain,
( ( ( f1 @ $false )
!= $false )
| ( $true
!= ( f1 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f487,plain,
( ( sF6 != $false )
| ( $true != sF6 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f486,plain,
( ( $false
!= ( f1 @ $true ) )
| ( $true
!= ( f1 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f485,plain,
( ( $true != sF11 )
| ( $false != sF11 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f484,plain,
( ( $true != sF10 )
| ( $false != sF10 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f483,plain,
( ( $true != sF7 )
| ( $false != sF7 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f482,plain,
( ( $true != sF8 )
| ( sF8 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f481,plain,
( ( $false != sF16 )
| ( $true != sF16 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f480,plain,
( ( $false
!= ( f4 @ $false ) )
| ( $true
!= ( f4 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f479,plain,
( ( $false
!= ( f4 @ $true ) )
| ( $true
!= ( f4 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f478,plain,
( ( $true != sF1 )
| ( sF1 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f477,plain,
( ( $true != sF2 )
| ( sF2 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f476,plain,
( ( $true != sF0 )
| ( $false != sF0 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f475,plain,
( ( $true != sF9 )
| ( $false != sF9 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f474,plain,
( ( $true != sF14 )
| ( sF14 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f473,plain,
( ( $true != sF3 )
| ( $false != sF3 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f472,plain,
( ( $true
!= ( f2 @ $false ) )
| ( ( f2 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f471,plain,
( ( $true != sF4 )
| ( sF4 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f470,plain,
( ( $true
!= ( f2 @ $true ) )
| ( ( f2 @ $true )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f469,plain,
( ( $true
!= ( f0 @ $false ) )
| ( ( f0 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f468,plain,
( ( $true
!= ( f0 @ $true ) )
| ( ( f0 @ $true )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f467,plain,
( ( $true != sF18 )
| ( sF18 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f466,plain,
( ( $true
!= ( f3 @ $false ) )
| ( $false
!= ( f3 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f465,plain,
( ( $true
!= ( f3 @ $true ) )
| ( $false
!= ( f3 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f464,plain,
( spl19_58
| spl19_53
| spl19_55 ),
inference(avatar_split_clause,[status(thm)],[f29,f406,f396,f428]) ).
thf(f428,definition,
( spl19_58
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl19_58])],[avatar_definition]) ).
thf(f396,definition,
( spl19_53
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_53])],[avatar_definition]) ).
thf(f406,definition,
( spl19_55
<=> ( $true
= ( f1 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_55])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( f1 @ $false ) )
| ( $true = sF5 )
| ( sF6 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true = sF5 )
| ( sF6
= ( f1 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f12,definition,
( sF6
= ( f1 @ sF5 ) ),
introduced(definition,[],[function_definition]) ).
thf(f463,plain,
( spl19_56
| spl19_57
| spl19_58 ),
inference(avatar_split_clause,[status(thm)],[f28,f428,f415,f410]) ).
thf(f410,definition,
( spl19_56
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl19_56])],[avatar_definition]) ).
thf(f415,definition,
( spl19_57
<=> ( ( f1 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl19_57])],[avatar_definition]) ).
thf(f28,plain,
( ( $true = sF6 )
| ( $true = sF5 )
| ( ( f1 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f462,plain,
( spl19_54
| spl19_59
| spl19_53 ),
inference(avatar_split_clause,[status(thm)],[f31,f396,f433,f401]) ).
thf(f401,definition,
( spl19_54
<=> ( $true
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_54])],[avatar_definition]) ).
thf(f433,definition,
( spl19_59
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_59])],[avatar_definition]) ).
thf(f31,plain,
( ( sF6 = $false )
| ( sF5 = $false )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sF6
= ( f1 @ $true ) )
| ( sF5 = $false ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f461,plain,
( spl19_59
| spl19_56
| spl19_52 ),
inference(avatar_split_clause,[status(thm)],[f30,f392,f410,f433]) ).
thf(f392,definition,
( spl19_52
<=> ( $false
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_52])],[avatar_definition]) ).
thf(f30,plain,
( ( sF5 = $false )
| ( $true = sF6 )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f460,plain,
( spl19_44
| spl19_23
| spl19_25 ),
inference(avatar_split_clause,[status(thm)],[f35,f255,f245,f349]) ).
thf(f349,definition,
( spl19_44
<=> ( $true = sF12 ) ),
introduced(definition,[new_symbols(naming,[spl19_44])],[avatar_definition]) ).
thf(f245,definition,
( spl19_23
<=> ( $true
= ( f2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_23])],[avatar_definition]) ).
thf(f255,definition,
( spl19_25
<=> ( sF13 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_25])],[avatar_definition]) ).
thf(f35,plain,
( ( sF13 = $false )
| ( $true
= ( f2 @ $false ) )
| ( $true = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( sF13
= ( f2 @ $false ) )
| ( $true = sF12 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f19,definition,
( sF13
= ( f2 @ sF12 ) ),
introduced(definition,[],[function_definition]) ).
thf(f459,plain,
( spl19_28
| spl19_24
| spl19_44 ),
inference(avatar_split_clause,[status(thm)],[f34,f349,f250,f269]) ).
thf(f269,definition,
( spl19_28
<=> ( $true = sF13 ) ),
introduced(definition,[new_symbols(naming,[spl19_28])],[avatar_definition]) ).
thf(f250,definition,
( spl19_24
<=> ( ( f2 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl19_24])],[avatar_definition]) ).
thf(f34,plain,
( ( $true = sF12 )
| ( $true = sF13 )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f458,plain,
( spl19_21
| spl19_28
| spl19_42 ),
inference(avatar_split_clause,[status(thm)],[f37,f340,f269,f236]) ).
thf(f236,definition,
( spl19_21
<=> ( ( f2 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl19_21])],[avatar_definition]) ).
thf(f340,definition,
( spl19_42
<=> ( $false = sF12 ) ),
introduced(definition,[new_symbols(naming,[spl19_42])],[avatar_definition]) ).
thf(f37,plain,
( ( ( f2 @ $true )
= $false )
| ( $true = sF13 )
| ( $false = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $false = sF12 )
| ( ( f2 @ $true )
= sF13 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f457,plain,
( spl19_25
| spl19_42
| spl19_20 ),
inference(avatar_split_clause,[status(thm)],[f36,f231,f340,f255]) ).
thf(f231,definition,
( spl19_20
<=> ( $true
= ( f2 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_20])],[avatar_definition]) ).
thf(f36,plain,
( ( $false = sF12 )
| ( $true
= ( f2 @ $true ) )
| ( sF13 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f456,plain,
( spl19_12
| spl19_46 ),
inference(avatar_split_clause,[status(thm)],[f39,f360,f192]) ).
thf(f192,definition,
( spl19_12
<=> ( sF18 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_12])],[avatar_definition]) ).
thf(f360,definition,
( spl19_46
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_46])],[avatar_definition]) ).
thf(f39,plain,
( ( sF18 = $false )
| ( sF8 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
sF18 != sF8,
inference(definition_folding,[status(thm)],[f5,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f6,f14,f13,f12,f11,f10,f9,f8,f7,f6]) ).
thf(f7,definition,
( ( f3 @ sF0 )
= sF1 ),
introduced(definition,[],[function_definition]) ).
thf(f8,definition,
( sF2
= ( f3 @ sF1 ) ),
introduced(definition,[],[function_definition]) ).
thf(f9,definition,
( ( f3 @ sF2 )
= sF3 ),
introduced(definition,[],[function_definition]) ).
thf(f10,definition,
( sF4
= ( f2 @ sF3 ) ),
introduced(definition,[],[function_definition]) ).
thf(f11,definition,
( sF5
= ( f1 @ sF4 ) ),
introduced(definition,[],[function_definition]) ).
thf(f13,definition,
( sF7
= ( f1 @ sF6 ) ),
introduced(definition,[],[function_definition]) ).
thf(f14,definition,
( sF8
= ( f0 @ sF7 ) ),
introduced(definition,[],[function_definition]) ).
thf(f6,definition,
( ( f4 @ x )
= sF0 ),
introduced(definition,[],[function_definition]) ).
thf(f15,definition,
( sF9
= ( f4 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f16,definition,
( ( f4 @ sF9 )
= sF10 ),
introduced(definition,[],[function_definition]) ).
thf(f17,definition,
( ( f3 @ sF10 )
= sF11 ),
introduced(definition,[],[function_definition]) ).
thf(f18,definition,
( ( f2 @ sF11 )
= sF12 ),
introduced(definition,[],[function_definition]) ).
thf(f20,definition,
( ( f2 @ sF13 )
= sF14 ),
introduced(definition,[],[function_definition]) ).
thf(f21,definition,
( sF15
= ( f1 @ sF14 ) ),
introduced(definition,[],[function_definition]) ).
thf(f22,definition,
( ( f0 @ sF15 )
= sF16 ),
introduced(definition,[],[function_definition]) ).
thf(f23,definition,
( ( f0 @ sF16 )
= sF17 ),
introduced(definition,[],[function_definition]) ).
thf(f24,definition,
( sF18
= ( f0 @ sF17 ) ),
introduced(definition,[],[function_definition]) ).
thf(f5,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.07oceyV6KT/DTF2THF_27972.p',kaminski5) ).
thf(f455,plain,
( spl19_48
| spl19_9 ),
inference(avatar_split_clause,[status(thm)],[f38,f179,f369]) ).
thf(f369,definition,
( spl19_48
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl19_48])],[avatar_definition]) ).
thf(f179,definition,
( spl19_9
<=> ( $true = sF18 ) ),
introduced(definition,[new_symbols(naming,[spl19_9])],[avatar_definition]) ).
thf(f38,plain,
( ( $true = sF8 )
| ( $true = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f454,plain,
( spl19_36
| spl19_30
| spl19_61 ),
inference(avatar_split_clause,[status(thm)],[f43,f450,f279,f306]) ).
thf(f306,definition,
( spl19_36
<=> ( $true
= ( f4 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_36])],[avatar_definition]) ).
thf(f279,definition,
( spl19_30
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl19_30])],[avatar_definition]) ).
thf(f450,definition,
( spl19_61
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl19_61])],[avatar_definition]) ).
thf(f43,plain,
( ( x = $true )
| ( $true
= ( f4 @ $false ) )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( x = $true )
| ( sF0
= ( f4 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f453,plain,
( spl19_34
| spl19_61
| spl19_35 ),
inference(avatar_split_clause,[status(thm)],[f42,f301,f450,f297]) ).
thf(f297,definition,
( spl19_34
<=> ( $false
= ( f4 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_34])],[avatar_definition]) ).
thf(f301,definition,
( spl19_35
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl19_35])],[avatar_definition]) ).
thf(f42,plain,
( ( x = $true )
| ( $false
= ( f4 @ $false ) )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f448,plain,
( spl19_60
| spl19_29
| spl19_30 ),
inference(avatar_split_clause,[status(thm)],[f45,f279,f275,f444]) ).
thf(f444,definition,
( spl19_60
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_60])],[avatar_definition]) ).
thf(f275,definition,
( spl19_29
<=> ( $true
= ( f4 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_29])],[avatar_definition]) ).
thf(f45,plain,
( ( x = $false )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( x = $false )
| ( sF0
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f447,plain,
( spl19_33
| spl19_60
| spl19_35 ),
inference(avatar_split_clause,[status(thm)],[f44,f301,f444,f292]) ).
thf(f292,definition,
( spl19_33
<=> ( $false
= ( f4 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_33])],[avatar_definition]) ).
thf(f44,plain,
( ( $false
= ( f4 @ $true ) )
| ( x = $false )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f442,plain,
( spl19_1
| spl19_35
| spl19_8 ),
inference(avatar_split_clause,[status(thm)],[f49,f174,f301,f143]) ).
thf(f143,definition,
( spl19_1
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_1])],[avatar_definition]) ).
