%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1.004 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.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 09:54:22 AM UTC 2026
% Result : Theorem 1.64s 1.35s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 90
% Syntax : Number of formulae : 250 ( 23 unt; 0 typ; 64 def)
% Number of atoms : 1594 ( 386 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 626 ( 54 ~; 322 |; 0 &; 201 @)
% ( 49 <=>; 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 : 72 ( 69 usr; 67 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(f397,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f126,f135,f144,f149,f154,f155,f160,f161,f170,f175,f180,f181,f194,f203,f212,f217,f230,f239,f248,f253,f258,f263,f264,f265,f270,f275,f276,f277,f286,f291,f300,f305,f306,f307,f308,f309,f314,f319,f324,f325,f326,f331,f336,f337,f338,f339,f340,f341,f342,f347,f352,f357,f362,f363,f364,f365,f366,f367,f368,f369,f370,f371,f372,f373,f374,f375,f376,f377,f378,f379,f380,f381,f382,f383,f384,f385,f386,f387,f388,f389,f390,f391,f392,f393,f394,f395,f396]) ).
thf(f396,plain,
( ( $true != sF6 )
| ( sF6 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f395,plain,
( ( $true != sF12 )
| ( sF12 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f394,plain,
( ( $true != sF4 )
| ( $false != sF4 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f393,plain,
( ( $true != sF1 )
| ( sF1 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f392,plain,
( ( $true
!= ( f2 @ $false ) )
| ( ( f2 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f391,plain,
( ( x != $true )
| ( x != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f390,plain,
( ( $true != sF8 )
| ( $false != sF8 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f389,plain,
( ( sF9 != $false )
| ( $true != sF9 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f388,plain,
( ( $true != sF11 )
| ( $false != sF11 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f387,plain,
( ( $false != sF13 )
| ( $true != sF13 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f386,plain,
( ( sF14 != $false )
| ( $true != sF14 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f385,plain,
( ( sF3 != $true )
| ( sF3 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f384,plain,
( ( $true
!= ( f2 @ $true ) )
| ( $false
!= ( f2 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f383,plain,
( ( sF2 != $true )
| ( sF2 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f382,plain,
( ( $true != sF7 )
| ( $false != sF7 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f381,plain,
( ( $true != sF5 )
| ( $false != sF5 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f380,plain,
( ( $true
!= ( f0 @ $false ) )
| ( $false
!= ( f0 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f379,plain,
( ( $true
!= ( f0 @ $true ) )
| ( ( f0 @ $true )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f378,plain,
( ( $true
!= ( f3 @ $false ) )
| ( $false
!= ( f3 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f377,plain,
( ( $true
!= ( f3 @ $true ) )
| ( $false
!= ( f3 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f376,plain,
( ( sF0 != $true )
| ( sF0 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f375,plain,
( ( $true != sF10 )
| ( sF10 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f374,plain,
( ( $true
!= ( f1 @ $false ) )
| ( $false
!= ( f1 @ $false ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f373,plain,
( ( $true
!= ( f1 @ $true ) )
| ( $false
!= ( f1 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f372,plain,
( spl15_48
| spl15_30
| spl15_47 ),
inference(avatar_split_clause,[status(thm)],[f25,f349,f250,f354]) ).
thf(f354,definition,
( spl15_48
<=> ( $true = sF13 ) ),
introduced(definition,[new_symbols(naming,[spl15_48])],[avatar_definition]) ).
thf(f250,definition,
( spl15_30
<=> ( $true
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_30])],[avatar_definition]) ).
thf(f349,definition,
( spl15_47
<=> ( sF14 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_47])],[avatar_definition]) ).
thf(f25,plain,
( ( $true = sF13 )
| ( $true
= ( f0 @ $false ) )
| ( sF14 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( sF14
= ( f0 @ $false ) )
| ( $true = sF13 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f20,definition,
( ( f0 @ sF13 )
= sF14 ),
introduced(definition,[],[function_definition]) ).
thf(f371,plain,
( spl15_46
| spl15_29
| spl15_48 ),
inference(avatar_split_clause,[status(thm)],[f24,f354,f245,f344]) ).
thf(f344,definition,
( spl15_46
<=> ( $true = sF14 ) ),
introduced(definition,[new_symbols(naming,[spl15_46])],[avatar_definition]) ).
thf(f245,definition,
( spl15_29
<=> ( $false
= ( f0 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_29])],[avatar_definition]) ).
thf(f24,plain,
( ( $false
= ( f0 @ $false ) )
| ( $true = sF13 )
| ( $true = sF14 ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f370,plain,
( spl15_49
| spl15_26
| spl15_46 ),
inference(avatar_split_clause,[status(thm)],[f27,f344,f232,f359]) ).
thf(f359,definition,
( spl15_49
<=> ( $false = sF13 ) ),
introduced(definition,[new_symbols(naming,[spl15_49])],[avatar_definition]) ).
thf(f232,definition,
( spl15_26
<=> ( ( f0 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl15_26])],[avatar_definition]) ).
