%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1.006 : 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 : n025.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 1.94s 1.64s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 134
% Syntax : Number of formulae : 374 ( 31 unt; 0 typ; 96 def)
% Number of atoms : 2406 ( 582 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 946 ( 78 ~; 490 |; 0 &; 305 @)
% ( 73 <=>; 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 : 106 ( 103 usr; 99 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
f0: $o > $o ).
thf(func_def_2,type,
f1: $o > $o ).
thf(func_def_3,type,
f2: $o > $o ).
thf(func_def_4,type,
f3: $o > $o ).
thf(func_def_5,type,
f4: $o > $o ).
thf(func_def_6,type,
f5: $o > $o ).
thf(f593,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f182,f191,f200,f205,f218,f227,f236,f241,f250,f259,f264,f269,f278,f287,f292,f297,f306,f311,f316,f317,f326,f331,f336,f337,f346,f355,f360,f365,f366,f367,f368,f369,f378,f383,f388,f389,f394,f395,f400,f401,f410,f415,f420,f421,f430,f439,f444,f449,f454,f459,f460,f461,f466,f467,f472,f473,f478,f483,f484,f485,f486,f487,f492,f497,f498,f499,f504,f505,f510,f511,f516,f517,f522,f523,f524,f525,f526,f527,f532,f533,f534,f535,f536,f541,f542,f547,f548,f549,f550,f551,f552,f553,f554,f555,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f568,f569,f570,f571,f572,f573,f574,f575,f576,f577,f578,f579,f580,f581,f582,f583,f584,f585,f586,f587,f588,f589,f590,f591,f592]) ).
thf(f592,plain,
( ( $true != sF21 )
| ( $false != sF21 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f591,plain,
( ( $true
!= ( f5 @ $false ) )
| ( $false
!= ( f5 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f590,plain,
( ( $true != sF13 )
| ( $false != sF13 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f589,plain,
( ( $false != sF16 )
| ( sF16 != $true )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f588,plain,
( ( sF2 != $true )
| ( $false != sF2 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f587,plain,
( ( $true != sF5 )
| ( $false != sF5 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f586,plain,
( ( $true != sF17 )
| ( $false != sF17 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f585,plain,
( ( x != $true )
| ( x != $false )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f584,plain,
( ( $true != sF20 )
| ( $false != sF20 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f583,plain,
( ( sF10 != $true )
| ( $false != sF10 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f582,plain,
( ( sF22 != $true )
| ( sF22 != $false )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f581,plain,
( ( $false
!= ( f5 @ $true ) )
| ( ( f5 @ $true )
!= $true )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f580,plain,
( ( $true != sF12 )
| ( $false != sF12 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f579,plain,
( ( $true != sF19 )
| ( $false != sF19 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f578,plain,
( ( $true != sF18 )
| ( $false != sF18 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f577,plain,
( ( $true != sF9 )
| ( $false != sF9 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f576,plain,
( ( $true != sF0 )
| ( $false != sF0 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f575,plain,
( ( sF1 != $true )
| ( sF1 != $false )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f574,plain,
( ( sF7 != $true )
| ( $false != sF7 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f573,plain,
( ( $true
!= ( f1 @ $false ) )
| ( $false
!= ( f1 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f572,plain,
( ( $true
!= ( f1 @ $true ) )
| ( $false
!= ( f1 @ $true ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f571,plain,
( ( sF8 != $true )
| ( sF8 != $false )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f570,plain,
( ( $true != sF6 )
| ( $false != sF6 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f569,plain,
( ( $true != sF14 )
| ( $false != sF14 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f568,plain,
( ( $false != sF4 )
| ( sF4 != $true )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f567,plain,
( ( $false != sF3 )
| ( $true != sF3 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f566,plain,
( ( $true != sF15 )
| ( $false != sF15 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f565,plain,
( ( $true
!= ( f2 @ $false ) )
| ( $false
!= ( f2 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f564,plain,
( ( ( f2 @ $true )
!= $true )
| ( ( f2 @ $true )
!= $false )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f563,plain,
( ( $true
!= ( f3 @ $false ) )
| ( $false
!= ( f3 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f562,plain,
( ( $true
!= ( f3 @ $true ) )
| ( $false
!= ( f3 @ $true ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f561,plain,
( ( $true
!= ( f0 @ $false ) )
| ( $false
!= ( f0 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f560,plain,
( ( $true
!= ( f0 @ $true ) )
| ( $false
!= ( f0 @ $true ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f559,plain,
( ( $true != sF11 )
| ( $false != sF11 )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f558,plain,
( ( ( f4 @ $false )
!= $true )
| ( $false
!= ( f4 @ $false ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f557,plain,
( ( $false
!= ( f4 @ $true ) )
| ( $true
!= ( f4 @ $true ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f556,plain,
( spl23_61
| spl23_56
| spl23_58 ),
inference(avatar_split_clause,[status(thm)],[f33,f446,f436,f463]) ).
thf(f463,definition,
( spl23_61
<=> ( $false = sF13 ) ),
introduced(definition,[new_symbols(naming,[spl23_61])],[avatar_definition]) ).
thf(f436,definition,
( spl23_56
<=> ( $true = sF12 ) ),
introduced(definition,[new_symbols(naming,[spl23_56])],[avatar_definition]) ).
thf(f446,definition,
( spl23_58
<=> ( $true
= ( f5 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_58])],[avatar_definition]) ).
thf(f33,plain,
( ( $true = sF12 )
| ( $false = sF13 )
| ( $true
= ( f5 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( sF13
= ( f5 @ $false ) )
| ( $true = sF12 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f19,definition,
( sF13
= ( f5 @ sF12 ) ),
introduced(definition,[],[function_definition]) ).
thf(f555,plain,
( spl23_56
| spl23_57
| spl23_62 ),
inference(avatar_split_clause,[status(thm)],[f32,f469,f441,f436]) ).
thf(f441,definition,
( spl23_57
<=> ( $false
= ( f5 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_57])],[avatar_definition]) ).
thf(f469,definition,
( spl23_62
<=> ( $true = sF13 ) ),
introduced(definition,[new_symbols(naming,[spl23_62])],[avatar_definition]) ).
thf(f32,plain,
( ( $false
= ( f5 @ $false ) )
| ( $true = sF13 )
| ( $true = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f554,plain,
( spl23_62
| spl23_55
| spl23_54 ),
inference(avatar_split_clause,[status(thm)],[f35,f427,f432,f469]) ).
thf(f432,definition,
( spl23_55
<=> ( $false
= ( f5 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_55])],[avatar_definition]) ).
thf(f427,definition,
( spl23_54
<=> ( $false = sF12 ) ),
introduced(definition,[new_symbols(naming,[spl23_54])],[avatar_definition]) ).
thf(f35,plain,
( ( $false = sF12 )
| ( $true = sF13 )
| ( $false
= ( f5 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( f5 @ $true )
= sF13 )
| ( $false = sF12 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f553,plain,
( spl23_53
| spl23_54
| spl23_61 ),
inference(avatar_split_clause,[status(thm)],[f34,f463,f427,f423]) ).
thf(f423,definition,
( spl23_53
<=> ( ( f5 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl23_53])],[avatar_definition]) ).
thf(f34,plain,
( ( $false = sF13 )
| ( $false = sF12 )
| ( ( f5 @ $true )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f552,plain,
( spl23_59
| spl23_72
| spl23_22 ),
inference(avatar_split_clause,[status(thm)],[f39,f266,f538,f451]) ).
thf(f451,definition,
( spl23_59
<=> ( sF16 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_59])],[avatar_definition]) ).
thf(f538,definition,
( spl23_72
<=> ( $false = sF17 ) ),
introduced(definition,[new_symbols(naming,[spl23_72])],[avatar_definition]) ).
thf(f266,definition,
( spl23_22
<=> ( $true
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_22])],[avatar_definition]) ).
thf(f39,plain,
( ( sF16 = $true )
| ( $false = sF17 )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( sF16 = $true )
| ( sF17
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f23,definition,
( sF17
= ( f3 @ sF16 ) ),
introduced(definition,[],[function_definition]) ).
thf(f551,plain,
( spl23_21
| spl23_59
| spl23_73 ),
inference(avatar_split_clause,[status(thm)],[f38,f544,f451,f261]) ).
thf(f261,definition,
( spl23_21
<=> ( $false
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_21])],[avatar_definition]) ).
thf(f544,definition,
( spl23_73
<=> ( $true = sF17 ) ),
introduced(definition,[new_symbols(naming,[spl23_73])],[avatar_definition]) ).
thf(f38,plain,
( ( $true = sF17 )
| ( sF16 = $true )
| ( $false
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f550,plain,
( spl23_19
| spl23_72
| spl23_60 ),
inference(avatar_split_clause,[status(thm)],[f41,f456,f538,f252]) ).
thf(f252,definition,
( spl23_19
<=> ( $true
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_19])],[avatar_definition]) ).
thf(f456,definition,
( spl23_60
<=> ( $false = sF16 ) ),
introduced(definition,[new_symbols(naming,[spl23_60])],[avatar_definition]) ).
thf(f41,plain,
( ( $false = sF16 )
| ( $false = sF17 )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false = sF16 )
| ( sF17
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f23]) ).
thf(f549,plain,
( spl23_60
| spl23_17
| spl23_73 ),
inference(avatar_split_clause,[status(thm)],[f40,f544,f243,f456]) ).
thf(f243,definition,
( spl23_17
<=> ( $false
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_17])],[avatar_definition]) ).
thf(f40,plain,
( ( $false = sF16 )
| ( $false
= ( f3 @ $true ) )
| ( $true = sF17 ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f548,plain,
( spl23_73
| spl23_52
| spl23_27 ),
inference(avatar_split_clause,[status(thm)],[f45,f289,f417,f544]) ).
thf(f417,definition,
( spl23_52
<=> ( $true = sF18 ) ),
introduced(definition,[new_symbols(naming,[spl23_52])],[avatar_definition]) ).
thf(f289,definition,
( spl23_27
<=> ( $false
= ( f2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_27])],[avatar_definition]) ).
thf(f45,plain,
( ( $false
= ( f2 @ $false ) )
| ( $true = sF17 )
| ( $true = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = sF17 )
| ( ( f2 @ $false )
= sF18 ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f24,definition,
( sF18
= ( f2 @ sF17 ) ),
introduced(definition,[],[function_definition]) ).
thf(f547,plain,
( spl23_28
| spl23_49
| spl23_73 ),
inference(avatar_split_clause,[status(thm)],[f44,f544,f403,f294]) ).
thf(f294,definition,
( spl23_28
<=> ( $true
= ( f2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_28])],[avatar_definition]) ).
thf(f403,definition,
( spl23_49
<=> ( $false = sF18 ) ),
introduced(definition,[new_symbols(naming,[spl23_49])],[avatar_definition]) ).
thf(f44,plain,
( ( $false = sF18 )
| ( $true = sF17 )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f542,plain,
( spl23_25
| spl23_72
| spl23_52 ),
inference(avatar_split_clause,[status(thm)],[f47,f417,f538,f280]) ).
thf(f280,definition,
( spl23_25
<=> ( ( f2 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl23_25])],[avatar_definition]) ).
thf(f47,plain,
( ( $false = sF17 )
| ( $true = sF18 )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false = sF17 )
| ( ( f2 @ $true )
= sF18 ) ),
inference(cases_simplifying,[status(thm)],[f24]) ).
thf(f541,plain,
( spl23_24
| spl23_72
| spl23_49 ),
inference(avatar_split_clause,[status(thm)],[f46,f403,f538,f275]) ).
thf(f275,definition,
( spl23_24
<=> ( ( f2 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl23_24])],[avatar_definition]) ).
thf(f46,plain,
( ( $false = sF18 )
| ( ( f2 @ $true )
= $true )
| ( $false = sF17 ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f536,plain,
( spl23_42
| spl23_67
| spl23_66 ),
inference(avatar_split_clause,[status(thm)],[f51,f494,f501,f362]) ).
thf(f362,definition,
( spl23_42
<=> ( $true
= ( f1 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_42])],[avatar_definition]) ).
thf(f501,definition,
( spl23_67
<=> ( $false = sF21 ) ),
introduced(definition,[new_symbols(naming,[spl23_67])],[avatar_definition]) ).
thf(f494,definition,
( spl23_66
<=> ( $true = sF20 ) ),
introduced(definition,[new_symbols(naming,[spl23_66])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
= ( f1 @ $false ) )
| ( $false = sF21 )
| ( $true = sF20 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true = sF20 )
| ( sF21
= ( f1 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f27]) ).
thf(f27,definition,
( sF21
= ( f1 @ sF20 ) ),
introduced(definition,[],[function_definition]) ).
thf(f535,plain,
( spl23_68
| spl23_41
| spl23_66 ),
inference(avatar_split_clause,[status(thm)],[f50,f494,f357,f507]) ).
thf(f507,definition,
( spl23_68
<=> ( $true = sF21 ) ),
introduced(definition,[new_symbols(naming,[spl23_68])],[avatar_definition]) ).
thf(f357,definition,
( spl23_41
<=> ( $false
= ( f1 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_41])],[avatar_definition]) ).
thf(f50,plain,
( ( $true = sF21 )
| ( $false
= ( f1 @ $false ) )
| ( $true = sF20 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f534,plain,
( spl23_40
| spl23_65
| spl23_67 ),
inference(avatar_split_clause,[status(thm)],[f53,f501,f489,f352]) ).
thf(f352,definition,
( spl23_40
<=> ( $true
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_40])],[avatar_definition]) ).
thf(f489,definition,
( spl23_65
<=> ( $false = sF20 ) ),
introduced(definition,[new_symbols(naming,[spl23_65])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
= ( f1 @ $true ) )
| ( $false = sF20 )
| ( $false = sF21 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( sF21
= ( f1 @ $true ) )
| ( $false = sF20 ) ),
inference(cases_simplifying,[status(thm)],[f27]) ).
thf(f533,plain,
( spl23_68
| spl23_38
| spl23_65 ),
inference(avatar_split_clause,[status(thm)],[f52,f489,f343,f507]) ).
thf(f343,definition,
( spl23_38
<=> ( $false
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_38])],[avatar_definition]) ).