thf(f174,definition,
( spl19_8
<=> ( $true
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_8])],[avatar_definition]) ).
thf(f49,plain,
( ( $true = sF0 )
| ( sF1 = $false )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( sF1
= ( f3 @ $false ) )
| ( $true = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f441,plain,
( spl19_7
| spl19_35
| spl19_6 ),
inference(avatar_split_clause,[status(thm)],[f48,f165,f301,f169]) ).
thf(f169,definition,
( spl19_7
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(naming,[spl19_7])],[avatar_definition]) ).
thf(f165,definition,
( spl19_6
<=> ( $false
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_6])],[avatar_definition]) ).
thf(f48,plain,
( ( $true = sF0 )
| ( $true = sF1 )
| ( $false
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f440,plain,
( spl19_1
| spl19_5
| spl19_30 ),
inference(avatar_split_clause,[status(thm)],[f51,f279,f160,f143]) ).
thf(f160,definition,
( spl19_5
<=> ( $true
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_5])],[avatar_definition]) ).
thf(f51,plain,
( ( $false = sF0 )
| ( sF1 = $false )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $false = sF0 )
| ( sF1
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f439,plain,
( spl19_7
| spl19_3
| spl19_30 ),
inference(avatar_split_clause,[status(thm)],[f50,f279,f151,f169]) ).
thf(f151,definition,
( spl19_3
<=> ( $false
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_3])],[avatar_definition]) ).
thf(f50,plain,
( ( $false = sF0 )
| ( $false
= ( f3 @ $true ) )
| ( $true = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f438,plain,
( spl19_57
| spl19_22
| spl19_58 ),
inference(avatar_split_clause,[status(thm)],[f55,f428,f240,f415]) ).
thf(f240,definition,
( spl19_22
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl19_22])],[avatar_definition]) ).
thf(f55,plain,
( ( ( f1 @ $false )
= $false )
| ( $true = sF5 )
| ( $true = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( f1 @ $false )
= sF5 )
| ( $true = sF4 ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f437,plain,
( spl19_22
| spl19_55
| spl19_59 ),
inference(avatar_split_clause,[status(thm)],[f54,f433,f406,f240]) ).
thf(f54,plain,
( ( $true = sF4 )
| ( sF5 = $false )
| ( $true
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f436,plain,
( spl19_54
| spl19_59
| spl19_19 ),
inference(avatar_split_clause,[status(thm)],[f57,f227,f433,f401]) ).
thf(f227,definition,
( spl19_19
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_19])],[avatar_definition]) ).
thf(f57,plain,
( ( sF5 = $false )
| ( sF4 = $false )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( sF5
= ( f1 @ $true ) )
| ( sF4 = $false ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f431,plain,
( spl19_19
| spl19_52
| spl19_58 ),
inference(avatar_split_clause,[status(thm)],[f56,f428,f392,f227]) ).
thf(f56,plain,
( ( $true = sF5 )
| ( sF4 = $false )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f426,plain,
( spl19_55
| spl19_27
| spl19_39 ),
inference(avatar_split_clause,[status(thm)],[f61,f320,f264,f406]) ).
thf(f264,definition,
( spl19_27
<=> ( $true = sF14 ) ),
introduced(definition,[new_symbols(naming,[spl19_27])],[avatar_definition]) ).
thf(f320,definition,
( spl19_39
<=> ( sF15 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_39])],[avatar_definition]) ).
thf(f61,plain,
( ( $true = sF14 )
| ( $true
= ( f1 @ $false ) )
| ( sF15 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true = sF14 )
| ( sF15
= ( f1 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f425,plain,
( spl19_57
| spl19_41
| spl19_27 ),
inference(avatar_split_clause,[status(thm)],[f60,f264,f330,f415]) ).
thf(f330,definition,
( spl19_41
<=> ( $true = sF15 ) ),
introduced(definition,[new_symbols(naming,[spl19_41])],[avatar_definition]) ).
thf(f60,plain,
( ( $true = sF14 )
| ( ( f1 @ $false )
= $false )
| ( $true = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f424,plain,
( spl19_26
| spl19_39
| spl19_54 ),
inference(avatar_split_clause,[status(thm)],[f63,f401,f320,f259]) ).
thf(f259,definition,
( spl19_26
<=> ( sF14 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_26])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( f1 @ $true ) )
| ( sF14 = $false )
| ( sF15 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( sF15
= ( f1 @ $true ) )
| ( sF14 = $false ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f423,plain,
( spl19_52
| spl19_41
| spl19_26 ),
inference(avatar_split_clause,[status(thm)],[f62,f259,f330,f392]) ).
thf(f62,plain,
( ( $false
= ( f1 @ $true ) )
| ( $true = sF15 )
| ( sF14 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f422,plain,
( spl19_43
| spl19_51
| spl19_8 ),
inference(avatar_split_clause,[status(thm)],[f67,f174,f385,f344]) ).
thf(f344,definition,
( spl19_43
<=> ( $false = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl19_43])],[avatar_definition]) ).
thf(f385,definition,
( spl19_51
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl19_51])],[avatar_definition]) ).
thf(f67,plain,
( ( $true = sF10 )
| ( $false = sF11 )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $true = sF10 )
| ( sF11
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f421,plain,
( spl19_51
| spl19_6
| spl19_45 ),
inference(avatar_split_clause,[status(thm)],[f66,f354,f165,f385]) ).
thf(f354,definition,
( spl19_45
<=> ( $true = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl19_45])],[avatar_definition]) ).
thf(f66,plain,
( ( $true = sF10 )
| ( $false
= ( f3 @ $false ) )
| ( $true = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f420,plain,
( spl19_50
| spl19_3
| spl19_45 ),
inference(avatar_split_clause,[status(thm)],[f69,f354,f151,f380]) ).
thf(f380,definition,
( spl19_50
<=> ( $false = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl19_50])],[avatar_definition]) ).
thf(f69,plain,
( ( $true = sF11 )
| ( $false = sF10 )
| ( $false
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( f3 @ $true )
= sF11 )
| ( $false = sF10 ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f419,plain,
( spl19_50
| spl19_43
| spl19_5 ),
inference(avatar_split_clause,[status(thm)],[f68,f160,f344,f380]) ).
thf(f68,plain,
( ( $false = sF11 )
| ( $false = sF10 )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f418,plain,
( spl19_56
| spl19_57
| spl19_49 ),
inference(avatar_split_clause,[status(thm)],[f73,f374,f415,f410]) ).
thf(f374,definition,
( spl19_49
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl19_49])],[avatar_definition]) ).
thf(f73,plain,
( ( $true = sF7 )
| ( ( f1 @ $false )
= $false )
| ( $true = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( f1 @ $false )
= sF7 )
| ( $true = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f413,plain,
( spl19_47
| spl19_55
| spl19_56 ),
inference(avatar_split_clause,[status(thm)],[f72,f410,f406,f364]) ).
thf(f364,definition,
( spl19_47
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl19_47])],[avatar_definition]) ).
thf(f72,plain,
( ( $false = sF7 )
| ( $true
= ( f1 @ $false ) )
| ( $true = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f404,plain,
( spl19_47
| spl19_53
| spl19_54 ),
inference(avatar_split_clause,[status(thm)],[f75,f401,f396,f364]) ).
thf(f75,plain,
( ( $true
= ( f1 @ $true ) )
| ( sF6 = $false )
| ( $false = sF7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( sF7
= ( f1 @ $true ) )
| ( sF6 = $false ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f399,plain,
( spl19_52
| spl19_53
| spl19_49 ),
inference(avatar_split_clause,[status(thm)],[f74,f374,f396,f392]) ).
thf(f74,plain,
( ( $true = sF7 )
| ( $false
= ( f1 @ $true ) )
| ( sF6 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f390,plain,
( spl19_32
| spl19_34
| spl19_51 ),
inference(avatar_split_clause,[status(thm)],[f79,f385,f297,f288]) ).
thf(f288,definition,
( spl19_32
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl19_32])],[avatar_definition]) ).
thf(f79,plain,
( ( $false
= ( f4 @ $false ) )
| ( $true = sF9 )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( f4 @ $false )
= sF10 )
| ( $true = sF9 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f389,plain,
( spl19_36
| spl19_50
| spl19_32 ),
inference(avatar_split_clause,[status(thm)],[f78,f288,f380,f306]) ).
thf(f78,plain,
( ( $true = sF9 )
| ( $false = sF10 )
| ( $true
= ( f4 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f388,plain,
( spl19_51
| spl19_31
| spl19_33 ),
inference(avatar_split_clause,[status(thm)],[f81,f292,f283,f385]) ).
thf(f283,definition,
( spl19_31
<=> ( $false = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl19_31])],[avatar_definition]) ).
thf(f81,plain,
( ( $false = sF9 )
| ( $false
= ( f4 @ $true ) )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false = sF9 )
| ( ( f4 @ $true )
= sF10 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f383,plain,
( spl19_50
| spl19_29
| spl19_31 ),
inference(avatar_split_clause,[status(thm)],[f80,f283,f275,f380]) ).
thf(f80,plain,
( ( $false = sF9 )
| ( $false = sF10 )
| ( $true
= ( f4 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f378,plain,
( spl19_48
| spl19_49
| spl19_15 ),
inference(avatar_split_clause,[status(thm)],[f85,f205,f374,f369]) ).
thf(f205,definition,
( spl19_15
<=> ( ( f0 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl19_15])],[avatar_definition]) ).
thf(f85,plain,
( ( $true = sF7 )
| ( $true = sF8 )
| ( ( f0 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( f0 @ $false )
= sF8 )
| ( $true = sF7 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f377,plain,
( spl19_16
| spl19_46
| spl19_49 ),
inference(avatar_split_clause,[status(thm)],[f84,f374,f360,f210]) ).
thf(f210,definition,
( spl19_16
<=> ( $true
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl19_16])],[avatar_definition]) ).
thf(f84,plain,
( ( $true = sF7 )
| ( $true
= ( f0 @ $false ) )
| ( sF8 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f372,plain,
( spl19_47
| spl19_48
| spl19_11 ),
inference(avatar_split_clause,[status(thm)],[f87,f187,f369,f364]) ).
thf(f187,definition,
( spl19_11
<=> ( ( f0 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl19_11])],[avatar_definition]) ).
thf(f87,plain,
( ( $false = sF7 )
| ( ( f0 @ $true )
= $false )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( f0 @ $true )
= sF8 )
| ( $false = sF7 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f367,plain,
( spl19_46
| spl19_47
| spl19_13 ),
inference(avatar_split_clause,[status(thm)],[f86,f196,f364,f360]) ).
thf(f196,definition,
( spl19_13
<=> ( $true
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl19_13])],[avatar_definition]) ).
thf(f86,plain,
( ( $false = sF7 )
| ( sF8 = $false )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f358,plain,
( spl19_44
| spl19_24
| spl19_45 ),
inference(avatar_split_clause,[status(thm)],[f91,f354,f250,f349]) ).
thf(f91,plain,
( ( $true = sF12 )
| ( $true = sF11 )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true = sF11 )
| ( ( f2 @ $false )
= sF12 ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f357,plain,
( spl19_45
| spl19_42
| spl19_23 ),
inference(avatar_split_clause,[status(thm)],[f90,f245,f340,f354]) ).
thf(f90,plain,
( ( $false = sF12 )
| ( $true = sF11 )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f352,plain,
( spl19_43
| spl19_44
| spl19_21 ),
inference(avatar_split_clause,[status(thm)],[f93,f236,f349,f344]) ).
thf(f93,plain,
( ( ( f2 @ $true )
= $false )
| ( $false = sF11 )
| ( $true = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( f2 @ $true )
= sF12 )
| ( $false = sF11 ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f347,plain,
( spl19_42
| spl19_43
| spl19_20 ),
inference(avatar_split_clause,[status(thm)],[f92,f231,f344,f340]) ).
thf(f92,plain,
( ( $false = sF11 )
| ( $true
= ( f2 @ $true ) )
| ( $false = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f338,plain,
( spl19_15
| spl19_40
| spl19_14 ),
inference(avatar_split_clause,[status(thm)],[f97,f201,f325,f205]) ).
thf(f325,definition,
( spl19_40
<=> ( $true = sF16 ) ),
introduced(definition,[new_symbols(naming,[spl19_40])],[avatar_definition]) ).
thf(f201,definition,
( spl19_14
<=> ( $true = sF17 ) ),
introduced(definition,[new_symbols(naming,[spl19_14])],[avatar_definition]) ).
thf(f97,plain,
( ( ( f0 @ $false )
= $false )
| ( $true = sF17 )
| ( $true = sF16 ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( f0 @ $false )
= sF17 )
| ( $true = sF16 ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f337,plain,
( spl19_40
| spl19_10
| spl19_16 ),
inference(avatar_split_clause,[status(thm)],[f96,f210,f183,f325]) ).
thf(f183,definition,
( spl19_10
<=> ( sF17 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_10])],[avatar_definition]) ).
thf(f96,plain,
( ( $true = sF16 )
| ( sF17 = $false )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f336,plain,
( spl19_38
| spl19_11
| spl19_14 ),
inference(avatar_split_clause,[status(thm)],[f99,f201,f187,f316]) ).
thf(f316,definition,
( spl19_38
<=> ( $false = sF16 ) ),
introduced(definition,[new_symbols(naming,[spl19_38])],[avatar_definition]) ).
thf(f99,plain,
( ( ( f0 @ $true )
= $false )
| ( $false = sF16 )
| ( $true = sF17 ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( f0 @ $true )
= sF17 )
| ( $false = sF16 ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f335,plain,
( spl19_38
| spl19_13
| spl19_10 ),
inference(avatar_split_clause,[status(thm)],[f98,f183,f196,f316]) ).
thf(f98,plain,
( ( $true
= ( f0 @ $true ) )
| ( $false = sF16 )
| ( sF17 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f334,plain,
( spl19_40
| spl19_41
| spl19_15 ),
inference(avatar_split_clause,[status(thm)],[f103,f205,f330,f325]) ).
thf(f103,plain,
( ( $true = sF16 )
| ( ( f0 @ $false )
= $false )
| ( $true = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( f0 @ $false )
= sF16 )
| ( $true = sF15 ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f333,plain,
( spl19_41
| spl19_38
| spl19_16 ),
inference(avatar_split_clause,[status(thm)],[f102,f210,f316,f330]) ).
thf(f102,plain,
( ( $true = sF15 )
| ( $false = sF16 )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f328,plain,
( spl19_40
| spl19_11
| spl19_39 ),
inference(avatar_split_clause,[status(thm)],[f105,f320,f187,f325]) ).
thf(f105,plain,
( ( sF15 = $false )
| ( ( f0 @ $true )
= $false )
| ( $true = sF16 ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( f0 @ $true )
= sF16 )
| ( sF15 = $false ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f323,plain,
( spl19_38
| spl19_39
| spl19_13 ),
inference(avatar_split_clause,[status(thm)],[f104,f196,f320,f316]) ).
thf(f104,plain,
( ( $true
= ( f0 @ $true ) )
| ( sF15 = $false )
| ( $false = sF16 ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f314,plain,
~ spl19_37,
inference(avatar_split_clause,[status(thm)],[f3,f311]) ).
thf(f311,definition,
( spl19_37
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_37])],[avatar_definition]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f309,plain,
( spl19_31
| spl19_35
| spl19_36 ),
inference(avatar_split_clause,[status(thm)],[f109,f306,f301,f283]) ).
thf(f109,plain,
( ( $false = sF9 )
| ( $true
= ( f4 @ $false ) )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true = sF0 )
| ( sF9
= ( f4 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f304,plain,
( spl19_32
| spl19_34
| spl19_35 ),
inference(avatar_split_clause,[status(thm)],[f108,f301,f297,f288]) ).
thf(f108,plain,
( ( $true = sF9 )
| ( $true = sF0 )
| ( $false
= ( f4 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f295,plain,
( spl19_32
| spl19_30
| spl19_33 ),
inference(avatar_split_clause,[status(thm)],[f111,f292,f279,f288]) ).
thf(f111,plain,
( ( $false
= ( f4 @ $true ) )
| ( $true = sF9 )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $false = sF0 )
| ( ( f4 @ $true )
= sF9 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f286,plain,
( spl19_29
| spl19_30
| spl19_31 ),
inference(avatar_split_clause,[status(thm)],[f110,f283,f279,f275]) ).
thf(f110,plain,
( ( $false = sF9 )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f273,plain,
( spl19_27
| spl19_28
| spl19_24 ),
inference(avatar_split_clause,[status(thm)],[f115,f250,f269,f264]) ).
thf(f115,plain,
( ( $true = sF14 )
| ( $true = sF13 )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( f2 @ $false )
= sF14 )
| ( $true = sF13 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f272,plain,
( spl19_28
| spl19_23
| spl19_26 ),
inference(avatar_split_clause,[status(thm)],[f114,f259,f245,f269]) ).
thf(f114,plain,
( ( sF14 = $false )
| ( $true
= ( f2 @ $false ) )
| ( $true = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f267,plain,
( spl19_21
| spl19_25
| spl19_27 ),
inference(avatar_split_clause,[status(thm)],[f117,f264,f255,f236]) ).
thf(f117,plain,
( ( $true = sF14 )
| ( sF13 = $false )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ( f2 @ $true )
= sF14 )
| ( sF13 = $false ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f262,plain,
( spl19_20
| spl19_25
| spl19_26 ),
inference(avatar_split_clause,[status(thm)],[f116,f259,f255,f231]) ).
thf(f116,plain,
( ( sF13 = $false )
| ( $true
= ( f2 @ $true ) )
| ( sF14 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f253,plain,
( spl19_22
| spl19_18
| spl19_24 ),
inference(avatar_split_clause,[status(thm)],[f121,f250,f220,f240]) ).
thf(f220,definition,
( spl19_18
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl19_18])],[avatar_definition]) ).
thf(f121,plain,
( ( ( f2 @ $false )
= $false )
| ( $true = sF3 )
| ( $true = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true = sF3 )
| ( ( f2 @ $false )
= sF4 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f248,plain,
( spl19_18
| spl19_19
| spl19_23 ),
inference(avatar_split_clause,[status(thm)],[f120,f245,f227,f220]) ).
thf(f120,plain,
( ( sF4 = $false )
| ( $true
= ( f2 @ $false ) )
| ( $true = sF3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f243,plain,
( spl19_21
| spl19_22
| spl19_17 ),
inference(avatar_split_clause,[status(thm)],[f123,f215,f240,f236]) ).
thf(f215,definition,
( spl19_17
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl19_17])],[avatar_definition]) ).
thf(f123,plain,
( ( $false = sF3 )
| ( $true = sF4 )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( ( f2 @ $true )
= sF4 )
| ( $false = sF3 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f234,plain,
( spl19_19
| spl19_17
| spl19_20 ),
inference(avatar_split_clause,[status(thm)],[f122,f231,f215,f227]) ).
thf(f122,plain,
( ( $true
= ( f2 @ $true ) )
| ( $false = sF3 )
| ( sF4 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f225,plain,
( spl19_8
| spl19_2
| spl19_17 ),
inference(avatar_split_clause,[status(thm)],[f127,f215,f147,f174]) ).
thf(f147,definition,
( spl19_2
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(naming,[spl19_2])],[avatar_definition]) ).
thf(f127,plain,
( ( $true
= ( f3 @ $false ) )
| ( $true = sF2 )
| ( $false = sF3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true = sF2 )
| ( sF3
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f224,plain,
( spl19_18
| spl19_2
| spl19_6 ),
inference(avatar_split_clause,[status(thm)],[f126,f165,f147,f220]) ).
thf(f126,plain,
( ( $true = sF3 )
| ( $true = sF2 )
| ( $false
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f223,plain,
( spl19_4
| spl19_18
| spl19_3 ),
inference(avatar_split_clause,[status(thm)],[f129,f151,f220,f156]) ).
thf(f156,definition,
( spl19_4
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl19_4])],[avatar_definition]) ).
thf(f129,plain,
( ( $false
= ( f3 @ $true ) )
| ( sF2 = $false )
| ( $true = sF3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( sF2 = $false )
| ( ( f3 @ $true )
= sF3 ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f218,plain,
( spl19_17
| spl19_5
| spl19_4 ),
inference(avatar_split_clause,[status(thm)],[f128,f156,f160,f215]) ).
thf(f128,plain,
( ( sF2 = $false )
| ( $false = sF3 )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f213,plain,
( spl19_14
| spl19_16
| spl19_12 ),
inference(avatar_split_clause,[status(thm)],[f133,f192,f210,f201]) ).
thf(f133,plain,
( ( $true
= ( f0 @ $false ) )
| ( $true = sF17 )
| ( sF18 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
( ( sF18
= ( f0 @ $false ) )
| ( $true = sF17 ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f208,plain,
( spl19_9
| spl19_14
| spl19_15 ),
inference(avatar_split_clause,[status(thm)],[f132,f205,f201,f179]) ).
thf(f132,plain,
( ( $true = sF17 )
| ( ( f0 @ $false )
= $false )
| ( $true = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f199,plain,
( spl19_12
| spl19_10
| spl19_13 ),
inference(avatar_split_clause,[status(thm)],[f135,f196,f183,f192]) ).
thf(f135,plain,
( ( $true
= ( f0 @ $true ) )
| ( sF17 = $false )
| ( sF18 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( sF18
= ( f0 @ $true ) )
| ( sF17 = $false ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f190,plain,
( spl19_9
| spl19_10
| spl19_11 ),
inference(avatar_split_clause,[status(thm)],[f134,f187,f183,f179]) ).
thf(f134,plain,
( ( sF17 = $false )
| ( ( f0 @ $true )
= $false )
| ( $true = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f177,plain,
( spl19_7
| spl19_4
| spl19_8 ),
inference(avatar_split_clause,[status(thm)],[f139,f174,f156,f169]) ).
thf(f139,plain,
( ( $true
= ( f3 @ $false ) )
| ( $true = sF1 )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $true = sF1 )
| ( sF2
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f172,plain,
( spl19_6
| spl19_2
| spl19_7 ),
inference(avatar_split_clause,[status(thm)],[f138,f169,f147,f165]) ).
thf(f138,plain,
( ( $false
= ( f3 @ $false ) )
| ( $true = sF1 )
| ( $true = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f163,plain,
( spl19_1
| spl19_4
| spl19_5 ),
inference(avatar_split_clause,[status(thm)],[f141,f160,f156,f143]) ).
thf(f141,plain,
( ( sF1 = $false )
| ( $true
= ( f3 @ $true ) )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( sF1 = $false )
| ( sF2
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f154,plain,
( spl19_1
| spl19_2
| spl19_3 ),
inference(avatar_split_clause,[status(thm)],[f140,f151,f147,f143]) ).
thf(f140,plain,
( ( sF1 = $false )
| ( $false
= ( f3 @ $true ) )
| ( $true = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO500^1.005 : 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
% 0.18/0.34 % Computer : n003.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:32:25 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SYO500^1.005 : TPTP v9.2.1. Released v4.1.0.
% 0.33/0.49 % Domain : Syntactic
% 0.33/0.49 % Problem : Five function variant of the Kaminski equation
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.33/0.49 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.33/0.49 % Source : [Bro09]
% 0.33/0.49 % Names : basic13 [Bro09]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.44 v9.1.0, 0.38 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
% 0.33/0.49 % Syntax : Number of formulae : 7 ( 1 unt; 6 typ; 0 def)
% 0.33/0.49 % Number of atoms : 23 ( 1 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 1 ( 23 avg)
% 0.33/0.49 % Number of connectives : 20 ( 0 ~; 0 |; 0 &; 20 @)
% 0.33/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 1 ( 1 avg)
% 0.33/0.49 % Number of types : 1 ( 0 usr)
% 0.33/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% 0.33/0.49 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments :
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(x,type,
% 0.33/0.49 x: $o ).