thf(f52,plain,
( ( $true = sF21 )
| ( $false = sF20 )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f532,plain,
~ spl23_71,
inference(avatar_split_clause,[status(thm)],[f3,f529]) ).
thf(f529,definition,
( spl23_71
<=> ( $false = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_71])],[avatar_definition]) ).
thf(f3,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f527,plain,
( spl23_43
| spl23_3
| spl23_6 ),
inference(avatar_split_clause,[status(thm)],[f57,f193,f179,f371]) ).
thf(f371,definition,
( spl23_43
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_43])],[avatar_definition]) ).
thf(f179,definition,
( spl23_3
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition]) ).
thf(f193,definition,
( spl23_6
<=> ( ( f4 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl23_6])],[avatar_definition]) ).
thf(f57,plain,
( ( ( f4 @ $false )
= $true )
| ( $false = sF2 )
| ( sF1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( sF2
= ( f4 @ $false ) )
| ( sF1 = $true ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f8,definition,
( sF2
= ( f4 @ sF1 ) ),
introduced(definition,[],[function_definition]) ).
thf(f526,plain,
( spl23_8
| spl23_7
| spl23_43 ),
inference(avatar_split_clause,[status(thm)],[f56,f371,f197,f202]) ).
thf(f202,definition,
( spl23_8
<=> ( $false
= ( f4 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_8])],[avatar_definition]) ).
thf(f197,definition,
( spl23_7
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_7])],[avatar_definition]) ).
thf(f56,plain,
( ( sF2 = $true )
| ( sF1 = $true )
| ( $false
= ( f4 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f525,plain,
( spl23_3
| spl23_4
| spl23_45 ),
inference(avatar_split_clause,[status(thm)],[f59,f380,f184,f179]) ).
thf(f184,definition,
( spl23_4
<=> ( $true
= ( f4 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition]) ).
thf(f380,definition,
( spl23_45
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl23_45])],[avatar_definition]) ).
thf(f59,plain,
( ( sF1 = $false )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( sF2
= ( f4 @ $true ) )
| ( sF1 = $false ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f524,plain,
( spl23_7
| spl23_2
| spl23_45 ),
inference(avatar_split_clause,[status(thm)],[f58,f380,f175,f197]) ).
thf(f175,definition,
( spl23_2
<=> ( $false
= ( f4 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition]) ).
thf(f58,plain,
( ( $false
= ( f4 @ $true ) )
| ( sF1 = $false )
| ( sF2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f523,plain,
( spl23_44
| spl23_58
| spl23_70 ),
inference(avatar_split_clause,[status(thm)],[f63,f519,f446,f375]) ).
thf(f375,definition,
( spl23_44
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl23_44])],[avatar_definition]) ).
thf(f519,definition,
( spl23_70
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_70])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( f5 @ $false ) )
| ( $false = sF0 )
| ( x = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( sF0
= ( f5 @ $false ) )
| ( x = $true ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f6,definition,
( ( f5 @ x )
= sF0 ),
introduced(definition,[],[function_definition]) ).
thf(f522,plain,
( spl23_46
| spl23_70
| spl23_57 ),
inference(avatar_split_clause,[status(thm)],[f62,f441,f519,f385]) ).
thf(f385,definition,
( spl23_46
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl23_46])],[avatar_definition]) ).
thf(f62,plain,
( ( $false
= ( f5 @ $false ) )
| ( $true = sF0 )
| ( x = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f517,plain,
( spl23_46
| spl23_55
| spl23_69 ),
inference(avatar_split_clause,[status(thm)],[f65,f513,f432,f385]) ).
thf(f513,definition,
( spl23_69
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl23_69])],[avatar_definition]) ).
thf(f65,plain,
( ( x = $false )
| ( $true = sF0 )
| ( $false
= ( f5 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( f5 @ $true )
= sF0 )
| ( x = $false ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f516,plain,
( spl23_44
| spl23_53
| spl23_69 ),
inference(avatar_split_clause,[status(thm)],[f64,f513,f423,f375]) ).
thf(f64,plain,
( ( ( f5 @ $true )
= $true )
| ( x = $false )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f511,plain,
( spl23_16
| spl23_64
| spl23_68 ),
inference(avatar_split_clause,[status(thm)],[f69,f507,f480,f238]) ).
thf(f238,definition,
( spl23_16
<=> ( $true
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_16])],[avatar_definition]) ).
thf(f480,definition,
( spl23_64
<=> ( sF22 = $false ) ),
introduced(definition,[new_symbols(naming,[spl23_64])],[avatar_definition]) ).
thf(f69,plain,
( ( $true
= ( f0 @ $false ) )
| ( sF22 = $false )
| ( $true = sF21 ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( sF22
= ( f0 @ $false ) )
| ( $true = sF21 ) ),
inference(cases_simplifying,[status(thm)],[f28]) ).
thf(f28,definition,
( sF22
= ( f0 @ sF21 ) ),
introduced(definition,[],[function_definition]) ).
thf(f510,plain,
( spl23_68
| spl23_14
| spl23_63 ),
inference(avatar_split_clause,[status(thm)],[f68,f475,f229,f507]) ).
thf(f229,definition,
( spl23_14
<=> ( $false
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl23_14])],[avatar_definition]) ).
thf(f475,definition,
( spl23_63
<=> ( sF22 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_63])],[avatar_definition]) ).
thf(f68,plain,
( ( $false
= ( f0 @ $false ) )
| ( sF22 = $true )
| ( $true = sF21 ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f505,plain,
( spl23_9
| spl23_67
| spl23_64 ),
inference(avatar_split_clause,[status(thm)],[f71,f480,f501,f207]) ).
thf(f207,definition,
( spl23_9
<=> ( $true
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_9])],[avatar_definition]) ).
thf(f71,plain,
( ( sF22 = $false )
| ( $true
= ( f0 @ $true ) )
| ( $false = sF21 ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = sF21 )
| ( sF22
= ( f0 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f28]) ).
thf(f504,plain,
( spl23_13
| spl23_67
| spl23_63 ),
inference(avatar_split_clause,[status(thm)],[f70,f475,f501,f224]) ).
thf(f224,definition,
( spl23_13
<=> ( $false
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_13])],[avatar_definition]) ).
thf(f70,plain,
( ( $false
= ( f0 @ $true ) )
| ( $false = sF21 )
| ( sF22 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f499,plain,
( spl23_50
| spl23_41
| spl23_66 ),
inference(avatar_split_clause,[status(thm)],[f75,f494,f357,f407]) ).
thf(f407,definition,
( spl23_50
<=> ( $true = sF19 ) ),
introduced(definition,[new_symbols(naming,[spl23_50])],[avatar_definition]) ).
thf(f75,plain,
( ( $true = sF20 )
| ( $true = sF19 )
| ( $false
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true = sF19 )
| ( ( f1 @ $false )
= sF20 ) ),
inference(cases_simplifying,[status(thm)],[f26]) ).
thf(f26,definition,
( ( f1 @ sF19 )
= sF20 ),
introduced(definition,[],[function_definition]) ).
thf(f498,plain,
( spl23_65
| spl23_42
| spl23_50 ),
inference(avatar_split_clause,[status(thm)],[f74,f407,f362,f489]) ).
thf(f74,plain,
( ( $false = sF20 )
| ( $true = sF19 )
| ( $true
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f497,plain,
( spl23_51
| spl23_38
| spl23_66 ),
inference(avatar_split_clause,[status(thm)],[f77,f494,f343,f412]) ).
thf(f412,definition,
( spl23_51
<=> ( $false = sF19 ) ),
introduced(definition,[new_symbols(naming,[spl23_51])],[avatar_definition]) ).
thf(f77,plain,
( ( $false
= ( f1 @ $true ) )
| ( $true = sF20 )
| ( $false = sF19 ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( f1 @ $true )
= sF20 )
| ( $false = sF19 ) ),
inference(cases_simplifying,[status(thm)],[f26]) ).
thf(f492,plain,
( spl23_51
| spl23_40
| spl23_65 ),
inference(avatar_split_clause,[status(thm)],[f76,f489,f352,f412]) ).
thf(f76,plain,
( ( $false = sF20 )
| ( $true
= ( f1 @ $true ) )
| ( $false = sF19 ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f487,plain,
( spl23_14
| spl23_48
| spl23_37 ),
inference(avatar_split_clause,[status(thm)],[f81,f339,f397,f229]) ).
thf(f397,definition,
( spl23_48
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl23_48])],[avatar_definition]) ).
thf(f339,definition,
( spl23_37
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_37])],[avatar_definition]) ).
thf(f81,plain,
( ( $true = sF9 )
| ( $false
= ( f0 @ $false ) )
| ( sF8 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( sF8 = $true )
| ( ( f0 @ $false )
= sF9 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f15,definition,
( ( f0 @ sF8 )
= sF9 ),
introduced(definition,[],[function_definition]) ).
thf(f486,plain,
( spl23_37
| spl23_16
| spl23_47 ),
inference(avatar_split_clause,[status(thm)],[f80,f391,f238,f339]) ).
thf(f391,definition,
( spl23_47
<=> ( $false = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl23_47])],[avatar_definition]) ).
thf(f80,plain,
( ( sF8 = $true )
| ( $true
= ( f0 @ $false ) )
| ( $false = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f485,plain,
( spl23_13
| spl23_39
| spl23_48 ),
inference(avatar_split_clause,[status(thm)],[f83,f397,f348,f224]) ).
thf(f348,definition,
( spl23_39
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(naming,[spl23_39])],[avatar_definition]) ).
thf(f83,plain,
( ( $true = sF9 )
| ( sF8 = $false )
| ( $false
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( f0 @ $true )
= sF9 )
| ( sF8 = $false ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f484,plain,
( spl23_39
| spl23_9
| spl23_47 ),
inference(avatar_split_clause,[status(thm)],[f82,f391,f207,f348]) ).
thf(f82,plain,
( ( sF8 = $false )
| ( $false = sF9 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f483,plain,
( spl23_11
| spl23_64 ),
inference(avatar_split_clause,[status(thm)],[f85,f480,f215]) ).
thf(f215,definition,
( spl23_11
<=> ( $false = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl23_11])],[avatar_definition]) ).
thf(f85,plain,
( ( sF22 = $false )
| ( $false = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
sF22 != sF11,
inference(definition_folding,[status(thm)],[f5,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f6,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6]) ).
thf(f7,definition,
( sF1
= ( f4 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f9,definition,
( ( f4 @ sF2 )
= sF3 ),
introduced(definition,[],[function_definition]) ).
thf(f10,definition,
( sF4
= ( f3 @ sF3 ) ),
introduced(definition,[],[function_definition]) ).
thf(f11,definition,
( sF5
= ( f2 @ sF4 ) ),
introduced(definition,[],[function_definition]) ).
thf(f12,definition,
( sF6
= ( f2 @ sF5 ) ),
introduced(definition,[],[function_definition]) ).
thf(f13,definition,
( sF7
= ( f2 @ sF6 ) ),
introduced(definition,[],[function_definition]) ).
thf(f14,definition,
( sF8
= ( f1 @ sF7 ) ),
introduced(definition,[],[function_definition]) ).
thf(f16,definition,
( ( f0 @ sF9 )
= sF10 ),
introduced(definition,[],[function_definition]) ).
thf(f17,definition,
( sF11
= ( f0 @ sF10 ) ),
introduced(definition,[],[function_definition]) ).
thf(f18,definition,
( ( f5 @ sF0 )
= sF12 ),
introduced(definition,[],[function_definition]) ).
thf(f20,definition,
( ( f4 @ sF13 )
= sF14 ),
introduced(definition,[],[function_definition]) ).
thf(f21,definition,
( ( f3 @ sF14 )
= sF15 ),
introduced(definition,[],[function_definition]) ).
thf(f22,definition,
( sF16
= ( f3 @ sF15 ) ),
introduced(definition,[],[function_definition]) ).
thf(f25,definition,
( sF19
= ( f1 @ sF18 ) ),
introduced(definition,[],[function_definition]) ).
thf(f5,plain,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9y7qOUSbQU/DTF2THF_3284.p',kaminski6) ).
thf(f478,plain,
( spl23_63
| spl23_12 ),
inference(avatar_split_clause,[status(thm)],[f84,f220,f475]) ).
thf(f220,definition,
( spl23_12
<=> ( $true = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl23_12])],[avatar_definition]) ).
thf(f84,plain,
( ( sF22 = $true )
| ( $true = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f473,plain,
( spl23_8
| spl23_32
| spl23_62 ),
inference(avatar_split_clause,[status(thm)],[f89,f469,f313,f202]) ).
thf(f313,definition,
( spl23_32
<=> ( $true = sF14 ) ),
introduced(definition,[new_symbols(naming,[spl23_32])],[avatar_definition]) ).
thf(f89,plain,
( ( $false
= ( f4 @ $false ) )
| ( $true = sF14 )
| ( $true = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $true = sF13 )
| ( ( f4 @ $false )
= sF14 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f472,plain,
( spl23_30
| spl23_6
| spl23_62 ),
inference(avatar_split_clause,[status(thm)],[f88,f469,f193,f303]) ).
thf(f303,definition,
( spl23_30
<=> ( $false = sF14 ) ),
introduced(definition,[new_symbols(naming,[spl23_30])],[avatar_definition]) ).
thf(f88,plain,
( ( ( f4 @ $false )
= $true )
| ( $false = sF14 )
| ( $true = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f467,plain,
( spl23_61
| spl23_2
| spl23_32 ),
inference(avatar_split_clause,[status(thm)],[f91,f313,f175,f463]) ).
thf(f91,plain,
( ( $false = sF13 )
| ( $true = sF14 )
| ( $false
= ( f4 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( f4 @ $true )
= sF14 )
| ( $false = sF13 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f466,plain,
( spl23_30
| spl23_4
| spl23_61 ),
inference(avatar_split_clause,[status(thm)],[f90,f463,f184,f303]) ).
thf(f90,plain,
( ( $false = sF14 )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f461,plain,
( spl23_60
| spl23_22
| spl23_29 ),
inference(avatar_split_clause,[status(thm)],[f95,f299,f266,f456]) ).
thf(f299,definition,
( spl23_29
<=> ( $true = sF15 ) ),
introduced(definition,[new_symbols(naming,[spl23_29])],[avatar_definition]) ).
thf(f95,plain,
( ( $true = sF15 )
| ( $true
= ( f3 @ $false ) )
| ( $false = sF16 ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( sF16
= ( f3 @ $false ) )
| ( $true = sF15 ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f460,plain,
( spl23_59
| spl23_29
| spl23_21 ),
inference(avatar_split_clause,[status(thm)],[f94,f261,f299,f451]) ).
thf(f94,plain,
( ( $true = sF15 )
| ( $false
= ( f3 @ $false ) )
| ( sF16 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f459,plain,
( spl23_31
| spl23_60
| spl23_19 ),
inference(avatar_split_clause,[status(thm)],[f97,f252,f456,f308]) ).
thf(f308,definition,
( spl23_31
<=> ( $false = sF15 ) ),
introduced(definition,[new_symbols(naming,[spl23_31])],[avatar_definition]) ).
thf(f97,plain,
( ( $false = sF16 )
| ( $true
= ( f3 @ $true ) )
| ( $false = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false = sF15 )
| ( sF16
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f22]) ).
thf(f454,plain,
( spl23_17
| spl23_31
| spl23_59 ),
inference(avatar_split_clause,[status(thm)],[f96,f451,f308,f243]) ).
thf(f96,plain,
( ( $false
= ( f3 @ $true ) )
| ( $false = sF15 )
| ( sF16 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f449,plain,
( spl23_58
| spl23_46
| spl23_54 ),
inference(avatar_split_clause,[status(thm)],[f101,f427,f385,f446]) ).
thf(f101,plain,
( ( $true = sF0 )
| ( $false = sF12 )
| ( $true
= ( f5 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true = sF0 )
| ( sF12
= ( f5 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f444,plain,
( spl23_57
| spl23_56
| spl23_46 ),
inference(avatar_split_clause,[status(thm)],[f100,f385,f436,f441]) ).
thf(f100,plain,
( ( $true = sF12 )
| ( $false
= ( f5 @ $false ) )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f439,plain,
( spl23_44
| spl23_55
| spl23_56 ),
inference(avatar_split_clause,[status(thm)],[f103,f436,f432,f375]) ).
thf(f103,plain,
( ( $false
= ( f5 @ $true ) )
| ( $false = sF0 )
| ( $true = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( f5 @ $true )
= sF12 )
| ( $false = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f430,plain,
( spl23_44
| spl23_53
| spl23_54 ),
inference(avatar_split_clause,[status(thm)],[f102,f427,f423,f375]) ).
thf(f102,plain,
( ( $false = sF12 )
| ( ( f5 @ $true )
= $true )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f421,plain,
( spl23_42
| spl23_51
| spl23_52 ),
inference(avatar_split_clause,[status(thm)],[f107,f417,f412,f362]) ).
thf(f107,plain,
( ( $true
= ( f1 @ $false ) )
| ( $false = sF19 )
| ( $true = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true = sF18 )
| ( sF19
= ( f1 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f25]) ).
thf(f420,plain,
( spl23_52
| spl23_41
| spl23_50 ),
inference(avatar_split_clause,[status(thm)],[f106,f407,f357,f417]) ).
thf(f106,plain,
( ( $true = sF18 )
| ( $false
= ( f1 @ $false ) )
| ( $true = sF19 ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f415,plain,
( spl23_49
| spl23_51
| spl23_40 ),
inference(avatar_split_clause,[status(thm)],[f109,f352,f412,f403]) ).
thf(f109,plain,
( ( $false = sF19 )
| ( $false = sF18 )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( sF19
= ( f1 @ $true ) )
| ( $false = sF18 ) ),
inference(cases_simplifying,[status(thm)],[f25]) ).
thf(f410,plain,
( spl23_49
| spl23_38
| spl23_50 ),
inference(avatar_split_clause,[status(thm)],[f108,f407,f343,f403]) ).
thf(f108,plain,
( ( $false
= ( f1 @ $true ) )
| ( $true = sF19 )
| ( $false = sF18 ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f401,plain,
( spl23_48
| spl23_16
| spl23_10 ),
inference(avatar_split_clause,[status(thm)],[f113,f211,f238,f397]) ).
thf(f211,definition,
( spl23_10
<=> ( $false = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl23_10])],[avatar_definition]) ).
thf(f113,plain,
( ( $false = sF10 )
| ( $true
= ( f0 @ $false ) )
| ( $true = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( sF10
= ( f0 @ $false ) )
| ( $true = sF9 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f400,plain,
( spl23_15
| spl23_48
| spl23_14 ),
inference(avatar_split_clause,[status(thm)],[f112,f229,f397,f233]) ).
thf(f233,definition,
( spl23_15
<=> ( sF10 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_15])],[avatar_definition]) ).
thf(f112,plain,
( ( $false
= ( f0 @ $false ) )
| ( $true = sF9 )
| ( sF10 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f395,plain,
( spl23_9
| spl23_47
| spl23_10 ),
inference(avatar_split_clause,[status(thm)],[f115,f211,f391,f207]) ).
thf(f115,plain,
( ( $false = sF9 )
| ( $false = sF10 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false = sF9 )
| ( sF10
= ( f0 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f394,plain,
( spl23_13
| spl23_47
| spl23_15 ),
inference(avatar_split_clause,[status(thm)],[f114,f233,f391,f224]) ).
thf(f114,plain,
( ( sF10 = $true )
| ( $false
= ( f0 @ $true ) )
| ( $false = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f389,plain,
( spl23_45
| spl23_46
| spl23_6 ),
inference(avatar_split_clause,[status(thm)],[f119,f193,f385,f380]) ).
thf(f119,plain,
( ( sF1 = $false )
| ( $true = sF0 )
| ( ( f4 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( sF1
= ( f4 @ $false ) )
| ( $true = sF0 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f388,plain,
( spl23_8
| spl23_46
| spl23_43 ),
inference(avatar_split_clause,[status(thm)],[f118,f371,f385,f202]) ).
thf(f118,plain,
( ( sF1 = $true )
| ( $true = sF0 )
| ( $false
= ( f4 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f383,plain,
( spl23_45
| spl23_44
| spl23_4 ),
inference(avatar_split_clause,[status(thm)],[f121,f184,f375,f380]) ).
thf(f121,plain,
( ( sF1 = $false )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $false = sF0 )
| ( sF1
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f378,plain,
( spl23_43
| spl23_44
| spl23_2 ),
inference(avatar_split_clause,[status(thm)],[f120,f175,f375,f371]) ).
thf(f120,plain,
( ( $false = sF0 )
| ( sF1 = $true )
| ( $false
= ( f4 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f369,plain,
( spl23_26
| spl23_27
| spl23_36 ),
inference(avatar_split_clause,[status(thm)],[f125,f333,f289,f284]) ).
thf(f284,definition,
( spl23_26
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl23_26])],[avatar_definition]) ).
thf(f333,definition,
( spl23_36
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl23_36])],[avatar_definition]) ).
thf(f125,plain,
( ( $false
= ( f2 @ $false ) )
| ( $true = sF5 )
| ( $true = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true = sF5 )
| ( ( f2 @ $false )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f368,plain,
( spl23_26
| spl23_33
| spl23_28 ),
inference(avatar_split_clause,[status(thm)],[f124,f294,f319,f284]) ).
thf(f319,definition,
( spl23_33
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl23_33])],[avatar_definition]) ).
thf(f124,plain,
( ( $true
= ( f2 @ $false ) )
| ( $true = sF5 )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f367,plain,
( spl23_25
| spl23_36
| spl23_23 ),
inference(avatar_split_clause,[status(thm)],[f127,f271,f333,f280]) ).
thf(f271,definition,
( spl23_23
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl23_23])],[avatar_definition]) ).
thf(f127,plain,
( ( $true = sF6 )
| ( ( f2 @ $true )
= $false )
| ( $false = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false = sF5 )
| ( ( f2 @ $true )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f366,plain,
( spl23_24
| spl23_23
| spl23_33 ),
inference(avatar_split_clause,[status(thm)],[f126,f319,f271,f275]) ).
thf(f126,plain,
( ( $false = sF6 )
| ( ( f2 @ $true )
= $true )
| ( $false = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f365,plain,
( spl23_42
| spl23_39
| spl23_35 ),
inference(avatar_split_clause,[status(thm)],[f131,f328,f348,f362]) ).
thf(f328,definition,
( spl23_35
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_35])],[avatar_definition]) ).
thf(f131,plain,
( ( sF8 = $false )
| ( $true
= ( f1 @ $false ) )
| ( sF7 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( sF8
= ( f1 @ $false ) )
| ( sF7 = $true ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f360,plain,
( spl23_37
| spl23_41
| spl23_35 ),
inference(avatar_split_clause,[status(thm)],[f130,f328,f357,f339]) ).
thf(f130,plain,
( ( sF8 = $true )
| ( $false
= ( f1 @ $false ) )
| ( sF7 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f355,plain,
( spl23_34
| spl23_39
| spl23_40 ),
inference(avatar_split_clause,[status(thm)],[f133,f352,f348,f323]) ).
thf(f323,definition,
( spl23_34
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl23_34])],[avatar_definition]) ).
thf(f133,plain,
( ( $true
= ( f1 @ $true ) )
| ( sF8 = $false )
| ( $false = sF7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( sF8
= ( f1 @ $true ) )
| ( $false = sF7 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f346,plain,
( spl23_37
| spl23_34
| spl23_38 ),
inference(avatar_split_clause,[status(thm)],[f132,f343,f323,f339]) ).
thf(f132,plain,
( ( $false
= ( f1 @ $true ) )
| ( sF8 = $true )
| ( $false = sF7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f337,plain,
( spl23_36
| spl23_28
| spl23_34 ),
inference(avatar_split_clause,[status(thm)],[f137,f323,f294,f333]) ).
thf(f137,plain,
( ( $true
= ( f2 @ $false ) )
| ( $true = sF6 )
| ( $false = sF7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( sF7
= ( f2 @ $false ) )
| ( $true = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f336,plain,
( spl23_27
| spl23_35
| spl23_36 ),
inference(avatar_split_clause,[status(thm)],[f136,f333,f328,f289]) ).
thf(f136,plain,
( ( $true = sF6 )
| ( $false
= ( f2 @ $false ) )
| ( sF7 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f331,plain,
( spl23_25
| spl23_33
| spl23_35 ),
inference(avatar_split_clause,[status(thm)],[f139,f328,f319,f280]) ).
thf(f139,plain,
( ( ( f2 @ $true )
= $false )
| ( sF7 = $true )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( f2 @ $true )
= sF7 )
| ( $false = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f326,plain,
( spl23_24
| spl23_33
| spl23_34 ),
inference(avatar_split_clause,[status(thm)],[f138,f323,f319,f275]) ).
thf(f138,plain,
( ( $false = sF7 )
| ( ( f2 @ $true )
= $true )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f317,plain,
( spl23_22
| spl23_31
| spl23_32 ),
inference(avatar_split_clause,[status(thm)],[f143,f313,f308,f266]) ).
thf(f143,plain,
( ( $true = sF14 )
| ( $false = sF15 )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( sF15
= ( f3 @ $false ) )
| ( $true = sF14 ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f316,plain,
( spl23_21
| spl23_32
| spl23_29 ),
inference(avatar_split_clause,[status(thm)],[f142,f299,f313,f261]) ).
thf(f142,plain,
( ( $true = sF14 )
| ( $false
= ( f3 @ $false ) )
| ( $true = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f311,plain,
( spl23_19
| spl23_31
| spl23_30 ),
inference(avatar_split_clause,[status(thm)],[f145,f303,f308,f252]) ).
thf(f145,plain,
( ( $false = sF14 )
| ( $true
= ( f3 @ $true ) )
| ( $false = sF15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $false = sF14 )
| ( sF15
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f21]) ).
thf(f306,plain,
( spl23_29
| spl23_17
| spl23_30 ),
inference(avatar_split_clause,[status(thm)],[f144,f303,f243,f299]) ).
thf(f144,plain,
( ( $false
= ( f3 @ $true ) )
| ( $true = sF15 )
| ( $false = sF14 ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f297,plain,
( spl23_23
| spl23_18
| spl23_28 ),
inference(avatar_split_clause,[status(thm)],[f149,f294,f247,f271]) ).
thf(f247,definition,
( spl23_18
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(naming,[spl23_18])],[avatar_definition]) ).
thf(f149,plain,
( ( sF4 = $true )
| ( $false = sF5 )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( sF4 = $true )
| ( sF5
= ( f2 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f292,plain,
( spl23_26
| spl23_18
| spl23_27 ),
inference(avatar_split_clause,[status(thm)],[f148,f289,f247,f284]) ).
thf(f148,plain,
( ( sF4 = $true )
| ( $true = sF5 )
| ( $false
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f287,plain,
( spl23_25
| spl23_26
| spl23_20 ),
inference(avatar_split_clause,[status(thm)],[f151,f256,f284,f280]) ).
thf(f256,definition,
( spl23_20
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl23_20])],[avatar_definition]) ).
thf(f151,plain,
( ( $false = sF4 )
| ( ( f2 @ $true )
= $false )
| ( $true = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( f2 @ $true )
= sF5 )
| ( $false = sF4 ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f278,plain,
( spl23_20
| spl23_23
| spl23_24 ),
inference(avatar_split_clause,[status(thm)],[f150,f275,f271,f256]) ).
thf(f150,plain,
( ( $false = sF5 )
| ( ( f2 @ $true )
= $true )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f269,plain,
( spl23_22
| spl23_20
| spl23_1 ),
inference(avatar_split_clause,[status(thm)],[f155,f171,f256,f266]) ).
thf(f171,definition,
( spl23_1
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition]) ).
thf(f155,plain,
( ( $false = sF4 )
| ( $true = sF3 )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
( ( sF4
= ( f3 @ $false ) )
| ( $true = sF3 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f264,plain,
( spl23_21
| spl23_18
| spl23_1 ),
inference(avatar_split_clause,[status(thm)],[f154,f171,f247,f261]) ).
thf(f154,plain,
( ( $true = sF3 )
| ( sF4 = $true )
| ( $false
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f259,plain,
( spl23_19
| spl23_20
| spl23_5 ),
inference(avatar_split_clause,[status(thm)],[f157,f188,f256,f252]) ).
thf(f188,definition,
( spl23_5
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition]) ).