% 0.33/0.49
% 0.33/0.49 thf(f0,type,
% 0.33/0.49 f0: $o > $o ).
% 0.33/0.49
% 0.33/0.49 thf(f1,type,
% 0.33/0.49 f1: $o > $o ).
% 0.33/0.49
% 0.33/0.49 thf(f2,type,
% 0.33/0.49 f2: $o > $o ).
% 0.33/0.49
% 0.33/0.49 thf(f3,type,
% 0.33/0.49 f3: $o > $o ).
% 0.33/0.49
% 0.33/0.49 thf(f4,type,
% 0.33/0.49 f4: $o > $o ).
% 0.33/0.49
% 0.33/0.49 thf(kaminski5,conjecture,
% 0.33/0.49 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
% 0.33/0.49 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.81/1.54 ---- Embedded in THF ---
% 1.81/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.81/1.54 %%% Generated on Tue Feb 24 14:32:27 EST 2026
% 1.81/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 1.81/1.54 %%% Logic specification used:
% 1.81/1.54 %%% thf(spec, logic, $$dhol).
% 1.81/1.54
% 1.81/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.07oceyV6KT/DTF2DTF27972.p
% See solution above
% 1.81/1.54 ------------------------
% 1.81/1.55 ---- Cleaned THF ---
% 1.81/1.55 thf(x,type,
% 1.81/1.55 x: $o ).
% 1.81/1.55
% 1.81/1.55 thf(f0,type,
% 1.81/1.55 f0: $o > $o ).
% 1.81/1.55
% 1.81/1.55 thf(f1,type,
% 1.81/1.55 f1: $o > $o ).
% 1.81/1.55
% 1.81/1.55 thf(f2,type,
% 1.81/1.55 f2: $o > $o ).
% 1.81/1.55
% 1.81/1.55 thf(f3,type,
% 1.81/1.55 f3: $o > $o ).
% 1.81/1.55
% 1.81/1.55 thf(f4,type,
% 1.81/1.55 f4: $o > $o ).
% 1.81/1.55
% 1.81/1.55 thf(kaminski5,conjecture,
% 1.81/1.55 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
% 1.81/1.55 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.81/1.55 ------------------------
% 1.81/1.57 % (28078)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/183Mi)
% 1.81/1.57 % (28080)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_27972 for (2999ds/27Mi)
% 1.81/1.57 % (28081)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/2Mi)
% 1.81/1.57 % (28084)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/18Mi)
% 1.81/1.57 % (28079)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_27972 for (2999ds/4Mi)
% 1.81/1.57 % (28082)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_27972 for (2999ds/2Mi)
% 1.81/1.57 % (28083)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_27972 for (2999ds/275Mi)
% 1.81/1.57 % (28081)Instruction limit reached!
% 1.81/1.57 % (28081)------------------------------
% 1.81/1.57 % (28081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (28081)Termination reason: Unknown
% 1.81/1.57 % (28081)Termination phase: Saturation
% 1.81/1.57 % (28082)Instruction limit reached!
% 1.81/1.57 % (28082)------------------------------
% 1.81/1.57 % (28082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57
% 1.81/1.57 % (28081)Memory used [KB]: 5500
% 1.81/1.57 % (28081)Time elapsed: 0.003 s
% 1.81/1.57 % (28081)Instructions burned: 2 (million)
% 1.81/1.57 % (28081)------------------------------
% 1.81/1.57 % (28081)------------------------------
% 1.81/1.57 % (28082)Termination reason: Unknown
% 1.81/1.57 % (28082)Termination phase: Saturation
% 1.81/1.57
% 1.81/1.57 % (28082)Memory used [KB]: 5500
% 1.81/1.57 % (28082)Time elapsed: 0.003 s
% 1.81/1.57 % (28082)Instructions burned: 3 (million)
% 1.81/1.57 % (28082)------------------------------
% 1.81/1.57 % (28082)------------------------------
% 1.81/1.57 % (28079)Instruction limit reached!
% 1.81/1.57 % (28079)------------------------------
% 1.81/1.57 % (28079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (28080)Refutation not found, incomplete strategy
% 1.81/1.57 % (28080)------------------------------
% 1.81/1.57 % (28080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (28079)Termination reason: Unknown
% 1.81/1.57 % (28080)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.57
% 1.81/1.57
% 1.81/1.57 % (28079)Termination phase: Saturation
% 1.81/1.57
% 1.81/1.57 % (28080)Memory used [KB]: 5500
% 1.81/1.57 % (28079)Memory used [KB]: 5500
% 1.81/1.57 % (28080)Time elapsed: 0.003 s
% 1.81/1.57 % (28079)Time elapsed: 0.004 s
% 1.81/1.57 % (28080)Instructions burned: 2 (million)
% 1.81/1.57 % (28079)Instructions burned: 4 (million)
% 1.81/1.57 % (28080)------------------------------
% 1.81/1.57 % (28080)------------------------------
% 1.81/1.57 % (28079)------------------------------
% 1.81/1.57 % (28079)------------------------------
% 1.81/1.57 % (28083)Refutation not found, incomplete strategy
% 1.81/1.57 % (28083)------------------------------
% 1.81/1.57 % (28083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (28083)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.57
% 1.81/1.57
% 1.81/1.57 % (28083)Memory used [KB]: 5500
% 1.81/1.57 % (28083)Time elapsed: 0.003 s
% 1.81/1.57 % (28083)Instructions burned: 2 (million)
% 1.81/1.57 % (28083)------------------------------
% 1.81/1.57 % (28083)------------------------------
% 1.81/1.58 % (28084)Instruction limit reached!
% 1.81/1.58 % (28084)------------------------------
% 1.81/1.58 % (28084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.58 % (28084)Termination reason: Unknown
% 1.81/1.58 % (28084)Termination phase: Saturation
% 1.81/1.58
% 1.81/1.58 % (28084)Memory used [KB]: 5628
% 1.81/1.58 % (28084)Time elapsed: 0.013 s
% 1.81/1.58 % (28084)Instructions burned: 19 (million)
% 1.81/1.58 % (28084)------------------------------
% 1.81/1.58 % (28084)------------------------------
% 1.81/1.59 % (28086)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_27972 for (2999ds/37Mi)
% 1.81/1.59 % (28085)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/3Mi)
% 1.81/1.59 % (28089)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_27972 for (2999ds/1041Mi)
% 1.81/1.59 % (28088)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_27972 for (2999ds/3Mi)
% 1.81/1.59 % (28087)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_27972 for (2999ds/15Mi)
% 1.81/1.59 % (28088)Refutation not found, incomplete strategy
% 1.81/1.59 % (28088)------------------------------
% 1.81/1.59 % (28088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.59 % (28085)Refutation not found, incomplete strategy
% 1.81/1.59 % (28085)------------------------------
% 1.81/1.59 % (28085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.59 % (28085)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.59
% 1.81/1.59
% 1.81/1.59 % (28085)Memory used [KB]: 5500
% 1.81/1.59 % (28085)Time elapsed: 0.003 s
% 1.81/1.59 % (28085)Instructions burned: 1 (million)
% 1.81/1.59 % (28085)------------------------------
% 1.81/1.59 % (28085)------------------------------
% 1.81/1.59 % (28088)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.59
% 1.81/1.59
% 1.81/1.59 % (28088)Memory used [KB]: 5500
% 1.81/1.59 % (28088)Time elapsed: 0.002 s
% 1.81/1.59 % (28088)Instructions burned: 1 (million)
% 1.81/1.59 % (28088)------------------------------
% 1.81/1.59 % (28088)------------------------------
% 1.81/1.59 % (28089)Refutation not found, incomplete strategy
% 1.81/1.59 % (28089)------------------------------
% 1.81/1.59 % (28089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.59 % (28089)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.59
% 1.81/1.59
% 1.81/1.59 % (28089)Memory used [KB]: 5500
% 1.81/1.59 % (28089)Time elapsed: 0.006 s
% 1.81/1.59 % (28089)Instructions burned: 7 (million)
% 1.81/1.59 % (28089)------------------------------
% 1.81/1.59 % (28089)------------------------------
% 1.89/1.60 % (28087)Instruction limit reached!
% 1.89/1.60 % (28087)------------------------------
% 1.89/1.60 % (28087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.60 % (28090)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/7Mi)
% 1.89/1.60 % (28087)Termination reason: Unknown
% 1.89/1.60 % (28087)Termination phase: Saturation
% 1.89/1.60
% 1.89/1.60 % (28087)Memory used [KB]: 5756
% 1.89/1.60 % (28087)Time elapsed: 0.011 s
% 1.89/1.60 % (28087)Instructions burned: 16 (million)
% 1.89/1.60 % (28087)------------------------------
% 1.89/1.60 % (28087)------------------------------
% 1.89/1.60 % (28090)Instruction limit reached!
% 1.89/1.60 % (28090)------------------------------
% 1.89/1.60 % (28090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.60 % (28090)Termination reason: Unknown
% 1.89/1.60 % (28090)Termination phase: Saturation
% 1.89/1.60
% 1.89/1.60 % (28090)Memory used [KB]: 1023
% 1.89/1.60 % (28090)Time elapsed: 0.007 s
% 1.89/1.60 % (28090)Instructions burned: 7 (million)
% 1.89/1.60 % (28090)------------------------------
% 1.89/1.60 % (28090)------------------------------
% 1.89/1.61 % (28086)Instruction limit reached!
% 1.89/1.61 % (28086)------------------------------
% 1.89/1.61 % (28086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (28086)Termination reason: Unknown
% 1.89/1.61 % (28091)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/16Mi)
% 1.89/1.61 % (28092)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_27972 for (2999ds/3Mi)
% 1.89/1.61 % (28086)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (28086)Memory used [KB]: 5628
% 1.89/1.61 % (28086)Time elapsed: 0.021 s
% 1.89/1.61 % (28086)Instructions burned: 38 (million)
% 1.89/1.61 % (28086)------------------------------
% 1.89/1.61 % (28086)------------------------------
% 1.89/1.61 % (28092)Instruction limit reached!
% 1.89/1.61 % (28092)------------------------------
% 1.89/1.61 % (28092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (28092)Termination reason: Unknown
% 1.89/1.61 % (28092)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (28092)Memory used [KB]: 5500
% 1.89/1.61 % (28092)Time elapsed: 0.004 s
% 1.89/1.61 % (28092)Instructions burned: 4 (million)
% 1.89/1.61 % (28092)------------------------------
% 1.89/1.61 % (28092)------------------------------
% 1.89/1.61 % (28093)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_27972 for (2999ds/3Mi)
% 1.89/1.61 % (28093)Instruction limit reached!
% 1.89/1.61 % (28093)------------------------------
% 1.89/1.61 % (28093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (28093)Termination reason: Unknown
% 1.89/1.61 % (28093)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (28093)Memory used [KB]: 5500
% 1.89/1.61 % (28093)Time elapsed: 0.004 s
% 1.89/1.61 % (28093)Instructions burned: 4 (million)
% 1.89/1.61 % (28093)------------------------------
% 1.89/1.61 % (28093)------------------------------
% 1.89/1.61 % (28091)First to succeed.
% 1.89/1.61 % (28094)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27972 for (2999ds/7Mi)
% 1.89/1.62 % (28091)Refutation found. Thanks to Tanya!
% 1.89/1.62 % SZS status Theorem for DTF2THF_27972
% 1.89/1.62 % SZS output start Proof for DTF2THF_27972
% 1.89/1.62 thf(func_def_1, type, f0: $o > $o).