thf(f157,plain,
( ( $false = sF4 )
| ( $false = sF3 )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( $false = sF3 )
| ( sF4
= ( f3 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f250,plain,
( spl23_17
| spl23_5
| spl23_18 ),
inference(avatar_split_clause,[status(thm)],[f156,f247,f188,f243]) ).
thf(f156,plain,
( ( $false
= ( f3 @ $true ) )
| ( $false = sF3 )
| ( sF4 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f241,plain,
( spl23_16
| spl23_15
| spl23_11 ),
inference(avatar_split_clause,[status(thm)],[f161,f215,f233,f238]) ).
thf(f161,plain,
( ( $true
= ( f0 @ $false ) )
| ( sF10 = $true )
| ( $false = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
( ( sF11
= ( f0 @ $false ) )
| ( sF10 = $true ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f236,plain,
( spl23_12
| spl23_14
| spl23_15 ),
inference(avatar_split_clause,[status(thm)],[f160,f233,f229,f220]) ).
thf(f160,plain,
( ( sF10 = $true )
| ( $true = sF11 )
| ( $false
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
thf(f227,plain,
( spl23_12
| spl23_13
| spl23_10 ),
inference(avatar_split_clause,[status(thm)],[f163,f211,f224,f220]) ).
thf(f163,plain,
( ( $true = sF11 )
| ( $false
= ( f0 @ $true ) )
| ( $false = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( f0 @ $true )
= sF11 )
| ( $false = sF10 ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f218,plain,
( spl23_9
| spl23_10
| spl23_11 ),
inference(avatar_split_clause,[status(thm)],[f162,f215,f211,f207]) ).
thf(f162,plain,
( ( $false = sF11 )
| ( $true
= ( f0 @ $true ) )
| ( $false = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f205,plain,
( spl23_7
| spl23_8
| spl23_1 ),
inference(avatar_split_clause,[status(thm)],[f167,f171,f202,f197]) ).
thf(f167,plain,
( ( $false
= ( f4 @ $false ) )
| ( $true = sF3 )
| ( sF2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
( ( sF2 = $true )
| ( ( f4 @ $false )
= sF3 ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f200,plain,
( spl23_6
| spl23_5
| spl23_7 ),
inference(avatar_split_clause,[status(thm)],[f166,f197,f188,f193]) ).
thf(f166,plain,
( ( $false = sF3 )
| ( sF2 = $true )
| ( ( f4 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f191,plain,
( spl23_3
| spl23_4
| spl23_5 ),
inference(avatar_split_clause,[status(thm)],[f169,f188,f184,f179]) ).
thf(f169,plain,
( ( $false = sF3 )
| ( $true
= ( f4 @ $true ) )
| ( $false = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $false = sF2 )
| ( sF3
= ( f4 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f182,plain,
( spl23_1
| spl23_2
| spl23_3 ),
inference(avatar_split_clause,[status(thm)],[f168,f179,f175,f171]) ).
thf(f168,plain,
( ( $true = sF3 )
| ( $false = sF2 )
| ( $false
= ( f4 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO500^1.006 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:32:57 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO500^1.006 : TPTP v9.2.1. Released v4.1.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : Six function variant of the Kaminski equation
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : basic14 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 1 unt; 7 typ; 0 def)
% 0.19/0.47 % Number of atoms : 27 ( 1 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 27 avg)
% 0.19/0.47 % Number of connectives : 24 ( 0 ~; 0 |; 0 &; 24 @)
% 0.19/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.19/0.47 % Number of types : 1 ( 0 usr)
% 0.19/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(x,type,
% 0.19/0.47 x: $o ).
% 0.19/0.47
% 0.19/0.47 thf(f0,type,
% 0.19/0.47 f0: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(f1,type,
% 0.19/0.47 f1: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(f2,type,
% 0.19/0.47 f2: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(f3,type,
% 0.19/0.47 f3: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(f4,type,
% 0.19/0.47 f4: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(f5,type,
% 0.19/0.47 f5: $o > $o ).
% 0.19/0.47
% 0.19/0.47 thf(kaminski6,conjecture,
% 0.19/0.47 ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
% 0.19/0.47 = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.82/1.55 ---- Embedded in THF ---
% 1.82/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.82/1.55 %%% Generated on Tue Feb 24 14:32:59 EST 2026
% 1.82/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 1.82/1.55 %%% Logic specification used:
% 1.82/1.55 %%% thf(spec, logic, $$dhol).
% 1.82/1.55
% 1.82/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9y7qOUSbQU/DTF2DTF3284.p
% See solution above
% 1.82/1.56 ------------------------
% 1.82/1.57 ---- Cleaned THF ---
% 1.82/1.57 thf(x,type,
% 1.82/1.57 x: $o ).
% 1.82/1.57
% 1.82/1.57 thf(f0,type,
% 1.82/1.57 f0: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(f1,type,
% 1.82/1.57 f1: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(f2,type,
% 1.82/1.57 f2: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(f3,type,
% 1.82/1.57 f3: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(f4,type,
% 1.82/1.57 f4: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(f5,type,
% 1.82/1.57 f5: $o > $o ).
% 1.82/1.57
% 1.82/1.57 thf(kaminski6,conjecture,
% 1.82/1.57 ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) )
% 1.82/1.57 = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ ( f5 @ ( f5 @ ( f5 @ x ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.82/1.57 ------------------------
% 1.82/1.59 % (3388)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/18Mi)
% 1.82/1.59 % (3382)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/183Mi)
% 1.82/1.59 % (3385)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/2Mi)
% 1.82/1.59 % (3386)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_3284 for (2999ds/2Mi)
% 1.82/1.59 % (3383)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_3284 for (2999ds/4Mi)
% 1.82/1.59 % (3387)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_3284 for (2999ds/275Mi)
% 1.82/1.59 % (3385)Instruction limit reached!
% 1.82/1.59 % (3385)------------------------------
% 1.82/1.59 % (3385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (3384)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_3284 for (2999ds/27Mi)
% 1.82/1.59 % (3385)Termination reason: Unknown
% 1.82/1.59 % (3386)Instruction limit reached!
% 1.82/1.59 % (3386)------------------------------
% 1.82/1.59 % (3386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (3386)Termination reason: Unknown
% 1.82/1.59 % (3386)Termination phase: Saturation
% 1.82/1.59
% 1.82/1.59 % (3386)Memory used [KB]: 5500
% 1.82/1.59 % (3386)Time elapsed: 0.003 s
% 1.82/1.59 % (3386)Instructions burned: 2 (million)
% 1.82/1.59 % (3386)------------------------------
% 1.82/1.59 % (3386)------------------------------
% 1.82/1.59 % (3385)Termination phase: Saturation
% 1.82/1.59
% 1.82/1.59 % (3385)Memory used [KB]: 5500
% 1.82/1.59 % (3385)Time elapsed: 0.003 s
% 1.82/1.59 % (3385)Instructions burned: 2 (million)
% 1.82/1.59 % (3385)------------------------------
% 1.82/1.59 % (3385)------------------------------
% 1.82/1.59 % (3383)Instruction limit reached!
% 1.82/1.59 % (3383)------------------------------
% 1.82/1.59 % (3383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (3383)Termination reason: Unknown
% 1.82/1.59 % (3383)Termination phase: Saturation
% 1.82/1.59
% 1.82/1.59 % (3383)Memory used [KB]: 5500
% 1.82/1.59 % (3383)Time elapsed: 0.004 s
% 1.82/1.59 % (3383)Instructions burned: 4 (million)
% 1.82/1.59 % (3383)------------------------------
% 1.82/1.59 % (3383)------------------------------
% 1.82/1.59 % (3387)Refutation not found, incomplete strategy
% 1.82/1.59 % (3387)------------------------------
% 1.82/1.59 % (3387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (3387)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.59
% 1.82/1.59
% 1.82/1.59 % (3387)Memory used [KB]: 5500
% 1.82/1.59 % (3387)Time elapsed: 0.002 s
% 1.82/1.59 % (3387)Instructions burned: 1 (million)
% 1.82/1.59 % (3387)------------------------------
% 1.82/1.59 % (3387)------------------------------
% 1.82/1.59 % (3384)Refutation not found, incomplete strategy
% 1.82/1.59 % (3384)------------------------------
% 1.82/1.59 % (3384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (3384)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.59
% 1.82/1.59
% 1.82/1.59 % (3384)Memory used [KB]: 5500
% 1.82/1.59 % (3384)Time elapsed: 0.004 s
% 1.82/1.59 % (3384)Instructions burned: 2 (million)
% 1.82/1.59 % (3384)------------------------------
% 1.82/1.59 % (3384)------------------------------
% 1.94/1.60 % (3388)Instruction limit reached!
% 1.94/1.60 % (3388)------------------------------
% 1.94/1.60 % (3388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.60 % (3388)Termination reason: Unknown
% 1.94/1.60 % (3388)Termination phase: Saturation
% 1.94/1.60
% 1.94/1.60 % (3388)Memory used [KB]: 5628
% 1.94/1.60 % (3388)Time elapsed: 0.012 s
% 1.94/1.60 % (3388)Instructions burned: 18 (million)
% 1.94/1.60 % (3388)------------------------------
% 1.94/1.60 % (3388)------------------------------
% 1.94/1.61 % (3391)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_3284 for (2999ds/15Mi)
% 1.94/1.61 % (3389)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/3Mi)
% 1.94/1.61 % (3392)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_3284 for (2999ds/3Mi)
% 1.94/1.61 % (3390)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_3284 for (2999ds/37Mi)
% 1.94/1.61 % (3389)Refutation not found, incomplete strategy
% 1.94/1.61 % (3389)------------------------------
% 1.94/1.61 % (3389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.61 % (3392)Refutation not found, incomplete strategy
% 1.94/1.61 % (3392)------------------------------
% 1.94/1.61 % (3392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.61 % (3392)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.61
% 1.94/1.61
% 1.94/1.61 % (3392)Memory used [KB]: 5500
% 1.94/1.61 % (3392)Time elapsed: 0.003 s
% 1.94/1.61 % (3392)Instructions burned: 2 (million)
% 1.94/1.61 % (3392)------------------------------
% 1.94/1.61 % (3392)------------------------------
% 1.94/1.61 % (3389)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.61
% 1.94/1.61
% 1.94/1.61 % (3389)Memory used [KB]: 5500
% 1.94/1.61 % (3389)Time elapsed: 0.003 s
% 1.94/1.61 % (3389)Instructions burned: 2 (million)
% 1.94/1.61 % (3389)------------------------------
% 1.94/1.61 % (3389)------------------------------
% 1.94/1.61 % (3393)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_3284 for (2999ds/1041Mi)
% 1.94/1.61 % (3394)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/7Mi)
% 1.94/1.61 % (3391)Instruction limit reached!
% 1.94/1.61 % (3391)------------------------------
% 1.94/1.61 % (3391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.62 % (3391)Termination reason: Unknown
% 1.94/1.62 % (3391)Termination phase: Saturation
% 1.94/1.62
% 1.94/1.62 % (3391)Memory used [KB]: 5756
% 1.94/1.62 % (3391)Time elapsed: 0.011 s
% 1.94/1.62 % (3391)Instructions burned: 16 (million)
% 1.94/1.62 % (3391)------------------------------
% 1.94/1.62 % (3391)------------------------------
% 1.94/1.62 % (3393)Refutation not found, incomplete strategy
% 1.94/1.62 % (3393)------------------------------
% 1.94/1.62 % (3393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.62 % (3393)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.62
% 1.94/1.62
% 1.94/1.62 % (3393)Memory used [KB]: 5500
% 1.94/1.62 % (3393)Time elapsed: 0.007 s
% 1.94/1.62 % (3393)Instructions burned: 8 (million)
% 1.94/1.62 % (3393)------------------------------
% 1.94/1.62 % (3393)------------------------------
% 1.94/1.62 % (3394)Instruction limit reached!
% 1.94/1.62 % (3394)------------------------------
% 1.94/1.62 % (3394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.62 % (3394)Termination reason: Unknown
% 1.94/1.62 % (3394)Termination phase: Saturation
% 1.94/1.62
% 1.94/1.62 % (3394)Memory used [KB]: 1023
% 1.94/1.62 % (3394)Time elapsed: 0.006 s
% 1.94/1.62 % (3394)Instructions burned: 8 (million)
% 1.94/1.62 % (3394)------------------------------
% 1.94/1.62 % (3394)------------------------------
% 1.94/1.63 % (3396)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_3284 for (2999ds/3Mi)
% 1.94/1.63 % (3395)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/16Mi)
% 1.94/1.63 % (3390)Instruction limit reached!
% 1.94/1.63 % (3390)------------------------------
% 1.94/1.63 % (3390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.63 % (3390)Termination reason: Unknown
% 1.94/1.63 % (3390)Termination phase: Saturation
% 1.94/1.63 % (3396)Instruction limit reached!
% 1.94/1.63 % (3396)------------------------------
% 1.94/1.63 % (3396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.63 % (3396)Termination reason: Unknown
% 1.94/1.63 % (3396)Termination phase: Saturation
% 1.94/1.63
% 1.94/1.63 % (3396)Memory used [KB]: 5500
% 1.94/1.63 % (3396)Time elapsed: 0.003 s
% 1.94/1.63 % (3396)Instructions burned: 3 (million)
% 1.94/1.63 % (3396)------------------------------
% 1.94/1.63 % (3396)------------------------------
% 1.94/1.63
% 1.94/1.63 % (3390)Memory used [KB]: 5628
% 1.94/1.63 % (3390)Time elapsed: 0.021 s
% 1.94/1.63 % (3390)Instructions burned: 38 (million)
% 1.94/1.63 % (3390)------------------------------
% 1.94/1.63 % (3390)------------------------------
% 1.94/1.63 % (3395)First to succeed.
% 1.94/1.63 % (3398)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/7Mi)
% 1.94/1.63 % (3399)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3284 for (2999ds/3Mi)
% 1.94/1.63 % (3397)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_3284 for (2999ds/3Mi)
% 1.94/1.64 % (3399)Instruction limit reached!
% 1.94/1.64 % (3399)------------------------------
% 1.94/1.64 % (3399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.64 % (3399)Termination reason: Unknown
% 1.94/1.64 % (3399)Termination phase: Saturation
% 1.94/1.64
% 1.94/1.64 % (3399)Memory used [KB]: 5500
% 1.94/1.64 % (3399)Time elapsed: 0.004 s
% 1.94/1.64 % (3399)Instructions burned: 3 (million)
% 1.94/1.64 % (3399)------------------------------
% 1.94/1.64 % (3399)------------------------------
% 1.94/1.64 % (3397)Instruction limit reached!
% 1.94/1.64 % (3397)------------------------------
% 1.94/1.64 % (3397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.64 % (3395)Refutation found. Thanks to Tanya!
% 1.94/1.64 % SZS status Theorem for DTF2THF_3284
% 1.94/1.64 % SZS output start Proof for DTF2THF_3284
% 1.94/1.64 thf(func_def_1, type, f0: $o > $o).
% 1.94/1.64 thf(func_def_2, type, f1: $o > $o).
% 1.94/1.64 thf(func_def_3, type, f2: $o > $o).
% 1.94/1.64 thf(func_def_4, type, f3: $o > $o).
% 1.94/1.64 thf(func_def_5, type, f4: $o > $o).
% 1.94/1.64 thf(func_def_6, type, f5: $o > $o).
% 1.94/1.64 thf(f593,plain,(
% 1.94/1.64 $false),
% 1.94/1.64 inference(avatar_sat_refutation,[status(thm)],[f182,f191,f200,f205,f218,f227,f236,f241,f250,f259,f264,f269,f278,f287,f292,f297,f306,f311,f316,f317,f326,f331,f336,f337,f346,f355,f360,f365,f366,f367,f368,f369,f378,f383,f388,f389,f394,f395,f400,f401,f410,f415,f420,f421,f430,f439,f444,f449,f454,f459,f460,f461,f466,f467,f472,f473,f478,f483,f484,f485,f486,f487,f492,f497,f498,f499,f504,f505,f510,f511,f516,f517,f522,f523,f524,f525,f526,f527,f532,f533,f534,f535,f536,f541,f542,f547,f548,f549,f550,f551,f552,f553,f554,f555,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f568,f569,f570,f571,f572,f573,f574,f575,f576,f577,f578,f579,f580,f581,f582,f583,f584,f585,f586,f587,f588,f589,f590,f591,f592])).
% 1.94/1.64 thf(f592,plain,(
% 1.94/1.64 ($true != sF21) | ($false != sF21) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f591,plain,(
% 1.94/1.64 ($true != (f5 @ $false)) | ($false != (f5 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f590,plain,(
% 1.94/1.64 ($true != sF13) | ($false != sF13) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f589,plain,(
% 1.94/1.64 ($false != sF16) | (sF16 != $true) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f588,plain,(
% 1.94/1.64 (sF2 != $true) | ($false != sF2) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f587,plain,(
% 1.94/1.64 ($true != sF5) | ($false != sF5) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f586,plain,(
% 1.94/1.64 ($true != sF17) | ($false != sF17) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f585,plain,(
% 1.94/1.64 (x != $true) | (x != $false) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f584,plain,(
% 1.94/1.64 ($true != sF20) | ($false != sF20) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f583,plain,(
% 1.94/1.64 (sF10 != $true) | ($false != sF10) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f582,plain,(
% 1.94/1.64 (sF22 != $true) | (sF22 != $false) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f581,plain,(
% 1.94/1.64 ($false != (f5 @ $true)) | ((f5 @ $true) != $true) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f580,plain,(
% 1.94/1.64 ($true != sF12) | ($false != sF12) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f579,plain,(
% 1.94/1.64 ($true != sF19) | ($false != sF19) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f578,plain,(
% 1.94/1.64 ($true != sF18) | ($false != sF18) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f577,plain,(
% 1.94/1.64 ($true != sF9) | ($false != sF9) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f576,plain,(
% 1.94/1.64 ($true != sF0) | ($false != sF0) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f575,plain,(
% 1.94/1.64 (sF1 != $true) | (sF1 != $false) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f574,plain,(
% 1.94/1.64 (sF7 != $true) | ($false != sF7) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f573,plain,(
% 1.94/1.64 ($true != (f1 @ $false)) | ($false != (f1 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f572,plain,(
% 1.94/1.64 ($true != (f1 @ $true)) | ($false != (f1 @ $true)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f571,plain,(
% 1.94/1.64 (sF8 != $true) | (sF8 != $false) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f570,plain,(
% 1.94/1.64 ($true != sF6) | ($false != sF6) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f569,plain,(
% 1.94/1.64 ($true != sF14) | ($false != sF14) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f568,plain,(
% 1.94/1.64 ($false != sF4) | (sF4 != $true) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f567,plain,(
% 1.94/1.64 ($false != sF3) | ($true != sF3) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f566,plain,(
% 1.94/1.64 ($true != sF15) | ($false != sF15) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f565,plain,(
% 1.94/1.64 ($true != (f2 @ $false)) | ($false != (f2 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f564,plain,(
% 1.94/1.64 ((f2 @ $true) != $true) | ((f2 @ $true) != $false) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f563,plain,(
% 1.94/1.64 ($true != (f3 @ $false)) | ($false != (f3 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f562,plain,(
% 1.94/1.64 ($true != (f3 @ $true)) | ($false != (f3 @ $true)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f561,plain,(
% 1.94/1.64 ($true != (f0 @ $false)) | ($false != (f0 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f560,plain,(
% 1.94/1.64 ($true != (f0 @ $true)) | ($false != (f0 @ $true)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f559,plain,(
% 1.94/1.64 ($true != sF11) | ($false != sF11) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f558,plain,(
% 1.94/1.64 ((f4 @ $false) != $true) | ($false != (f4 @ $false)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f557,plain,(
% 1.94/1.64 ($false != (f4 @ $true)) | ($true != (f4 @ $true)) | ($false = $true)),
% 1.94/1.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.94/1.64 thf(f556,plain,(
% 1.94/1.64 spl23_61 | spl23_56 | spl23_58),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f33,f446,f436,f463])).
% 1.94/1.64 thf(f463,definition,(
% 1.94/1.64 spl23_61 <=> ($false = sF13)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_61])],[avatar_definition])).
% 1.94/1.64 thf(f436,definition,(
% 1.94/1.64 spl23_56 <=> ($true = sF12)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_56])],[avatar_definition])).
% 1.94/1.64 thf(f446,definition,(
% 1.94/1.64 spl23_58 <=> ($true = (f5 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_58])],[avatar_definition])).
% 1.94/1.64 thf(f33,plain,(
% 1.94/1.64 ($true = sF12) | ($false = sF13) | ($true = (f5 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.94/1.64 thf(f31,plain,(
% 1.94/1.64 (sF13 = (f5 @ $false)) | ($true = sF12)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f19])).
% 1.94/1.64 thf(f19,definition,(
% 1.94/1.64 (sF13 = (f5 @ sF12))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f555,plain,(
% 1.94/1.64 spl23_56 | spl23_57 | spl23_62),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f32,f469,f441,f436])).
% 1.94/1.64 thf(f441,definition,(
% 1.94/1.64 spl23_57 <=> ($false = (f5 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_57])],[avatar_definition])).
% 1.94/1.64 thf(f469,definition,(
% 1.94/1.64 spl23_62 <=> ($true = sF13)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_62])],[avatar_definition])).
% 1.94/1.64 thf(f32,plain,(
% 1.94/1.64 ($false = (f5 @ $false)) | ($true = sF13) | ($true = sF12)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.94/1.64 thf(f554,plain,(
% 1.94/1.64 spl23_62 | spl23_55 | spl23_54),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f35,f427,f432,f469])).
% 1.94/1.64 thf(f432,definition,(
% 1.94/1.64 spl23_55 <=> ($false = (f5 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_55])],[avatar_definition])).
% 1.94/1.64 thf(f427,definition,(
% 1.94/1.64 spl23_54 <=> ($false = sF12)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_54])],[avatar_definition])).
% 1.94/1.64 thf(f35,plain,(
% 1.94/1.64 ($false = sF12) | ($true = sF13) | ($false = (f5 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.94/1.64 thf(f30,plain,(
% 1.94/1.64 ((f5 @ $true) = sF13) | ($false = sF12)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f19])).
% 1.94/1.64 thf(f553,plain,(
% 1.94/1.64 spl23_53 | spl23_54 | spl23_61),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f34,f463,f427,f423])).
% 1.94/1.64 thf(f423,definition,(
% 1.94/1.64 spl23_53 <=> ((f5 @ $true) = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_53])],[avatar_definition])).
% 1.94/1.64 thf(f34,plain,(
% 1.94/1.64 ($false = sF13) | ($false = sF12) | ((f5 @ $true) = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.94/1.64 thf(f552,plain,(
% 1.94/1.64 spl23_59 | spl23_72 | spl23_22),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f39,f266,f538,f451])).
% 1.94/1.64 thf(f451,definition,(
% 1.94/1.64 spl23_59 <=> (sF16 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_59])],[avatar_definition])).
% 1.94/1.64 thf(f538,definition,(
% 1.94/1.64 spl23_72 <=> ($false = sF17)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_72])],[avatar_definition])).
% 1.94/1.64 thf(f266,definition,(
% 1.94/1.64 spl23_22 <=> ($true = (f3 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_22])],[avatar_definition])).
% 1.94/1.64 thf(f39,plain,(
% 1.94/1.64 (sF16 = $true) | ($false = sF17) | ($true = (f3 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.94/1.64 thf(f37,plain,(
% 1.94/1.64 (sF16 = $true) | (sF17 = (f3 @ $false))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f23])).
% 1.94/1.64 thf(f23,definition,(
% 1.94/1.64 (sF17 = (f3 @ sF16))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f551,plain,(
% 1.94/1.64 spl23_21 | spl23_59 | spl23_73),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f38,f544,f451,f261])).
% 1.94/1.64 thf(f261,definition,(
% 1.94/1.64 spl23_21 <=> ($false = (f3 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_21])],[avatar_definition])).
% 1.94/1.64 thf(f544,definition,(
% 1.94/1.64 spl23_73 <=> ($true = sF17)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_73])],[avatar_definition])).
% 1.94/1.64 thf(f38,plain,(
% 1.94/1.64 ($true = sF17) | (sF16 = $true) | ($false = (f3 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.94/1.64 thf(f550,plain,(
% 1.94/1.64 spl23_19 | spl23_72 | spl23_60),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f41,f456,f538,f252])).
% 1.94/1.64 thf(f252,definition,(
% 1.94/1.64 spl23_19 <=> ($true = (f3 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_19])],[avatar_definition])).
% 1.94/1.64 thf(f456,definition,(
% 1.94/1.64 spl23_60 <=> ($false = sF16)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_60])],[avatar_definition])).
% 1.94/1.64 thf(f41,plain,(
% 1.94/1.64 ($false = sF16) | ($false = sF17) | ($true = (f3 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.94/1.64 thf(f36,plain,(
% 1.94/1.64 ($false = sF16) | (sF17 = (f3 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f23])).
% 1.94/1.64 thf(f549,plain,(
% 1.94/1.64 spl23_60 | spl23_17 | spl23_73),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f40,f544,f243,f456])).
% 1.94/1.64 thf(f243,definition,(
% 1.94/1.64 spl23_17 <=> ($false = (f3 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_17])],[avatar_definition])).
% 1.94/1.64 thf(f40,plain,(
% 1.94/1.64 ($false = sF16) | ($false = (f3 @ $true)) | ($true = sF17)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.94/1.64 thf(f548,plain,(
% 1.94/1.64 spl23_73 | spl23_52 | spl23_27),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f45,f289,f417,f544])).
% 1.94/1.64 thf(f417,definition,(
% 1.94/1.64 spl23_52 <=> ($true = sF18)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_52])],[avatar_definition])).
% 1.94/1.64 thf(f289,definition,(
% 1.94/1.64 spl23_27 <=> ($false = (f2 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_27])],[avatar_definition])).
% 1.94/1.64 thf(f45,plain,(
% 1.94/1.64 ($false = (f2 @ $false)) | ($true = sF17) | ($true = sF18)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.94/1.64 thf(f43,plain,(
% 1.94/1.64 ($true = sF17) | ((f2 @ $false) = sF18)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f24])).
% 1.94/1.64 thf(f24,definition,(
% 1.94/1.64 (sF18 = (f2 @ sF17))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f547,plain,(
% 1.94/1.64 spl23_28 | spl23_49 | spl23_73),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f44,f544,f403,f294])).
% 1.94/1.64 thf(f294,definition,(
% 1.94/1.64 spl23_28 <=> ($true = (f2 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_28])],[avatar_definition])).
% 1.94/1.64 thf(f403,definition,(
% 1.94/1.64 spl23_49 <=> ($false = sF18)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_49])],[avatar_definition])).
% 1.94/1.64 thf(f44,plain,(
% 1.94/1.64 ($false = sF18) | ($true = sF17) | ($true = (f2 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.94/1.64 thf(f542,plain,(
% 1.94/1.64 spl23_25 | spl23_72 | spl23_52),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f47,f417,f538,f280])).
% 1.94/1.64 thf(f280,definition,(
% 1.94/1.64 spl23_25 <=> ((f2 @ $true) = $false)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_25])],[avatar_definition])).
% 1.94/1.64 thf(f47,plain,(
% 1.94/1.64 ($false = sF17) | ($true = sF18) | ((f2 @ $true) = $false)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.94/1.64 thf(f42,plain,(
% 1.94/1.64 ($false = sF17) | ((f2 @ $true) = sF18)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f24])).
% 1.94/1.64 thf(f541,plain,(
% 1.94/1.64 spl23_24 | spl23_72 | spl23_49),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f46,f403,f538,f275])).
% 1.94/1.64 thf(f275,definition,(
% 1.94/1.64 spl23_24 <=> ((f2 @ $true) = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_24])],[avatar_definition])).
% 1.94/1.64 thf(f46,plain,(
% 1.94/1.64 ($false = sF18) | ((f2 @ $true) = $true) | ($false = sF17)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.94/1.64 thf(f536,plain,(
% 1.94/1.64 spl23_42 | spl23_67 | spl23_66),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f51,f494,f501,f362])).
% 1.94/1.64 thf(f362,definition,(
% 1.94/1.64 spl23_42 <=> ($true = (f1 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_42])],[avatar_definition])).