% 1.89/1.62 thf(func_def_2, type, f1: $o > $o).
% 1.89/1.62 thf(func_def_3, type, f2: $o > $o).
% 1.89/1.62 thf(func_def_4, type, f3: $o > $o).
% 1.89/1.62 thf(func_def_5, type, f4: $o > $o).
% 1.89/1.62 thf(f495,plain,(
% 1.89/1.62 $false),
% 1.89/1.62 inference(avatar_sat_refutation,[status(thm)],[f154,f163,f172,f177,f190,f199,f208,f213,f218,f223,f224,f225,f234,f243,f248,f253,f262,f267,f272,f273,f286,f295,f304,f309,f314,f323,f328,f333,f334,f335,f336,f337,f338,f347,f352,f357,f358,f367,f372,f377,f378,f383,f388,f389,f390,f399,f404,f413,f418,f419,f420,f421,f422,f423,f424,f425,f426,f431,f436,f437,f438,f439,f440,f441,f442,f447,f448,f453,f454,f455,f456,f457,f458,f459,f460,f461,f462,f463,f464,f465,f466,f467,f468,f469,f470,f471,f472,f473,f474,f475,f476,f477,f478,f479,f480,f481,f482,f483,f484,f485,f486,f487,f488,f489,f490,f491,f492,f493,f494])).
% 1.89/1.62 thf(f494,plain,(
% 1.89/1.62 ($true != sF5) | (sF5 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f493,plain,(
% 1.89/1.62 ($true != sF17) | (sF17 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f492,plain,(
% 1.89/1.62 (x != $false) | (x != $true) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f491,plain,(
% 1.89/1.62 ($false != sF12) | ($true != sF12) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f490,plain,(
% 1.89/1.62 ($true != sF13) | (sF13 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f489,plain,(
% 1.89/1.62 (sF15 != $false) | ($true != sF15) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f488,plain,(
% 1.89/1.62 ((f1 @ $false) != $false) | ($true != (f1 @ $false)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f487,plain,(
% 1.89/1.62 (sF6 != $false) | ($true != sF6) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f486,plain,(
% 1.89/1.62 ($false != (f1 @ $true)) | ($true != (f1 @ $true)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f485,plain,(
% 1.89/1.62 ($true != sF11) | ($false != sF11) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f484,plain,(
% 1.89/1.62 ($true != sF10) | ($false != sF10) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f483,plain,(
% 1.89/1.62 ($true != sF7) | ($false != sF7) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f482,plain,(
% 1.89/1.62 ($true != sF8) | (sF8 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f481,plain,(
% 1.89/1.62 ($false != sF16) | ($true != sF16) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f480,plain,(
% 1.89/1.62 ($false != (f4 @ $false)) | ($true != (f4 @ $false)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f479,plain,(
% 1.89/1.62 ($false != (f4 @ $true)) | ($true != (f4 @ $true)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f478,plain,(
% 1.89/1.62 ($true != sF1) | (sF1 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f477,plain,(
% 1.89/1.62 ($true != sF2) | (sF2 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f476,plain,(
% 1.89/1.62 ($true != sF0) | ($false != sF0) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f475,plain,(
% 1.89/1.62 ($true != sF9) | ($false != sF9) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f474,plain,(
% 1.89/1.62 ($true != sF14) | (sF14 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f473,plain,(
% 1.89/1.62 ($true != sF3) | ($false != sF3) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f472,plain,(
% 1.89/1.62 ($true != (f2 @ $false)) | ((f2 @ $false) != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f471,plain,(
% 1.89/1.62 ($true != sF4) | (sF4 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f470,plain,(
% 1.89/1.62 ($true != (f2 @ $true)) | ((f2 @ $true) != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f469,plain,(
% 1.89/1.62 ($true != (f0 @ $false)) | ((f0 @ $false) != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f468,plain,(
% 1.89/1.62 ($true != (f0 @ $true)) | ((f0 @ $true) != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f467,plain,(
% 1.89/1.62 ($true != sF18) | (sF18 != $false) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f466,plain,(
% 1.89/1.62 ($true != (f3 @ $false)) | ($false != (f3 @ $false)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f465,plain,(
% 1.89/1.62 ($true != (f3 @ $true)) | ($false != (f3 @ $true)) | ($true = $false)),
% 1.89/1.62 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.89/1.62 thf(f464,plain,(
% 1.89/1.62 spl19_58 | spl19_53 | spl19_55),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f29,f406,f396,f428])).
% 1.89/1.62 thf(f428,definition,(
% 1.89/1.62 spl19_58 <=> ($true = sF5)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_58])],[avatar_definition])).
% 1.89/1.62 thf(f396,definition,(
% 1.89/1.62 spl19_53 <=> (sF6 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_53])],[avatar_definition])).
% 1.89/1.62 thf(f406,definition,(
% 1.89/1.62 spl19_55 <=> ($true = (f1 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_55])],[avatar_definition])).
% 1.89/1.62 thf(f29,plain,(
% 1.89/1.62 ($true = (f1 @ $false)) | ($true = sF5) | (sF6 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.89/1.62 thf(f27,plain,(
% 1.89/1.62 ($true = sF5) | (sF6 = (f1 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f12])).
% 1.89/1.62 thf(f12,definition,(
% 1.89/1.62 (sF6 = (f1 @ sF5))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f463,plain,(
% 1.89/1.62 spl19_56 | spl19_57 | spl19_58),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f28,f428,f415,f410])).
% 1.89/1.62 thf(f410,definition,(
% 1.89/1.62 spl19_56 <=> ($true = sF6)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_56])],[avatar_definition])).
% 1.89/1.62 thf(f415,definition,(
% 1.89/1.62 spl19_57 <=> ((f1 @ $false) = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_57])],[avatar_definition])).
% 1.89/1.62 thf(f28,plain,(
% 1.89/1.62 ($true = sF6) | ($true = sF5) | ((f1 @ $false) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.89/1.62 thf(f462,plain,(
% 1.89/1.62 spl19_54 | spl19_59 | spl19_53),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f31,f396,f433,f401])).
% 1.89/1.62 thf(f401,definition,(
% 1.89/1.62 spl19_54 <=> ($true = (f1 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_54])],[avatar_definition])).
% 1.89/1.62 thf(f433,definition,(
% 1.89/1.62 spl19_59 <=> (sF5 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_59])],[avatar_definition])).
% 1.89/1.62 thf(f31,plain,(
% 1.89/1.62 (sF6 = $false) | (sF5 = $false) | ($true = (f1 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.89/1.62 thf(f26,plain,(
% 1.89/1.62 (sF6 = (f1 @ $true)) | (sF5 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f12])).
% 1.89/1.62 thf(f461,plain,(
% 1.89/1.62 spl19_59 | spl19_56 | spl19_52),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f30,f392,f410,f433])).
% 1.89/1.62 thf(f392,definition,(
% 1.89/1.62 spl19_52 <=> ($false = (f1 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_52])],[avatar_definition])).
% 1.89/1.62 thf(f30,plain,(
% 1.89/1.62 (sF5 = $false) | ($true = sF6) | ($false = (f1 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.89/1.62 thf(f460,plain,(
% 1.89/1.62 spl19_44 | spl19_23 | spl19_25),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f35,f255,f245,f349])).
% 1.89/1.62 thf(f349,definition,(
% 1.89/1.62 spl19_44 <=> ($true = sF12)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_44])],[avatar_definition])).
% 1.89/1.62 thf(f245,definition,(
% 1.89/1.62 spl19_23 <=> ($true = (f2 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_23])],[avatar_definition])).
% 1.89/1.62 thf(f255,definition,(
% 1.89/1.62 spl19_25 <=> (sF13 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_25])],[avatar_definition])).
% 1.89/1.62 thf(f35,plain,(
% 1.89/1.62 (sF13 = $false) | ($true = (f2 @ $false)) | ($true = sF12)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.89/1.62 thf(f33,plain,(
% 1.89/1.62 (sF13 = (f2 @ $false)) | ($true = sF12)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f19])).
% 1.89/1.62 thf(f19,definition,(
% 1.89/1.62 (sF13 = (f2 @ sF12))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f459,plain,(
% 1.89/1.62 spl19_28 | spl19_24 | spl19_44),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f34,f349,f250,f269])).
% 1.89/1.62 thf(f269,definition,(
% 1.89/1.62 spl19_28 <=> ($true = sF13)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_28])],[avatar_definition])).
% 1.89/1.62 thf(f250,definition,(
% 1.89/1.62 spl19_24 <=> ((f2 @ $false) = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_24])],[avatar_definition])).
% 1.89/1.62 thf(f34,plain,(
% 1.89/1.62 ($true = sF12) | ($true = sF13) | ((f2 @ $false) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.89/1.62 thf(f458,plain,(
% 1.89/1.62 spl19_21 | spl19_28 | spl19_42),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f37,f340,f269,f236])).
% 1.89/1.62 thf(f236,definition,(
% 1.89/1.62 spl19_21 <=> ((f2 @ $true) = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_21])],[avatar_definition])).
% 1.89/1.62 thf(f340,definition,(
% 1.89/1.62 spl19_42 <=> ($false = sF12)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_42])],[avatar_definition])).
% 1.89/1.62 thf(f37,plain,(
% 1.89/1.62 ((f2 @ $true) = $false) | ($true = sF13) | ($false = sF12)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.89/1.62 thf(f32,plain,(
% 1.89/1.62 ($false = sF12) | ((f2 @ $true) = sF13)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f19])).
% 1.89/1.62 thf(f457,plain,(
% 1.89/1.62 spl19_25 | spl19_42 | spl19_20),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f36,f231,f340,f255])).
% 1.89/1.62 thf(f231,definition,(
% 1.89/1.62 spl19_20 <=> ($true = (f2 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_20])],[avatar_definition])).
% 1.89/1.62 thf(f36,plain,(
% 1.89/1.62 ($false = sF12) | ($true = (f2 @ $true)) | (sF13 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.89/1.62 thf(f456,plain,(
% 1.89/1.62 spl19_12 | spl19_46),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f39,f360,f192])).
% 1.89/1.62 thf(f192,definition,(
% 1.89/1.62 spl19_12 <=> (sF18 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_12])],[avatar_definition])).
% 1.89/1.62 thf(f360,definition,(
% 1.89/1.62 spl19_46 <=> (sF8 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_46])],[avatar_definition])).
% 1.89/1.62 thf(f39,plain,(
% 1.89/1.62 (sF18 = $false) | (sF8 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.89/1.62 thf(f25,plain,(
% 1.89/1.62 (sF18 != sF8)),
% 1.89/1.62 inference(definition_folding,[status(thm)],[f5,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f6,f14,f13,f12,f11,f10,f9,f8,f7,f6])).
% 1.89/1.62 thf(f7,definition,(
% 1.89/1.62 ((f3 @ sF0) = sF1)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f8,definition,(
% 1.89/1.62 (sF2 = (f3 @ sF1))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f9,definition,(
% 1.89/1.62 ((f3 @ sF2) = sF3)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f10,definition,(
% 1.89/1.62 (sF4 = (f2 @ sF3))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f11,definition,(
% 1.89/1.62 (sF5 = (f1 @ sF4))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f13,definition,(
% 1.89/1.62 (sF7 = (f1 @ sF6))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f14,definition,(
% 1.89/1.62 (sF8 = (f0 @ sF7))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f6,definition,(
% 1.89/1.62 ((f4 @ x) = sF0)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f15,definition,(
% 1.89/1.62 (sF9 = (f4 @ sF0))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f16,definition,(
% 1.89/1.62 ((f4 @ sF9) = sF10)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f17,definition,(
% 1.89/1.62 ((f3 @ sF10) = sF11)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f18,definition,(
% 1.89/1.62 ((f2 @ sF11) = sF12)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f20,definition,(
% 1.89/1.62 ((f2 @ sF13) = sF14)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f21,definition,(
% 1.89/1.62 (sF15 = (f1 @ sF14))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f22,definition,(
% 1.89/1.62 ((f0 @ sF15) = sF16)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f23,definition,(
% 1.89/1.62 ((f0 @ sF16) = sF17)),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f24,definition,(
% 1.89/1.62 (sF18 = (f0 @ sF17))),
% 1.89/1.62 introduced(definition,[],[function_definition])).