% 1.94/1.64 thf(f501,definition,(
% 1.94/1.64 spl23_67 <=> ($false = sF21)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_67])],[avatar_definition])).
% 1.94/1.64 thf(f494,definition,(
% 1.94/1.64 spl23_66 <=> ($true = sF20)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_66])],[avatar_definition])).
% 1.94/1.64 thf(f51,plain,(
% 1.94/1.64 ($true = (f1 @ $false)) | ($false = sF21) | ($true = sF20)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.94/1.64 thf(f49,plain,(
% 1.94/1.64 ($true = sF20) | (sF21 = (f1 @ $false))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f27])).
% 1.94/1.64 thf(f27,definition,(
% 1.94/1.64 (sF21 = (f1 @ sF20))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f535,plain,(
% 1.94/1.64 spl23_68 | spl23_41 | spl23_66),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f50,f494,f357,f507])).
% 1.94/1.64 thf(f507,definition,(
% 1.94/1.64 spl23_68 <=> ($true = sF21)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_68])],[avatar_definition])).
% 1.94/1.64 thf(f357,definition,(
% 1.94/1.64 spl23_41 <=> ($false = (f1 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_41])],[avatar_definition])).
% 1.94/1.64 thf(f50,plain,(
% 1.94/1.64 ($true = sF21) | ($false = (f1 @ $false)) | ($true = sF20)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.94/1.64 thf(f534,plain,(
% 1.94/1.64 spl23_40 | spl23_65 | spl23_67),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f53,f501,f489,f352])).
% 1.94/1.64 thf(f352,definition,(
% 1.94/1.64 spl23_40 <=> ($true = (f1 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_40])],[avatar_definition])).
% 1.94/1.64 thf(f489,definition,(
% 1.94/1.64 spl23_65 <=> ($false = sF20)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_65])],[avatar_definition])).
% 1.94/1.64 thf(f53,plain,(
% 1.94/1.64 ($true = (f1 @ $true)) | ($false = sF20) | ($false = sF21)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.94/1.64 thf(f48,plain,(
% 1.94/1.64 (sF21 = (f1 @ $true)) | ($false = sF20)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f27])).
% 1.94/1.64 thf(f533,plain,(
% 1.94/1.64 spl23_68 | spl23_38 | spl23_65),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f52,f489,f343,f507])).
% 1.94/1.64 thf(f343,definition,(
% 1.94/1.64 spl23_38 <=> ($false = (f1 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_38])],[avatar_definition])).
% 1.94/1.64 thf(f52,plain,(
% 1.94/1.64 ($true = sF21) | ($false = sF20) | ($false = (f1 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.94/1.64 thf(f532,plain,(
% 1.94/1.64 ~spl23_71),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f3,f529])).
% 1.94/1.64 thf(f529,definition,(
% 1.94/1.64 spl23_71 <=> ($false = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_71])],[avatar_definition])).
% 1.94/1.64 thf(f3,plain,(
% 1.94/1.64 ($false != $true)),
% 1.94/1.64 introduced(definition,[],[fool_axiom])).
% 1.94/1.64 thf(f527,plain,(
% 1.94/1.64 spl23_43 | spl23_3 | spl23_6),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f57,f193,f179,f371])).
% 1.94/1.64 thf(f371,definition,(
% 1.94/1.64 spl23_43 <=> (sF1 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_43])],[avatar_definition])).
% 1.94/1.64 thf(f179,definition,(
% 1.94/1.64 spl23_3 <=> ($false = sF2)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition])).
% 1.94/1.64 thf(f193,definition,(
% 1.94/1.64 spl23_6 <=> ((f4 @ $false) = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_6])],[avatar_definition])).
% 1.94/1.64 thf(f57,plain,(
% 1.94/1.64 ((f4 @ $false) = $true) | ($false = sF2) | (sF1 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.94/1.64 thf(f55,plain,(
% 1.94/1.64 (sF2 = (f4 @ $false)) | (sF1 = $true)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f8])).
% 1.94/1.64 thf(f8,definition,(
% 1.94/1.64 (sF2 = (f4 @ sF1))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f526,plain,(
% 1.94/1.64 spl23_8 | spl23_7 | spl23_43),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f56,f371,f197,f202])).
% 1.94/1.64 thf(f202,definition,(
% 1.94/1.64 spl23_8 <=> ($false = (f4 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_8])],[avatar_definition])).
% 1.94/1.64 thf(f197,definition,(
% 1.94/1.64 spl23_7 <=> (sF2 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_7])],[avatar_definition])).
% 1.94/1.64 thf(f56,plain,(
% 1.94/1.64 (sF2 = $true) | (sF1 = $true) | ($false = (f4 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.94/1.64 thf(f525,plain,(
% 1.94/1.64 spl23_3 | spl23_4 | spl23_45),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f59,f380,f184,f179])).
% 1.94/1.64 thf(f184,definition,(
% 1.94/1.64 spl23_4 <=> ($true = (f4 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition])).
% 1.94/1.64 thf(f380,definition,(
% 1.94/1.64 spl23_45 <=> (sF1 = $false)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_45])],[avatar_definition])).
% 1.94/1.64 thf(f59,plain,(
% 1.94/1.64 (sF1 = $false) | ($true = (f4 @ $true)) | ($false = sF2)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.94/1.64 thf(f54,plain,(
% 1.94/1.64 (sF2 = (f4 @ $true)) | (sF1 = $false)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f8])).
% 1.94/1.64 thf(f524,plain,(
% 1.94/1.64 spl23_7 | spl23_2 | spl23_45),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f58,f380,f175,f197])).
% 1.94/1.64 thf(f175,definition,(
% 1.94/1.64 spl23_2 <=> ($false = (f4 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition])).
% 1.94/1.64 thf(f58,plain,(
% 1.94/1.64 ($false = (f4 @ $true)) | (sF1 = $false) | (sF2 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.94/1.64 thf(f523,plain,(
% 1.94/1.64 spl23_44 | spl23_58 | spl23_70),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f63,f519,f446,f375])).
% 1.94/1.64 thf(f375,definition,(
% 1.94/1.64 spl23_44 <=> ($false = sF0)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_44])],[avatar_definition])).
% 1.94/1.64 thf(f519,definition,(
% 1.94/1.64 spl23_70 <=> (x = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_70])],[avatar_definition])).
% 1.94/1.64 thf(f63,plain,(
% 1.94/1.64 ($true = (f5 @ $false)) | ($false = sF0) | (x = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.94/1.64 thf(f61,plain,(
% 1.94/1.64 (sF0 = (f5 @ $false)) | (x = $true)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f6])).
% 1.94/1.64 thf(f6,definition,(
% 1.94/1.64 ((f5 @ x) = sF0)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f522,plain,(
% 1.94/1.64 spl23_46 | spl23_70 | spl23_57),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f62,f441,f519,f385])).
% 1.94/1.64 thf(f385,definition,(
% 1.94/1.64 spl23_46 <=> ($true = sF0)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_46])],[avatar_definition])).
% 1.94/1.64 thf(f62,plain,(
% 1.94/1.64 ($false = (f5 @ $false)) | ($true = sF0) | (x = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.94/1.64 thf(f517,plain,(
% 1.94/1.64 spl23_46 | spl23_55 | spl23_69),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f65,f513,f432,f385])).
% 1.94/1.64 thf(f513,definition,(
% 1.94/1.64 spl23_69 <=> (x = $false)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_69])],[avatar_definition])).
% 1.94/1.64 thf(f65,plain,(
% 1.94/1.64 (x = $false) | ($true = sF0) | ($false = (f5 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.94/1.64 thf(f60,plain,(
% 1.94/1.64 ((f5 @ $true) = sF0) | (x = $false)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f6])).
% 1.94/1.64 thf(f516,plain,(
% 1.94/1.64 spl23_44 | spl23_53 | spl23_69),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f64,f513,f423,f375])).
% 1.94/1.64 thf(f64,plain,(
% 1.94/1.64 ((f5 @ $true) = $true) | (x = $false) | ($false = sF0)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.94/1.64 thf(f511,plain,(
% 1.94/1.64 spl23_16 | spl23_64 | spl23_68),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f69,f507,f480,f238])).
% 1.94/1.64 thf(f238,definition,(
% 1.94/1.64 spl23_16 <=> ($true = (f0 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_16])],[avatar_definition])).
% 1.94/1.64 thf(f480,definition,(
% 1.94/1.64 spl23_64 <=> (sF22 = $false)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_64])],[avatar_definition])).
% 1.94/1.64 thf(f69,plain,(
% 1.94/1.64 ($true = (f0 @ $false)) | (sF22 = $false) | ($true = sF21)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.94/1.64 thf(f67,plain,(
% 1.94/1.64 (sF22 = (f0 @ $false)) | ($true = sF21)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f28])).
% 1.94/1.64 thf(f28,definition,(
% 1.94/1.64 (sF22 = (f0 @ sF21))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f510,plain,(
% 1.94/1.64 spl23_68 | spl23_14 | spl23_63),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f68,f475,f229,f507])).
% 1.94/1.64 thf(f229,definition,(
% 1.94/1.64 spl23_14 <=> ($false = (f0 @ $false))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_14])],[avatar_definition])).
% 1.94/1.64 thf(f475,definition,(
% 1.94/1.64 spl23_63 <=> (sF22 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_63])],[avatar_definition])).
% 1.94/1.64 thf(f68,plain,(
% 1.94/1.64 ($false = (f0 @ $false)) | (sF22 = $true) | ($true = sF21)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.94/1.64 thf(f505,plain,(
% 1.94/1.64 spl23_9 | spl23_67 | spl23_64),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f71,f480,f501,f207])).
% 1.94/1.64 thf(f207,definition,(
% 1.94/1.64 spl23_9 <=> ($true = (f0 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_9])],[avatar_definition])).
% 1.94/1.64 thf(f71,plain,(
% 1.94/1.64 (sF22 = $false) | ($true = (f0 @ $true)) | ($false = sF21)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.94/1.64 thf(f66,plain,(
% 1.94/1.64 ($false = sF21) | (sF22 = (f0 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f28])).
% 1.94/1.64 thf(f504,plain,(
% 1.94/1.64 spl23_13 | spl23_67 | spl23_63),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f70,f475,f501,f224])).
% 1.94/1.64 thf(f224,definition,(
% 1.94/1.64 spl23_13 <=> ($false = (f0 @ $true))),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_13])],[avatar_definition])).
% 1.94/1.64 thf(f70,plain,(
% 1.94/1.64 ($false = (f0 @ $true)) | ($false = sF21) | (sF22 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.94/1.64 thf(f499,plain,(
% 1.94/1.64 spl23_50 | spl23_41 | spl23_66),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f75,f494,f357,f407])).
% 1.94/1.64 thf(f407,definition,(
% 1.94/1.64 spl23_50 <=> ($true = sF19)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_50])],[avatar_definition])).
% 1.94/1.64 thf(f75,plain,(
% 1.94/1.64 ($true = sF20) | ($true = sF19) | ($false = (f1 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.94/1.64 thf(f73,plain,(
% 1.94/1.64 ($true = sF19) | ((f1 @ $false) = sF20)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f26])).
% 1.94/1.64 thf(f26,definition,(
% 1.94/1.64 ((f1 @ sF19) = sF20)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f498,plain,(
% 1.94/1.64 spl23_65 | spl23_42 | spl23_50),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f74,f407,f362,f489])).
% 1.94/1.64 thf(f74,plain,(
% 1.94/1.64 ($false = sF20) | ($true = sF19) | ($true = (f1 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.94/1.64 thf(f497,plain,(
% 1.94/1.64 spl23_51 | spl23_38 | spl23_66),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f77,f494,f343,f412])).
% 1.94/1.64 thf(f412,definition,(
% 1.94/1.64 spl23_51 <=> ($false = sF19)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_51])],[avatar_definition])).
% 1.94/1.64 thf(f77,plain,(
% 1.94/1.64 ($false = (f1 @ $true)) | ($true = sF20) | ($false = sF19)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.94/1.64 thf(f72,plain,(
% 1.94/1.64 ((f1 @ $true) = sF20) | ($false = sF19)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f26])).
% 1.94/1.64 thf(f492,plain,(
% 1.94/1.64 spl23_51 | spl23_40 | spl23_65),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f76,f489,f352,f412])).
% 1.94/1.64 thf(f76,plain,(
% 1.94/1.64 ($false = sF20) | ($true = (f1 @ $true)) | ($false = sF19)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.94/1.64 thf(f487,plain,(
% 1.94/1.64 spl23_14 | spl23_48 | spl23_37),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f81,f339,f397,f229])).
% 1.94/1.64 thf(f397,definition,(
% 1.94/1.64 spl23_48 <=> ($true = sF9)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_48])],[avatar_definition])).
% 1.94/1.64 thf(f339,definition,(
% 1.94/1.64 spl23_37 <=> (sF8 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_37])],[avatar_definition])).
% 1.94/1.64 thf(f81,plain,(
% 1.94/1.64 ($true = sF9) | ($false = (f0 @ $false)) | (sF8 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.94/1.64 thf(f79,plain,(
% 1.94/1.64 (sF8 = $true) | ((f0 @ $false) = sF9)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f15])).
% 1.94/1.64 thf(f15,definition,(
% 1.94/1.64 ((f0 @ sF8) = sF9)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f486,plain,(
% 1.94/1.64 spl23_37 | spl23_16 | spl23_47),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f80,f391,f238,f339])).
% 1.94/1.64 thf(f391,definition,(
% 1.94/1.64 spl23_47 <=> ($false = sF9)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_47])],[avatar_definition])).
% 1.94/1.64 thf(f80,plain,(
% 1.94/1.64 (sF8 = $true) | ($true = (f0 @ $false)) | ($false = sF9)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.94/1.64 thf(f485,plain,(
% 1.94/1.64 spl23_13 | spl23_39 | spl23_48),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f83,f397,f348,f224])).
% 1.94/1.64 thf(f348,definition,(
% 1.94/1.64 spl23_39 <=> (sF8 = $false)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_39])],[avatar_definition])).
% 1.94/1.64 thf(f83,plain,(
% 1.94/1.64 ($true = sF9) | (sF8 = $false) | ($false = (f0 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.94/1.64 thf(f78,plain,(
% 1.94/1.64 ((f0 @ $true) = sF9) | (sF8 = $false)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f15])).