% 1.89/1.62 thf(f5,plain,(
% 1.89/1.62 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ x))))))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ x))))))))))))),
% 1.89/1.62 inference(cnf_transformation,[status(thm)],[f4])).
% 1.89/1.62 thf(f4,plain,(
% 1.89/1.62 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ x))))))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ x))))))))))))),
% 1.89/1.62 inference(flattening,[status(thm)],[f2])).
% 1.89/1.62 thf(f2,negated_conjecture,(
% 1.89/1.62 ~((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ x))))))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ x))))))))))))),
% 1.89/1.62 inference(negated_conjecture,[status(cth)],[f1])).
% 1.89/1.62 thf(f1,conjecture,(
% 1.89/1.62 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ x))))))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ x))))))))))))),
% 1.89/1.62 file('/export/starexec/sandbox/tmp/tmp.07oceyV6KT/DTF2THF_27972.p',kaminski5)).
% 1.89/1.62 thf(f455,plain,(
% 1.89/1.62 spl19_48 | spl19_9),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f38,f179,f369])).
% 1.89/1.62 thf(f369,definition,(
% 1.89/1.62 spl19_48 <=> ($true = sF8)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_48])],[avatar_definition])).
% 1.89/1.62 thf(f179,definition,(
% 1.89/1.62 spl19_9 <=> ($true = sF18)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_9])],[avatar_definition])).
% 1.89/1.62 thf(f38,plain,(
% 1.89/1.62 ($true = sF8) | ($true = sF18)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.89/1.62 thf(f454,plain,(
% 1.89/1.62 spl19_36 | spl19_30 | spl19_61),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f43,f450,f279,f306])).
% 1.89/1.62 thf(f306,definition,(
% 1.89/1.62 spl19_36 <=> ($true = (f4 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_36])],[avatar_definition])).
% 1.89/1.62 thf(f279,definition,(
% 1.89/1.62 spl19_30 <=> ($false = sF0)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_30])],[avatar_definition])).
% 1.89/1.62 thf(f450,definition,(
% 1.89/1.62 spl19_61 <=> (x = $true)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_61])],[avatar_definition])).
% 1.89/1.62 thf(f43,plain,(
% 1.89/1.62 (x = $true) | ($true = (f4 @ $false)) | ($false = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.89/1.62 thf(f41,plain,(
% 1.89/1.62 (x = $true) | (sF0 = (f4 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f6])).
% 1.89/1.62 thf(f453,plain,(
% 1.89/1.62 spl19_34 | spl19_61 | spl19_35),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f42,f301,f450,f297])).
% 1.89/1.62 thf(f297,definition,(
% 1.89/1.62 spl19_34 <=> ($false = (f4 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_34])],[avatar_definition])).
% 1.89/1.62 thf(f301,definition,(
% 1.89/1.62 spl19_35 <=> ($true = sF0)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_35])],[avatar_definition])).
% 1.89/1.62 thf(f42,plain,(
% 1.89/1.62 (x = $true) | ($false = (f4 @ $false)) | ($true = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.89/1.62 thf(f448,plain,(
% 1.89/1.62 spl19_60 | spl19_29 | spl19_30),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f45,f279,f275,f444])).
% 1.89/1.62 thf(f444,definition,(
% 1.89/1.62 spl19_60 <=> (x = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_60])],[avatar_definition])).
% 1.89/1.62 thf(f275,definition,(
% 1.89/1.62 spl19_29 <=> ($true = (f4 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_29])],[avatar_definition])).
% 1.89/1.62 thf(f45,plain,(
% 1.89/1.62 (x = $false) | ($true = (f4 @ $true)) | ($false = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.89/1.62 thf(f40,plain,(
% 1.89/1.62 (x = $false) | (sF0 = (f4 @ $true))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f6])).
% 1.89/1.62 thf(f447,plain,(
% 1.89/1.62 spl19_33 | spl19_60 | spl19_35),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f44,f301,f444,f292])).
% 1.89/1.62 thf(f292,definition,(
% 1.89/1.62 spl19_33 <=> ($false = (f4 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_33])],[avatar_definition])).
% 1.89/1.62 thf(f44,plain,(
% 1.89/1.62 ($false = (f4 @ $true)) | (x = $false) | ($true = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.89/1.62 thf(f442,plain,(
% 1.89/1.62 spl19_1 | spl19_35 | spl19_8),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f49,f174,f301,f143])).
% 1.89/1.62 thf(f143,definition,(
% 1.89/1.62 spl19_1 <=> (sF1 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_1])],[avatar_definition])).
% 1.89/1.62 thf(f174,definition,(
% 1.89/1.62 spl19_8 <=> ($true = (f3 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_8])],[avatar_definition])).
% 1.89/1.62 thf(f49,plain,(
% 1.89/1.62 ($true = sF0) | (sF1 = $false) | ($true = (f3 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.89/1.62 thf(f47,plain,(
% 1.89/1.62 (sF1 = (f3 @ $false)) | ($true = sF0)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f7])).
% 1.89/1.62 thf(f441,plain,(
% 1.89/1.62 spl19_7 | spl19_35 | spl19_6),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f48,f165,f301,f169])).
% 1.89/1.62 thf(f169,definition,(
% 1.89/1.62 spl19_7 <=> ($true = sF1)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_7])],[avatar_definition])).
% 1.89/1.62 thf(f165,definition,(
% 1.89/1.62 spl19_6 <=> ($false = (f3 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_6])],[avatar_definition])).
% 1.89/1.62 thf(f48,plain,(
% 1.89/1.62 ($true = sF0) | ($true = sF1) | ($false = (f3 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.89/1.62 thf(f440,plain,(
% 1.89/1.62 spl19_1 | spl19_5 | spl19_30),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f51,f279,f160,f143])).
% 1.89/1.62 thf(f160,definition,(
% 1.89/1.62 spl19_5 <=> ($true = (f3 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_5])],[avatar_definition])).
% 1.89/1.62 thf(f51,plain,(
% 1.89/1.62 ($false = sF0) | (sF1 = $false) | ($true = (f3 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.89/1.62 thf(f46,plain,(
% 1.89/1.62 ($false = sF0) | (sF1 = (f3 @ $true))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f7])).
% 1.89/1.62 thf(f439,plain,(
% 1.89/1.62 spl19_7 | spl19_3 | spl19_30),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f50,f279,f151,f169])).
% 1.89/1.62 thf(f151,definition,(
% 1.89/1.62 spl19_3 <=> ($false = (f3 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_3])],[avatar_definition])).
% 1.89/1.62 thf(f50,plain,(
% 1.89/1.62 ($false = sF0) | ($false = (f3 @ $true)) | ($true = sF1)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.89/1.62 thf(f438,plain,(
% 1.89/1.62 spl19_57 | spl19_22 | spl19_58),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f55,f428,f240,f415])).
% 1.89/1.62 thf(f240,definition,(
% 1.89/1.62 spl19_22 <=> ($true = sF4)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_22])],[avatar_definition])).
% 1.89/1.62 thf(f55,plain,(
% 1.89/1.62 ((f1 @ $false) = $false) | ($true = sF5) | ($true = sF4)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.89/1.62 thf(f53,plain,(
% 1.89/1.62 ((f1 @ $false) = sF5) | ($true = sF4)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f11])).
% 1.89/1.62 thf(f437,plain,(
% 1.89/1.62 spl19_22 | spl19_55 | spl19_59),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f54,f433,f406,f240])).
% 1.89/1.62 thf(f54,plain,(
% 1.89/1.62 ($true = sF4) | (sF5 = $false) | ($true = (f1 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.89/1.62 thf(f436,plain,(
% 1.89/1.62 spl19_54 | spl19_59 | spl19_19),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f57,f227,f433,f401])).
% 1.89/1.62 thf(f227,definition,(
% 1.89/1.62 spl19_19 <=> (sF4 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_19])],[avatar_definition])).
% 1.89/1.62 thf(f57,plain,(
% 1.89/1.62 (sF5 = $false) | (sF4 = $false) | ($true = (f1 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.89/1.62 thf(f52,plain,(
% 1.89/1.62 (sF5 = (f1 @ $true)) | (sF4 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f11])).
% 1.89/1.62 thf(f431,plain,(
% 1.89/1.62 spl19_19 | spl19_52 | spl19_58),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f56,f428,f392,f227])).
% 1.89/1.62 thf(f56,plain,(
% 1.89/1.62 ($true = sF5) | (sF4 = $false) | ($false = (f1 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.89/1.62 thf(f426,plain,(
% 1.89/1.62 spl19_55 | spl19_27 | spl19_39),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f61,f320,f264,f406])).
% 1.89/1.62 thf(f264,definition,(
% 1.89/1.62 spl19_27 <=> ($true = sF14)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_27])],[avatar_definition])).
% 1.89/1.62 thf(f320,definition,(
% 1.89/1.62 spl19_39 <=> (sF15 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_39])],[avatar_definition])).
% 1.89/1.62 thf(f61,plain,(
% 1.89/1.62 ($true = sF14) | ($true = (f1 @ $false)) | (sF15 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.89/1.62 thf(f59,plain,(
% 1.89/1.62 ($true = sF14) | (sF15 = (f1 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f21])).
% 1.89/1.62 thf(f425,plain,(
% 1.89/1.62 spl19_57 | spl19_41 | spl19_27),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f60,f264,f330,f415])).
% 1.89/1.62 thf(f330,definition,(
% 1.89/1.62 spl19_41 <=> ($true = sF15)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_41])],[avatar_definition])).
% 1.89/1.62 thf(f60,plain,(
% 1.89/1.62 ($true = sF14) | ((f1 @ $false) = $false) | ($true = sF15)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.89/1.62 thf(f424,plain,(
% 1.89/1.62 spl19_26 | spl19_39 | spl19_54),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f63,f401,f320,f259])).
% 1.89/1.62 thf(f259,definition,(
% 1.89/1.62 spl19_26 <=> (sF14 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_26])],[avatar_definition])).
% 1.89/1.62 thf(f63,plain,(
% 1.89/1.62 ($true = (f1 @ $true)) | (sF14 = $false) | (sF15 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.89/1.62 thf(f58,plain,(
% 1.89/1.62 (sF15 = (f1 @ $true)) | (sF14 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f21])).
% 1.89/1.62 thf(f423,plain,(
% 1.89/1.62 spl19_52 | spl19_41 | spl19_26),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f62,f259,f330,f392])).
% 1.89/1.62 thf(f62,plain,(
% 1.89/1.62 ($false = (f1 @ $true)) | ($true = sF15) | (sF14 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.89/1.62 thf(f422,plain,(
% 1.89/1.62 spl19_43 | spl19_51 | spl19_8),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f67,f174,f385,f344])).
% 1.89/1.62 thf(f344,definition,(
% 1.89/1.62 spl19_43 <=> ($false = sF11)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_43])],[avatar_definition])).
% 1.89/1.62 thf(f385,definition,(
% 1.89/1.62 spl19_51 <=> ($true = sF10)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_51])],[avatar_definition])).
% 1.89/1.62 thf(f67,plain,(
% 1.89/1.62 ($true = sF10) | ($false = sF11) | ($true = (f3 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.89/1.62 thf(f65,plain,(
% 1.89/1.62 ($true = sF10) | (sF11 = (f3 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f17])).
% 1.89/1.62 thf(f421,plain,(
% 1.89/1.62 spl19_51 | spl19_6 | spl19_45),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f66,f354,f165,f385])).
% 1.89/1.62 thf(f354,definition,(
% 1.89/1.62 spl19_45 <=> ($true = sF11)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_45])],[avatar_definition])).
% 1.89/1.62 thf(f66,plain,(
% 1.89/1.62 ($true = sF10) | ($false = (f3 @ $false)) | ($true = sF11)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.89/1.62 thf(f420,plain,(
% 1.89/1.62 spl19_50 | spl19_3 | spl19_45),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f69,f354,f151,f380])).
% 1.89/1.62 thf(f380,definition,(
% 1.89/1.62 spl19_50 <=> ($false = sF10)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_50])],[avatar_definition])).
% 1.89/1.62 thf(f69,plain,(
% 1.89/1.62 ($true = sF11) | ($false = sF10) | ($false = (f3 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.89/1.62 thf(f64,plain,(
% 1.89/1.62 ((f3 @ $true) = sF11) | ($false = sF10)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f17])).
% 1.89/1.62 thf(f419,plain,(
% 1.89/1.62 spl19_50 | spl19_43 | spl19_5),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f68,f160,f344,f380])).
% 1.89/1.62 thf(f68,plain,(
% 1.89/1.62 ($false = sF11) | ($false = sF10) | ($true = (f3 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.89/1.62 thf(f418,plain,(
% 1.89/1.62 spl19_56 | spl19_57 | spl19_49),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f73,f374,f415,f410])).
% 1.89/1.62 thf(f374,definition,(
% 1.89/1.62 spl19_49 <=> ($true = sF7)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_49])],[avatar_definition])).
% 1.89/1.62 thf(f73,plain,(
% 1.89/1.62 ($true = sF7) | ((f1 @ $false) = $false) | ($true = sF6)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.89/1.62 thf(f71,plain,(
% 1.89/1.62 ((f1 @ $false) = sF7) | ($true = sF6)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f13])).
% 1.89/1.62 thf(f413,plain,(
% 1.89/1.62 spl19_47 | spl19_55 | spl19_56),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f72,f410,f406,f364])).
% 1.89/1.62 thf(f364,definition,(
% 1.89/1.62 spl19_47 <=> ($false = sF7)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_47])],[avatar_definition])).
% 1.89/1.62 thf(f72,plain,(
% 1.89/1.62 ($false = sF7) | ($true = (f1 @ $false)) | ($true = sF6)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.89/1.62 thf(f404,plain,(
% 1.89/1.62 spl19_47 | spl19_53 | spl19_54),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f75,f401,f396,f364])).
% 1.89/1.62 thf(f75,plain,(
% 1.89/1.62 ($true = (f1 @ $true)) | (sF6 = $false) | ($false = sF7)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.89/1.62 thf(f70,plain,(
% 1.89/1.62 (sF7 = (f1 @ $true)) | (sF6 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f13])).
% 1.89/1.62 thf(f399,plain,(
% 1.89/1.62 spl19_52 | spl19_53 | spl19_49),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f74,f374,f396,f392])).
% 1.89/1.62 thf(f74,plain,(
% 1.89/1.62 ($true = sF7) | ($false = (f1 @ $true)) | (sF6 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.89/1.62 thf(f390,plain,(
% 1.89/1.62 spl19_32 | spl19_34 | spl19_51),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f79,f385,f297,f288])).
% 1.89/1.62 thf(f288,definition,(
% 1.89/1.62 spl19_32 <=> ($true = sF9)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_32])],[avatar_definition])).
% 1.89/1.62 thf(f79,plain,(
% 1.89/1.62 ($false = (f4 @ $false)) | ($true = sF9) | ($true = sF10)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.89/1.62 thf(f77,plain,(
% 1.89/1.62 ((f4 @ $false) = sF10) | ($true = sF9)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f16])).
% 1.89/1.62 thf(f389,plain,(
% 1.89/1.62 spl19_36 | spl19_50 | spl19_32),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f78,f288,f380,f306])).
% 1.89/1.62 thf(f78,plain,(
% 1.89/1.62 ($true = sF9) | ($false = sF10) | ($true = (f4 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.89/1.62 thf(f388,plain,(
% 1.89/1.62 spl19_51 | spl19_31 | spl19_33),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f81,f292,f283,f385])).
% 1.89/1.62 thf(f283,definition,(
% 1.89/1.62 spl19_31 <=> ($false = sF9)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_31])],[avatar_definition])).
% 1.89/1.62 thf(f81,plain,(
% 1.89/1.62 ($false = sF9) | ($false = (f4 @ $true)) | ($true = sF10)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.89/1.62 thf(f76,plain,(
% 1.89/1.62 ($false = sF9) | ((f4 @ $true) = sF10)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f16])).
% 1.89/1.62 thf(f383,plain,(
% 1.89/1.62 spl19_50 | spl19_29 | spl19_31),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f80,f283,f275,f380])).
% 1.89/1.62 thf(f80,plain,(
% 1.89/1.62 ($false = sF9) | ($false = sF10) | ($true = (f4 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.89/1.62 thf(f378,plain,(
% 1.89/1.62 spl19_48 | spl19_49 | spl19_15),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f85,f205,f374,f369])).
% 1.89/1.62 thf(f205,definition,(
% 1.89/1.62 spl19_15 <=> ((f0 @ $false) = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_15])],[avatar_definition])).
% 1.89/1.62 thf(f85,plain,(
% 1.89/1.62 ($true = sF7) | ($true = sF8) | ((f0 @ $false) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.89/1.62 thf(f83,plain,(
% 1.89/1.62 ((f0 @ $false) = sF8) | ($true = sF7)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f14])).
% 1.89/1.62 thf(f377,plain,(
% 1.89/1.62 spl19_16 | spl19_46 | spl19_49),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f84,f374,f360,f210])).
% 1.89/1.62 thf(f210,definition,(
% 1.89/1.62 spl19_16 <=> ($true = (f0 @ $false))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_16])],[avatar_definition])).
% 1.89/1.62 thf(f84,plain,(
% 1.89/1.62 ($true = sF7) | ($true = (f0 @ $false)) | (sF8 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.89/1.62 thf(f372,plain,(
% 1.89/1.62 spl19_47 | spl19_48 | spl19_11),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f87,f187,f369,f364])).
% 1.89/1.62 thf(f187,definition,(
% 1.89/1.62 spl19_11 <=> ((f0 @ $true) = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_11])],[avatar_definition])).
% 1.89/1.62 thf(f87,plain,(
% 1.89/1.62 ($false = sF7) | ((f0 @ $true) = $false) | ($true = sF8)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.89/1.62 thf(f82,plain,(
% 1.89/1.62 ((f0 @ $true) = sF8) | ($false = sF7)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f14])).
% 1.89/1.62 thf(f367,plain,(
% 1.89/1.62 spl19_46 | spl19_47 | spl19_13),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f86,f196,f364,f360])).
% 1.89/1.62 thf(f196,definition,(
% 1.89/1.62 spl19_13 <=> ($true = (f0 @ $true))),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_13])],[avatar_definition])).
% 1.89/1.62 thf(f86,plain,(
% 1.89/1.62 ($false = sF7) | (sF8 = $false) | ($true = (f0 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.89/1.62 thf(f358,plain,(
% 1.89/1.62 spl19_44 | spl19_24 | spl19_45),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f91,f354,f250,f349])).
% 1.89/1.62 thf(f91,plain,(
% 1.89/1.62 ($true = sF12) | ($true = sF11) | ((f2 @ $false) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.89/1.62 thf(f89,plain,(
% 1.89/1.62 ($true = sF11) | ((f2 @ $false) = sF12)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f18])).
% 1.89/1.62 thf(f357,plain,(
% 1.89/1.62 spl19_45 | spl19_42 | spl19_23),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f90,f245,f340,f354])).
% 1.89/1.62 thf(f90,plain,(
% 1.89/1.62 ($false = sF12) | ($true = sF11) | ($true = (f2 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.89/1.62 thf(f352,plain,(
% 1.89/1.62 spl19_43 | spl19_44 | spl19_21),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f93,f236,f349,f344])).
% 1.89/1.62 thf(f93,plain,(
% 1.89/1.62 ((f2 @ $true) = $false) | ($false = sF11) | ($true = sF12)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.89/1.62 thf(f88,plain,(
% 1.89/1.62 ((f2 @ $true) = sF12) | ($false = sF11)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f18])).
% 1.89/1.62 thf(f347,plain,(
% 1.89/1.62 spl19_42 | spl19_43 | spl19_20),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f92,f231,f344,f340])).
% 1.89/1.62 thf(f92,plain,(
% 1.89/1.62 ($false = sF11) | ($true = (f2 @ $true)) | ($false = sF12)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.89/1.62 thf(f338,plain,(
% 1.89/1.62 spl19_15 | spl19_40 | spl19_14),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f97,f201,f325,f205])).
% 1.89/1.62 thf(f325,definition,(
% 1.89/1.62 spl19_40 <=> ($true = sF16)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_40])],[avatar_definition])).
% 1.89/1.62 thf(f201,definition,(
% 1.89/1.62 spl19_14 <=> ($true = sF17)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_14])],[avatar_definition])).
% 1.89/1.62 thf(f97,plain,(
% 1.89/1.62 ((f0 @ $false) = $false) | ($true = sF17) | ($true = sF16)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.89/1.62 thf(f95,plain,(
% 1.89/1.62 ((f0 @ $false) = sF17) | ($true = sF16)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f23])).
% 1.89/1.62 thf(f337,plain,(
% 1.89/1.62 spl19_40 | spl19_10 | spl19_16),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f96,f210,f183,f325])).
% 1.89/1.62 thf(f183,definition,(
% 1.89/1.62 spl19_10 <=> (sF17 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_10])],[avatar_definition])).
% 1.89/1.62 thf(f96,plain,(
% 1.89/1.62 ($true = sF16) | (sF17 = $false) | ($true = (f0 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.89/1.62 thf(f336,plain,(
% 1.89/1.62 spl19_38 | spl19_11 | spl19_14),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f99,f201,f187,f316])).
% 1.89/1.62 thf(f316,definition,(
% 1.89/1.62 spl19_38 <=> ($false = sF16)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_38])],[avatar_definition])).
% 1.89/1.62 thf(f99,plain,(
% 1.89/1.62 ((f0 @ $true) = $false) | ($false = sF16) | ($true = sF17)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.89/1.62 thf(f94,plain,(
% 1.89/1.62 ((f0 @ $true) = sF17) | ($false = sF16)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f23])).
% 1.89/1.62 thf(f335,plain,(
% 1.89/1.62 spl19_38 | spl19_13 | spl19_10),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f98,f183,f196,f316])).
% 1.89/1.62 thf(f98,plain,(
% 1.89/1.62 ($true = (f0 @ $true)) | ($false = sF16) | (sF17 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.89/1.62 thf(f334,plain,(
% 1.89/1.62 spl19_40 | spl19_41 | spl19_15),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f103,f205,f330,f325])).
% 1.89/1.62 thf(f103,plain,(
% 1.89/1.62 ($true = sF16) | ((f0 @ $false) = $false) | ($true = sF15)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.89/1.62 thf(f101,plain,(
% 1.89/1.62 ((f0 @ $false) = sF16) | ($true = sF15)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f22])).
% 1.89/1.62 thf(f333,plain,(
% 1.89/1.62 spl19_41 | spl19_38 | spl19_16),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f102,f210,f316,f330])).
% 1.89/1.62 thf(f102,plain,(
% 1.89/1.62 ($true = sF15) | ($false = sF16) | ($true = (f0 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.89/1.62 thf(f328,plain,(
% 1.89/1.62 spl19_40 | spl19_11 | spl19_39),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f105,f320,f187,f325])).