% 1.94/1.64 thf(f484,plain,(
% 1.94/1.64 spl23_39 | spl23_9 | spl23_47),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f82,f391,f207,f348])).
% 1.94/1.64 thf(f82,plain,(
% 1.94/1.64 (sF8 = $false) | ($false = sF9) | ($true = (f0 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.94/1.64 thf(f483,plain,(
% 1.94/1.64 spl23_11 | spl23_64),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f85,f480,f215])).
% 1.94/1.64 thf(f215,definition,(
% 1.94/1.64 spl23_11 <=> ($false = sF11)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_11])],[avatar_definition])).
% 1.94/1.64 thf(f85,plain,(
% 1.94/1.64 (sF22 = $false) | ($false = sF11)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.94/1.64 thf(f29,plain,(
% 1.94/1.64 (sF22 != sF11)),
% 1.94/1.64 inference(definition_folding,[status(thm)],[f5,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f6,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6])).
% 1.94/1.64 thf(f7,definition,(
% 1.94/1.64 (sF1 = (f4 @ sF0))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f9,definition,(
% 1.94/1.64 ((f4 @ sF2) = sF3)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f10,definition,(
% 1.94/1.64 (sF4 = (f3 @ sF3))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f11,definition,(
% 1.94/1.64 (sF5 = (f2 @ sF4))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f12,definition,(
% 1.94/1.64 (sF6 = (f2 @ sF5))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f13,definition,(
% 1.94/1.64 (sF7 = (f2 @ sF6))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f14,definition,(
% 1.94/1.64 (sF8 = (f1 @ sF7))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f16,definition,(
% 1.94/1.64 ((f0 @ sF9) = sF10)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f17,definition,(
% 1.94/1.64 (sF11 = (f0 @ sF10))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f18,definition,(
% 1.94/1.64 ((f5 @ sF0) = sF12)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f20,definition,(
% 1.94/1.64 ((f4 @ sF13) = sF14)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f21,definition,(
% 1.94/1.64 ((f3 @ sF14) = sF15)),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f22,definition,(
% 1.94/1.64 (sF16 = (f3 @ sF15))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f25,definition,(
% 1.94/1.64 (sF19 = (f1 @ sF18))),
% 1.94/1.64 introduced(definition,[],[function_definition])).
% 1.94/1.64 thf(f5,plain,(
% 1.94/1.64 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ x)))))))))))) != (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ x)))))))))))))),
% 1.94/1.64 inference(cnf_transformation,[status(thm)],[f4])).
% 1.94/1.64 thf(f4,plain,(
% 1.94/1.64 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ x)))))))))))) != (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ x)))))))))))))),
% 1.94/1.64 inference(flattening,[status(thm)],[f2])).
% 1.94/1.64 thf(f2,negated_conjecture,(
% 1.94/1.64 ~((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ x)))))))))))) = (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ x)))))))))))))),
% 1.94/1.64 inference(negated_conjecture,[status(cth)],[f1])).
% 1.94/1.64 thf(f1,conjecture,(
% 1.94/1.64 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ (f4 @ (f4 @ (f4 @ (f5 @ x)))))))))))) = (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ (f4 @ (f5 @ (f5 @ (f5 @ x)))))))))))))),
% 1.94/1.64 file('/export/starexec/sandbox/tmp/tmp.9y7qOUSbQU/DTF2THF_3284.p',kaminski6)).
% 1.94/1.64 thf(f478,plain,(
% 1.94/1.64 spl23_63 | spl23_12),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f84,f220,f475])).
% 1.94/1.64 thf(f220,definition,(
% 1.94/1.64 spl23_12 <=> ($true = sF11)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_12])],[avatar_definition])).
% 1.94/1.64 thf(f84,plain,(
% 1.94/1.64 (sF22 = $true) | ($true = sF11)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.94/1.64 thf(f473,plain,(
% 1.94/1.64 spl23_8 | spl23_32 | spl23_62),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f89,f469,f313,f202])).
% 1.94/1.64 thf(f313,definition,(
% 1.94/1.64 spl23_32 <=> ($true = sF14)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_32])],[avatar_definition])).
% 1.94/1.64 thf(f89,plain,(
% 1.94/1.64 ($false = (f4 @ $false)) | ($true = sF14) | ($true = sF13)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.94/1.64 thf(f87,plain,(
% 1.94/1.64 ($true = sF13) | ((f4 @ $false) = sF14)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f20])).
% 1.94/1.64 thf(f472,plain,(
% 1.94/1.64 spl23_30 | spl23_6 | spl23_62),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f88,f469,f193,f303])).
% 1.94/1.64 thf(f303,definition,(
% 1.94/1.64 spl23_30 <=> ($false = sF14)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_30])],[avatar_definition])).
% 1.94/1.64 thf(f88,plain,(
% 1.94/1.64 ((f4 @ $false) = $true) | ($false = sF14) | ($true = sF13)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.94/1.64 thf(f467,plain,(
% 1.94/1.64 spl23_61 | spl23_2 | spl23_32),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f91,f313,f175,f463])).
% 1.94/1.64 thf(f91,plain,(
% 1.94/1.64 ($false = sF13) | ($true = sF14) | ($false = (f4 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.94/1.64 thf(f86,plain,(
% 1.94/1.64 ((f4 @ $true) = sF14) | ($false = sF13)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f20])).
% 1.94/1.64 thf(f466,plain,(
% 1.94/1.64 spl23_30 | spl23_4 | spl23_61),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f90,f463,f184,f303])).
% 1.94/1.64 thf(f90,plain,(
% 1.94/1.64 ($false = sF14) | ($true = (f4 @ $true)) | ($false = sF13)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.94/1.64 thf(f461,plain,(
% 1.94/1.64 spl23_60 | spl23_22 | spl23_29),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f95,f299,f266,f456])).
% 1.94/1.64 thf(f299,definition,(
% 1.94/1.64 spl23_29 <=> ($true = sF15)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_29])],[avatar_definition])).
% 1.94/1.64 thf(f95,plain,(
% 1.94/1.64 ($true = sF15) | ($true = (f3 @ $false)) | ($false = sF16)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.94/1.64 thf(f93,plain,(
% 1.94/1.64 (sF16 = (f3 @ $false)) | ($true = sF15)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f22])).
% 1.94/1.64 thf(f460,plain,(
% 1.94/1.64 spl23_59 | spl23_29 | spl23_21),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f94,f261,f299,f451])).
% 1.94/1.64 thf(f94,plain,(
% 1.94/1.64 ($true = sF15) | ($false = (f3 @ $false)) | (sF16 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.94/1.64 thf(f459,plain,(
% 1.94/1.64 spl23_31 | spl23_60 | spl23_19),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f97,f252,f456,f308])).
% 1.94/1.64 thf(f308,definition,(
% 1.94/1.64 spl23_31 <=> ($false = sF15)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_31])],[avatar_definition])).
% 1.94/1.64 thf(f97,plain,(
% 1.94/1.64 ($false = sF16) | ($true = (f3 @ $true)) | ($false = sF15)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.94/1.64 thf(f92,plain,(
% 1.94/1.64 ($false = sF15) | (sF16 = (f3 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f22])).
% 1.94/1.64 thf(f454,plain,(
% 1.94/1.64 spl23_17 | spl23_31 | spl23_59),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f96,f451,f308,f243])).
% 1.94/1.64 thf(f96,plain,(
% 1.94/1.64 ($false = (f3 @ $true)) | ($false = sF15) | (sF16 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.94/1.64 thf(f449,plain,(
% 1.94/1.64 spl23_58 | spl23_46 | spl23_54),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f101,f427,f385,f446])).
% 1.94/1.64 thf(f101,plain,(
% 1.94/1.64 ($true = sF0) | ($false = sF12) | ($true = (f5 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.94/1.64 thf(f99,plain,(
% 1.94/1.64 ($true = sF0) | (sF12 = (f5 @ $false))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f18])).
% 1.94/1.64 thf(f444,plain,(
% 1.94/1.64 spl23_57 | spl23_56 | spl23_46),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f100,f385,f436,f441])).
% 1.94/1.64 thf(f100,plain,(
% 1.94/1.64 ($true = sF12) | ($false = (f5 @ $false)) | ($true = sF0)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.94/1.64 thf(f439,plain,(
% 1.94/1.64 spl23_44 | spl23_55 | spl23_56),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f103,f436,f432,f375])).
% 1.94/1.64 thf(f103,plain,(
% 1.94/1.64 ($false = (f5 @ $true)) | ($false = sF0) | ($true = sF12)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.94/1.64 thf(f98,plain,(
% 1.94/1.64 ((f5 @ $true) = sF12) | ($false = sF0)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f18])).
% 1.94/1.64 thf(f430,plain,(
% 1.94/1.64 spl23_44 | spl23_53 | spl23_54),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f102,f427,f423,f375])).
% 1.94/1.64 thf(f102,plain,(
% 1.94/1.64 ($false = sF12) | ((f5 @ $true) = $true) | ($false = sF0)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.94/1.64 thf(f421,plain,(
% 1.94/1.64 spl23_42 | spl23_51 | spl23_52),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f107,f417,f412,f362])).
% 1.94/1.64 thf(f107,plain,(
% 1.94/1.64 ($true = (f1 @ $false)) | ($false = sF19) | ($true = sF18)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.94/1.64 thf(f105,plain,(
% 1.94/1.64 ($true = sF18) | (sF19 = (f1 @ $false))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f25])).
% 1.94/1.64 thf(f420,plain,(
% 1.94/1.64 spl23_52 | spl23_41 | spl23_50),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f106,f407,f357,f417])).
% 1.94/1.64 thf(f106,plain,(
% 1.94/1.64 ($true = sF18) | ($false = (f1 @ $false)) | ($true = sF19)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.94/1.64 thf(f415,plain,(
% 1.94/1.64 spl23_49 | spl23_51 | spl23_40),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f109,f352,f412,f403])).
% 1.94/1.64 thf(f109,plain,(
% 1.94/1.64 ($false = sF19) | ($false = sF18) | ($true = (f1 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.94/1.64 thf(f104,plain,(
% 1.94/1.64 (sF19 = (f1 @ $true)) | ($false = sF18)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f25])).
% 1.94/1.64 thf(f410,plain,(
% 1.94/1.64 spl23_49 | spl23_38 | spl23_50),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f108,f407,f343,f403])).
% 1.94/1.64 thf(f108,plain,(
% 1.94/1.64 ($false = (f1 @ $true)) | ($true = sF19) | ($false = sF18)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.94/1.64 thf(f401,plain,(
% 1.94/1.64 spl23_48 | spl23_16 | spl23_10),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f113,f211,f238,f397])).
% 1.94/1.64 thf(f211,definition,(
% 1.94/1.64 spl23_10 <=> ($false = sF10)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_10])],[avatar_definition])).
% 1.94/1.64 thf(f113,plain,(
% 1.94/1.64 ($false = sF10) | ($true = (f0 @ $false)) | ($true = sF9)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.94/1.64 thf(f111,plain,(
% 1.94/1.64 (sF10 = (f0 @ $false)) | ($true = sF9)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f16])).
% 1.94/1.64 thf(f400,plain,(
% 1.94/1.64 spl23_15 | spl23_48 | spl23_14),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f112,f229,f397,f233])).
% 1.94/1.64 thf(f233,definition,(
% 1.94/1.64 spl23_15 <=> (sF10 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_15])],[avatar_definition])).
% 1.94/1.64 thf(f112,plain,(
% 1.94/1.64 ($false = (f0 @ $false)) | ($true = sF9) | (sF10 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.94/1.64 thf(f395,plain,(
% 1.94/1.64 spl23_9 | spl23_47 | spl23_10),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f115,f211,f391,f207])).
% 1.94/1.64 thf(f115,plain,(
% 1.94/1.64 ($false = sF9) | ($false = sF10) | ($true = (f0 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.94/1.64 thf(f110,plain,(
% 1.94/1.64 ($false = sF9) | (sF10 = (f0 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f16])).
% 1.94/1.64 thf(f394,plain,(
% 1.94/1.64 spl23_13 | spl23_47 | spl23_15),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f114,f233,f391,f224])).
% 1.94/1.64 thf(f114,plain,(
% 1.94/1.64 (sF10 = $true) | ($false = (f0 @ $true)) | ($false = sF9)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.94/1.64 thf(f389,plain,(
% 1.94/1.64 spl23_45 | spl23_46 | spl23_6),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f119,f193,f385,f380])).
% 1.94/1.64 thf(f119,plain,(
% 1.94/1.64 (sF1 = $false) | ($true = sF0) | ((f4 @ $false) = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.94/1.64 thf(f117,plain,(
% 1.94/1.64 (sF1 = (f4 @ $false)) | ($true = sF0)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f7])).
% 1.94/1.64 thf(f388,plain,(
% 1.94/1.64 spl23_8 | spl23_46 | spl23_43),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f118,f371,f385,f202])).
% 1.94/1.64 thf(f118,plain,(
% 1.94/1.64 (sF1 = $true) | ($true = sF0) | ($false = (f4 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.94/1.64 thf(f383,plain,(
% 1.94/1.64 spl23_45 | spl23_44 | spl23_4),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f121,f184,f375,f380])).
% 1.94/1.64 thf(f121,plain,(
% 1.94/1.64 (sF1 = $false) | ($true = (f4 @ $true)) | ($false = sF0)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.94/1.64 thf(f116,plain,(
% 1.94/1.64 ($false = sF0) | (sF1 = (f4 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f7])).
% 1.94/1.64 thf(f378,plain,(
% 1.94/1.64 spl23_43 | spl23_44 | spl23_2),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f120,f175,f375,f371])).
% 1.94/1.64 thf(f120,plain,(
% 1.94/1.64 ($false = sF0) | (sF1 = $true) | ($false = (f4 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.94/1.64 thf(f369,plain,(
% 1.94/1.64 spl23_26 | spl23_27 | spl23_36),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f125,f333,f289,f284])).
% 1.94/1.64 thf(f284,definition,(
% 1.94/1.64 spl23_26 <=> ($true = sF5)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_26])],[avatar_definition])).
% 1.94/1.64 thf(f333,definition,(
% 1.94/1.64 spl23_36 <=> ($true = sF6)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_36])],[avatar_definition])).
% 1.94/1.64 thf(f125,plain,(
% 1.94/1.64 ($false = (f2 @ $false)) | ($true = sF5) | ($true = sF6)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.94/1.64 thf(f123,plain,(
% 1.94/1.64 ($true = sF5) | ((f2 @ $false) = sF6)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f12])).
% 1.94/1.64 thf(f368,plain,(
% 1.94/1.64 spl23_26 | spl23_33 | spl23_28),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f124,f294,f319,f284])).
% 1.94/1.64 thf(f319,definition,(
% 1.94/1.64 spl23_33 <=> ($false = sF6)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_33])],[avatar_definition])).
% 1.94/1.64 thf(f124,plain,(
% 1.94/1.64 ($true = (f2 @ $false)) | ($true = sF5) | ($false = sF6)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.94/1.64 thf(f367,plain,(
% 1.94/1.64 spl23_25 | spl23_36 | spl23_23),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f127,f271,f333,f280])).
% 1.94/1.64 thf(f271,definition,(
% 1.94/1.64 spl23_23 <=> ($false = sF5)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_23])],[avatar_definition])).
% 1.94/1.64 thf(f127,plain,(
% 1.94/1.64 ($true = sF6) | ((f2 @ $true) = $false) | ($false = sF5)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.94/1.64 thf(f122,plain,(
% 1.94/1.64 ($false = sF5) | ((f2 @ $true) = sF6)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f12])).
% 1.94/1.64 thf(f366,plain,(
% 1.94/1.64 spl23_24 | spl23_23 | spl23_33),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f126,f319,f271,f275])).
% 1.94/1.64 thf(f126,plain,(
% 1.94/1.64 ($false = sF6) | ((f2 @ $true) = $true) | ($false = sF5)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.94/1.64 thf(f365,plain,(
% 1.94/1.64 spl23_42 | spl23_39 | spl23_35),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f131,f328,f348,f362])).
% 1.94/1.64 thf(f328,definition,(
% 1.94/1.64 spl23_35 <=> (sF7 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_35])],[avatar_definition])).
% 1.94/1.64 thf(f131,plain,(
% 1.94/1.64 (sF8 = $false) | ($true = (f1 @ $false)) | (sF7 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.94/1.64 thf(f129,plain,(
% 1.94/1.64 (sF8 = (f1 @ $false)) | (sF7 = $true)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f14])).
% 1.94/1.64 thf(f360,plain,(
% 1.94/1.64 spl23_37 | spl23_41 | spl23_35),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f130,f328,f357,f339])).
% 1.94/1.64 thf(f130,plain,(
% 1.94/1.64 (sF8 = $true) | ($false = (f1 @ $false)) | (sF7 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.94/1.64 thf(f355,plain,(
% 1.94/1.64 spl23_34 | spl23_39 | spl23_40),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f133,f352,f348,f323])).
% 1.94/1.64 thf(f323,definition,(
% 1.94/1.64 spl23_34 <=> ($false = sF7)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_34])],[avatar_definition])).
% 1.94/1.64 thf(f133,plain,(
% 1.94/1.64 ($true = (f1 @ $true)) | (sF8 = $false) | ($false = sF7)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.94/1.64 thf(f128,plain,(
% 1.94/1.64 (sF8 = (f1 @ $true)) | ($false = sF7)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f14])).
% 1.94/1.64 thf(f346,plain,(
% 1.94/1.64 spl23_37 | spl23_34 | spl23_38),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f132,f343,f323,f339])).
% 1.94/1.64 thf(f132,plain,(
% 1.94/1.64 ($false = (f1 @ $true)) | (sF8 = $true) | ($false = sF7)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.94/1.64 thf(f337,plain,(
% 1.94/1.64 spl23_36 | spl23_28 | spl23_34),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f137,f323,f294,f333])).
% 1.94/1.64 thf(f137,plain,(
% 1.94/1.64 ($true = (f2 @ $false)) | ($true = sF6) | ($false = sF7)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.94/1.64 thf(f135,plain,(
% 1.94/1.64 (sF7 = (f2 @ $false)) | ($true = sF6)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f13])).
% 1.94/1.64 thf(f336,plain,(
% 1.94/1.64 spl23_27 | spl23_35 | spl23_36),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f136,f333,f328,f289])).
% 1.94/1.64 thf(f136,plain,(
% 1.94/1.64 ($true = sF6) | ($false = (f2 @ $false)) | (sF7 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.94/1.64 thf(f331,plain,(
% 1.94/1.64 spl23_25 | spl23_33 | spl23_35),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f139,f328,f319,f280])).
% 1.94/1.64 thf(f139,plain,(
% 1.94/1.64 ((f2 @ $true) = $false) | (sF7 = $true) | ($false = sF6)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.94/1.64 thf(f134,plain,(
% 1.94/1.64 ((f2 @ $true) = sF7) | ($false = sF6)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f13])).
% 1.94/1.64 thf(f326,plain,(
% 1.94/1.64 spl23_24 | spl23_33 | spl23_34),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f138,f323,f319,f275])).
% 1.94/1.64 thf(f138,plain,(
% 1.94/1.64 ($false = sF7) | ((f2 @ $true) = $true) | ($false = sF6)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.94/1.64 thf(f317,plain,(
% 1.94/1.64 spl23_22 | spl23_31 | spl23_32),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f143,f313,f308,f266])).
% 1.94/1.64 thf(f143,plain,(
% 1.94/1.64 ($true = sF14) | ($false = sF15) | ($true = (f3 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.94/1.64 thf(f141,plain,(
% 1.94/1.64 (sF15 = (f3 @ $false)) | ($true = sF14)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f21])).
% 1.94/1.64 thf(f316,plain,(
% 1.94/1.64 spl23_21 | spl23_32 | spl23_29),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f142,f299,f313,f261])).
% 1.94/1.64 thf(f142,plain,(
% 1.94/1.64 ($true = sF14) | ($false = (f3 @ $false)) | ($true = sF15)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.94/1.64 thf(f311,plain,(
% 1.94/1.64 spl23_19 | spl23_31 | spl23_30),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f145,f303,f308,f252])).
% 1.94/1.64 thf(f145,plain,(
% 1.94/1.64 ($false = sF14) | ($true = (f3 @ $true)) | ($false = sF15)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.94/1.64 thf(f140,plain,(
% 1.94/1.64 ($false = sF14) | (sF15 = (f3 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f21])).
% 1.94/1.64 thf(f306,plain,(
% 1.94/1.64 spl23_29 | spl23_17 | spl23_30),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f144,f303,f243,f299])).
% 1.94/1.64 thf(f144,plain,(
% 1.94/1.64 ($false = (f3 @ $true)) | ($true = sF15) | ($false = sF14)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.94/1.64 thf(f297,plain,(
% 1.94/1.64 spl23_23 | spl23_18 | spl23_28),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f149,f294,f247,f271])).
% 1.94/1.64 thf(f247,definition,(
% 1.94/1.64 spl23_18 <=> (sF4 = $true)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_18])],[avatar_definition])).
% 1.94/1.64 thf(f149,plain,(
% 1.94/1.64 (sF4 = $true) | ($false = sF5) | ($true = (f2 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.94/1.64 thf(f147,plain,(
% 1.94/1.64 (sF4 = $true) | (sF5 = (f2 @ $false))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f11])).
% 1.94/1.64 thf(f292,plain,(
% 1.94/1.64 spl23_26 | spl23_18 | spl23_27),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f148,f289,f247,f284])).
% 1.94/1.64 thf(f148,plain,(
% 1.94/1.64 (sF4 = $true) | ($true = sF5) | ($false = (f2 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.94/1.64 thf(f287,plain,(
% 1.94/1.64 spl23_25 | spl23_26 | spl23_20),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f151,f256,f284,f280])).
% 1.94/1.64 thf(f256,definition,(
% 1.94/1.64 spl23_20 <=> ($false = sF4)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_20])],[avatar_definition])).
% 1.94/1.64 thf(f151,plain,(
% 1.94/1.64 ($false = sF4) | ((f2 @ $true) = $false) | ($true = sF5)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.94/1.64 thf(f146,plain,(
% 1.94/1.64 ((f2 @ $true) = sF5) | ($false = sF4)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f11])).
% 1.94/1.64 thf(f278,plain,(
% 1.94/1.64 spl23_20 | spl23_23 | spl23_24),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f150,f275,f271,f256])).
% 1.94/1.64 thf(f150,plain,(
% 1.94/1.64 ($false = sF5) | ((f2 @ $true) = $true) | ($false = sF4)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.94/1.64 thf(f269,plain,(
% 1.94/1.64 spl23_22 | spl23_20 | spl23_1),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f155,f171,f256,f266])).
% 1.94/1.64 thf(f171,definition,(
% 1.94/1.64 spl23_1 <=> ($true = sF3)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition])).
% 1.94/1.64 thf(f155,plain,(
% 1.94/1.64 ($false = sF4) | ($true = sF3) | ($true = (f3 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.94/1.64 thf(f153,plain,(
% 1.94/1.64 (sF4 = (f3 @ $false)) | ($true = sF3)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f10])).
% 1.94/1.64 thf(f264,plain,(
% 1.94/1.64 spl23_21 | spl23_18 | spl23_1),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f154,f171,f247,f261])).
% 1.94/1.64 thf(f154,plain,(
% 1.94/1.64 ($true = sF3) | (sF4 = $true) | ($false = (f3 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.94/1.64 thf(f259,plain,(
% 1.94/1.64 spl23_19 | spl23_20 | spl23_5),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f157,f188,f256,f252])).
% 1.94/1.64 thf(f188,definition,(
% 1.94/1.64 spl23_5 <=> ($false = sF3)),
% 1.94/1.64 introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition])).
% 1.94/1.64 thf(f157,plain,(
% 1.94/1.64 ($false = sF4) | ($false = sF3) | ($true = (f3 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.94/1.64 thf(f152,plain,(
% 1.94/1.64 ($false = sF3) | (sF4 = (f3 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f10])).
% 1.94/1.64 thf(f250,plain,(
% 1.94/1.64 spl23_17 | spl23_5 | spl23_18),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f156,f247,f188,f243])).
% 1.94/1.64 thf(f156,plain,(
% 1.94/1.64 ($false = (f3 @ $true)) | ($false = sF3) | (sF4 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.94/1.64 thf(f241,plain,(
% 1.94/1.64 spl23_16 | spl23_15 | spl23_11),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f161,f215,f233,f238])).
% 1.94/1.64 thf(f161,plain,(
% 1.94/1.64 ($true = (f0 @ $false)) | (sF10 = $true) | ($false = sF11)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 1.94/1.64 thf(f159,plain,(
% 1.94/1.64 (sF11 = (f0 @ $false)) | (sF10 = $true)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f17])).
% 1.94/1.64 thf(f236,plain,(
% 1.94/1.64 spl23_12 | spl23_14 | spl23_15),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f160,f233,f229,f220])).
% 1.94/1.64 thf(f160,plain,(
% 1.94/1.64 (sF10 = $true) | ($true = sF11) | ($false = (f0 @ $false))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 1.94/1.64 thf(f227,plain,(
% 1.94/1.64 spl23_12 | spl23_13 | spl23_10),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f163,f211,f224,f220])).
% 1.94/1.64 thf(f163,plain,(
% 1.94/1.64 ($true = sF11) | ($false = (f0 @ $true)) | ($false = sF10)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.94/1.64 thf(f158,plain,(
% 1.94/1.64 ((f0 @ $true) = sF11) | ($false = sF10)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f17])).
% 1.94/1.64 thf(f218,plain,(
% 1.94/1.64 spl23_9 | spl23_10 | spl23_11),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f162,f215,f211,f207])).
% 1.94/1.64 thf(f162,plain,(
% 1.94/1.64 ($false = sF11) | ($true = (f0 @ $true)) | ($false = sF10)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.94/1.64 thf(f205,plain,(
% 1.94/1.64 spl23_7 | spl23_8 | spl23_1),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f167,f171,f202,f197])).
% 1.94/1.64 thf(f167,plain,(
% 1.94/1.64 ($false = (f4 @ $false)) | ($true = sF3) | (sF2 = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 1.94/1.64 thf(f165,plain,(
% 1.94/1.64 (sF2 = $true) | ((f4 @ $false) = sF3)),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f9])).
% 1.94/1.64 thf(f200,plain,(
% 1.94/1.64 spl23_6 | spl23_5 | spl23_7),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f166,f197,f188,f193])).
% 1.94/1.64 thf(f166,plain,(
% 1.94/1.64 ($false = sF3) | (sF2 = $true) | ((f4 @ $false) = $true)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 1.94/1.64 thf(f191,plain,(
% 1.94/1.64 spl23_3 | spl23_4 | spl23_5),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f169,f188,f184,f179])).
% 1.94/1.64 thf(f169,plain,(
% 1.94/1.64 ($false = sF3) | ($true = (f4 @ $true)) | ($false = sF2)),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 1.94/1.64 thf(f164,plain,(
% 1.94/1.64 ($false = sF2) | (sF3 = (f4 @ $true))),
% 1.94/1.64 inference(cases_simplifying,[status(thm)],[f9])).
% 1.94/1.64 thf(f182,plain,(
% 1.94/1.64 spl23_1 | spl23_2 | spl23_3),
% 1.94/1.64 inference(avatar_split_clause,[status(thm)],[f168,f179,f175,f171])).
% 1.94/1.64 thf(f168,plain,(
% 1.94/1.64 ($true = sF3) | ($false = sF2) | ($false = (f4 @ $true))),
% 1.94/1.64 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 1.94/1.64 % SZS output end Proof for DTF2THF_3284
% 1.94/1.64 % (3395)------------------------------
% 1.94/1.64 % (3395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.64 % (3395)Termination reason: Refutation
% 1.94/1.64
% 1.94/1.64 % (3395)Memory used [KB]: 5756
% 1.94/1.64 % (3395)Time elapsed: 0.012 s
% 1.94/1.64 % (3395)Instructions burned: 10 (million)
% 1.94/1.64 % (3395)------------------------------
% 1.94/1.64 % (3395)------------------------------
% 1.94/1.64 % (3381)Success in time 0.061 s
%------------------------------------------------------------------------------