% 1.89/1.62 thf(f105,plain,(
% 1.89/1.62 (sF15 = $false) | ((f0 @ $true) = $false) | ($true = sF16)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.89/1.62 thf(f100,plain,(
% 1.89/1.62 ((f0 @ $true) = sF16) | (sF15 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f22])).
% 1.89/1.62 thf(f323,plain,(
% 1.89/1.62 spl19_38 | spl19_39 | spl19_13),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f104,f196,f320,f316])).
% 1.89/1.62 thf(f104,plain,(
% 1.89/1.62 ($true = (f0 @ $true)) | (sF15 = $false) | ($false = sF16)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.89/1.62 thf(f314,plain,(
% 1.89/1.62 ~spl19_37),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f3,f311])).
% 1.89/1.62 thf(f311,definition,(
% 1.89/1.62 spl19_37 <=> ($true = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_37])],[avatar_definition])).
% 1.89/1.62 thf(f3,plain,(
% 1.89/1.62 ($true != $false)),
% 1.89/1.62 introduced(definition,[],[fool_axiom])).
% 1.89/1.62 thf(f309,plain,(
% 1.89/1.62 spl19_31 | spl19_35 | spl19_36),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f109,f306,f301,f283])).
% 1.89/1.62 thf(f109,plain,(
% 1.89/1.62 ($false = sF9) | ($true = (f4 @ $false)) | ($true = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.89/1.62 thf(f107,plain,(
% 1.89/1.62 ($true = sF0) | (sF9 = (f4 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f15])).
% 1.89/1.62 thf(f304,plain,(
% 1.89/1.62 spl19_32 | spl19_34 | spl19_35),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f108,f301,f297,f288])).
% 1.89/1.62 thf(f108,plain,(
% 1.89/1.62 ($true = sF9) | ($true = sF0) | ($false = (f4 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.89/1.62 thf(f295,plain,(
% 1.89/1.62 spl19_32 | spl19_30 | spl19_33),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f111,f292,f279,f288])).
% 1.89/1.62 thf(f111,plain,(
% 1.89/1.62 ($false = (f4 @ $true)) | ($true = sF9) | ($false = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.89/1.62 thf(f106,plain,(
% 1.89/1.62 ($false = sF0) | ((f4 @ $true) = sF9)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f15])).
% 1.89/1.62 thf(f286,plain,(
% 1.89/1.62 spl19_29 | spl19_30 | spl19_31),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f110,f283,f279,f275])).
% 1.89/1.62 thf(f110,plain,(
% 1.89/1.62 ($false = sF9) | ($true = (f4 @ $true)) | ($false = sF0)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.89/1.62 thf(f273,plain,(
% 1.89/1.62 spl19_27 | spl19_28 | spl19_24),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f115,f250,f269,f264])).
% 1.89/1.62 thf(f115,plain,(
% 1.89/1.62 ($true = sF14) | ($true = sF13) | ((f2 @ $false) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.89/1.62 thf(f113,plain,(
% 1.89/1.62 ((f2 @ $false) = sF14) | ($true = sF13)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f20])).
% 1.89/1.62 thf(f272,plain,(
% 1.89/1.62 spl19_28 | spl19_23 | spl19_26),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f114,f259,f245,f269])).
% 1.89/1.62 thf(f114,plain,(
% 1.89/1.62 (sF14 = $false) | ($true = (f2 @ $false)) | ($true = sF13)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.89/1.62 thf(f267,plain,(
% 1.89/1.62 spl19_21 | spl19_25 | spl19_27),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f117,f264,f255,f236])).
% 1.89/1.62 thf(f117,plain,(
% 1.89/1.62 ($true = sF14) | (sF13 = $false) | ((f2 @ $true) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.89/1.62 thf(f112,plain,(
% 1.89/1.62 ((f2 @ $true) = sF14) | (sF13 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f20])).
% 1.89/1.62 thf(f262,plain,(
% 1.89/1.62 spl19_20 | spl19_25 | spl19_26),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f116,f259,f255,f231])).
% 1.89/1.62 thf(f116,plain,(
% 1.89/1.62 (sF13 = $false) | ($true = (f2 @ $true)) | (sF14 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.89/1.62 thf(f253,plain,(
% 1.89/1.62 spl19_22 | spl19_18 | spl19_24),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f121,f250,f220,f240])).
% 1.89/1.62 thf(f220,definition,(
% 1.89/1.62 spl19_18 <=> ($true = sF3)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_18])],[avatar_definition])).
% 1.89/1.62 thf(f121,plain,(
% 1.89/1.62 ((f2 @ $false) = $false) | ($true = sF3) | ($true = sF4)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.89/1.62 thf(f119,plain,(
% 1.89/1.62 ($true = sF3) | ((f2 @ $false) = sF4)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f10])).
% 1.89/1.62 thf(f248,plain,(
% 1.89/1.62 spl19_18 | spl19_19 | spl19_23),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f120,f245,f227,f220])).
% 1.89/1.62 thf(f120,plain,(
% 1.89/1.62 (sF4 = $false) | ($true = (f2 @ $false)) | ($true = sF3)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.89/1.62 thf(f243,plain,(
% 1.89/1.62 spl19_21 | spl19_22 | spl19_17),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f123,f215,f240,f236])).
% 1.89/1.62 thf(f215,definition,(
% 1.89/1.62 spl19_17 <=> ($false = sF3)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_17])],[avatar_definition])).
% 1.89/1.62 thf(f123,plain,(
% 1.89/1.62 ($false = sF3) | ($true = sF4) | ((f2 @ $true) = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.89/1.62 thf(f118,plain,(
% 1.89/1.62 ((f2 @ $true) = sF4) | ($false = sF3)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f10])).
% 1.89/1.62 thf(f234,plain,(
% 1.89/1.62 spl19_19 | spl19_17 | spl19_20),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f122,f231,f215,f227])).
% 1.89/1.62 thf(f122,plain,(
% 1.89/1.62 ($true = (f2 @ $true)) | ($false = sF3) | (sF4 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.89/1.62 thf(f225,plain,(
% 1.89/1.62 spl19_8 | spl19_2 | spl19_17),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f127,f215,f147,f174])).
% 1.89/1.62 thf(f147,definition,(
% 1.89/1.62 spl19_2 <=> ($true = sF2)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_2])],[avatar_definition])).
% 1.89/1.62 thf(f127,plain,(
% 1.89/1.62 ($true = (f3 @ $false)) | ($true = sF2) | ($false = sF3)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.89/1.62 thf(f125,plain,(
% 1.89/1.62 ($true = sF2) | (sF3 = (f3 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f9])).
% 1.89/1.62 thf(f224,plain,(
% 1.89/1.62 spl19_18 | spl19_2 | spl19_6),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f126,f165,f147,f220])).
% 1.89/1.62 thf(f126,plain,(
% 1.89/1.62 ($true = sF3) | ($true = sF2) | ($false = (f3 @ $false))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.89/1.62 thf(f223,plain,(
% 1.89/1.62 spl19_4 | spl19_18 | spl19_3),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f129,f151,f220,f156])).
% 1.89/1.62 thf(f156,definition,(
% 1.89/1.62 spl19_4 <=> (sF2 = $false)),
% 1.89/1.62 introduced(definition,[new_symbols(naming,[spl19_4])],[avatar_definition])).
% 1.89/1.62 thf(f129,plain,(
% 1.89/1.62 ($false = (f3 @ $true)) | (sF2 = $false) | ($true = sF3)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.89/1.62 thf(f124,plain,(
% 1.89/1.62 (sF2 = $false) | ((f3 @ $true) = sF3)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f9])).
% 1.89/1.62 thf(f218,plain,(
% 1.89/1.62 spl19_17 | spl19_5 | spl19_4),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f128,f156,f160,f215])).
% 1.89/1.62 thf(f128,plain,(
% 1.89/1.62 (sF2 = $false) | ($false = sF3) | ($true = (f3 @ $true))),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.89/1.62 thf(f213,plain,(
% 1.89/1.62 spl19_14 | spl19_16 | spl19_12),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f133,f192,f210,f201])).
% 1.89/1.62 thf(f133,plain,(
% 1.89/1.62 ($true = (f0 @ $false)) | ($true = sF17) | (sF18 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.89/1.62 thf(f131,plain,(
% 1.89/1.62 (sF18 = (f0 @ $false)) | ($true = sF17)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f24])).
% 1.89/1.62 thf(f208,plain,(
% 1.89/1.62 spl19_9 | spl19_14 | spl19_15),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f132,f205,f201,f179])).
% 1.89/1.62 thf(f132,plain,(
% 1.89/1.62 ($true = sF17) | ((f0 @ $false) = $false) | ($true = sF18)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.89/1.62 thf(f199,plain,(
% 1.89/1.62 spl19_12 | spl19_10 | spl19_13),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f135,f196,f183,f192])).
% 1.89/1.62 thf(f135,plain,(
% 1.89/1.62 ($true = (f0 @ $true)) | (sF17 = $false) | (sF18 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.89/1.62 thf(f130,plain,(
% 1.89/1.62 (sF18 = (f0 @ $true)) | (sF17 = $false)),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f24])).
% 1.89/1.62 thf(f190,plain,(
% 1.89/1.62 spl19_9 | spl19_10 | spl19_11),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f134,f187,f183,f179])).
% 1.89/1.62 thf(f134,plain,(
% 1.89/1.62 (sF17 = $false) | ((f0 @ $true) = $false) | ($true = sF18)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.89/1.62 thf(f177,plain,(
% 1.89/1.62 spl19_7 | spl19_4 | spl19_8),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f139,f174,f156,f169])).
% 1.89/1.62 thf(f139,plain,(
% 1.89/1.62 ($true = (f3 @ $false)) | ($true = sF1) | (sF2 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.89/1.62 thf(f137,plain,(
% 1.89/1.62 ($true = sF1) | (sF2 = (f3 @ $false))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f8])).
% 1.89/1.62 thf(f172,plain,(
% 1.89/1.62 spl19_6 | spl19_2 | spl19_7),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f138,f169,f147,f165])).
% 1.89/1.62 thf(f138,plain,(
% 1.89/1.62 ($false = (f3 @ $false)) | ($true = sF1) | ($true = sF2)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.89/1.62 thf(f163,plain,(
% 1.89/1.62 spl19_1 | spl19_4 | spl19_5),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f141,f160,f156,f143])).
% 1.89/1.62 thf(f141,plain,(
% 1.89/1.62 (sF1 = $false) | ($true = (f3 @ $true)) | (sF2 = $false)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.89/1.62 thf(f136,plain,(
% 1.89/1.62 (sF1 = $false) | (sF2 = (f3 @ $true))),
% 1.89/1.62 inference(cases_simplifying,[status(thm)],[f8])).
% 1.89/1.62 thf(f154,plain,(
% 1.89/1.62 spl19_1 | spl19_2 | spl19_3),
% 1.89/1.62 inference(avatar_split_clause,[status(thm)],[f140,f151,f147,f143])).
% 1.89/1.62 thf(f140,plain,(
% 1.89/1.62 (sF1 = $false) | ($false = (f3 @ $true)) | ($true = sF2)),
% 1.89/1.62 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.89/1.62 % SZS output end Proof for DTF2THF_27972
% 1.89/1.62 % (28091)------------------------------
% 1.89/1.62 % (28091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.62 % (28091)Termination reason: Refutation
% 1.89/1.62
% 1.89/1.62 % (28091)Memory used [KB]: 5756
% 1.89/1.62 % (28091)Time elapsed: 0.011 s
% 1.89/1.62 % (28091)Instructions burned: 8 (million)
% 1.89/1.62 % (28091)------------------------------
% 1.89/1.62 % (28091)------------------------------
% 1.89/1.62 % (28077)Success in time 0.059 s
%------------------------------------------------------------------------------