thf(f27,plain,
( ( $true = sF14 )
| ( $false = sF13 )
| ( ( f0 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false = sF13 )
| ( ( f0 @ $true )
= sF14 ) ),
inference(cases_simplifying,[status(thm)],[f20]) ).
thf(f369,plain,
( spl15_24
| spl15_47
| spl15_49 ),
inference(avatar_split_clause,[status(thm)],[f26,f359,f349,f223]) ).
thf(f223,definition,
( spl15_24
<=> ( $true
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_24])],[avatar_definition]) ).
thf(f26,plain,
( ( sF14 = $false )
| ( $false = sF13 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f368,plain,
( spl15_39
| spl15_10
| spl15_44 ),
inference(avatar_split_clause,[status(thm)],[f31,f328,f157,f297]) ).
thf(f297,definition,
( spl15_39
<=> ( ( f2 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl15_39])],[avatar_definition]) ).
thf(f157,definition,
( spl15_10
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl15_10])],[avatar_definition]) ).
thf(f328,definition,
( spl15_44
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(naming,[spl15_44])],[avatar_definition]) ).
thf(f31,plain,
( ( ( f2 @ $false )
= $false )
| ( $true = sF10 )
| ( $true = sF9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( f2 @ $false )
= sF10 )
| ( $true = sF9 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f16,definition,
( sF10
= ( f2 @ sF9 ) ),
introduced(definition,[],[function_definition]) ).
thf(f367,plain,
( spl15_9
| spl15_44
| spl15_40 ),
inference(avatar_split_clause,[status(thm)],[f30,f302,f328,f151]) ).
thf(f151,definition,
( spl15_9
<=> ( sF10 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_9])],[avatar_definition]) ).
thf(f302,definition,
( spl15_40
<=> ( $true
= ( f2 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_40])],[avatar_definition]) ).
thf(f30,plain,
( ( sF10 = $false )
| ( $true = sF9 )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f366,plain,
( spl15_37
| spl15_9
| spl15_45 ),
inference(avatar_split_clause,[status(thm)],[f33,f333,f151,f288]) ).
thf(f288,definition,
( spl15_37
<=> ( $true
= ( f2 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_37])],[avatar_definition]) ).
thf(f333,definition,
( spl15_45
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_45])],[avatar_definition]) ).
thf(f33,plain,
( ( sF9 = $false )
| ( sF10 = $false )
| ( $true
= ( f2 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( sF9 = $false )
| ( sF10
= ( f2 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f365,plain,
( spl15_10
| spl15_35
| spl15_45 ),
inference(avatar_split_clause,[status(thm)],[f32,f333,f279,f157]) ).
thf(f279,definition,
( spl15_35
<=> ( $false
= ( f2 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_35])],[avatar_definition]) ).
thf(f32,plain,
( ( sF9 = $false )
| ( $false
= ( f2 @ $true ) )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f364,plain,
( spl15_3
| spl15_6
| spl15_48 ),
inference(avatar_split_clause,[status(thm)],[f37,f354,f137,f123]) ).
thf(f123,definition,
( spl15_3
<=> ( $true = sF12 ) ),
introduced(definition,[new_symbols(naming,[spl15_3])],[avatar_definition]) ).
thf(f137,definition,
( spl15_6
<=> ( $false
= ( f1 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_6])],[avatar_definition]) ).
thf(f37,plain,
( ( $false
= ( f1 @ $false ) )
| ( $true = sF12 )
| ( $true = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( f1 @ $false )
= sF13 )
| ( $true = sF12 ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f19,definition,
( ( f1 @ sF12 )
= sF13 ),
introduced(definition,[],[function_definition]) ).
thf(f363,plain,
( spl15_49
| spl15_3
| spl15_8 ),
inference(avatar_split_clause,[status(thm)],[f36,f146,f123,f359]) ).
thf(f146,definition,
( spl15_8
<=> ( $true
= ( f1 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_8])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
= ( f1 @ $false ) )
| ( $false = sF13 )
| ( $true = sF12 ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f362,plain,
( spl15_4
| spl15_49
| spl15_5 ),
inference(avatar_split_clause,[status(thm)],[f39,f132,f359,f128]) ).
thf(f128,definition,
( spl15_4
<=> ( sF12 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_4])],[avatar_definition]) ).
thf(f132,definition,
( spl15_5
<=> ( $true
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_5])],[avatar_definition]) ).
thf(f39,plain,
( ( sF12 = $false )
| ( $false = sF13 )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( sF12 = $false )
| ( sF13
= ( f1 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f19]) ).
thf(f357,plain,
( spl15_48
| spl15_2
| spl15_4 ),
inference(avatar_split_clause,[status(thm)],[f38,f128,f119,f354]) ).
thf(f119,definition,
( spl15_2
<=> ( $false
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( f1 @ $true ) )
| ( sF12 = $false )
| ( $true = sF13 ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f352,plain,
( spl15_47
| spl15_31 ),
inference(avatar_split_clause,[status(thm)],[f41,f255,f349]) ).
thf(f255,definition,
( spl15_31
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl15_31])],[avatar_definition]) ).
thf(f41,plain,
( ( $false = sF7 )
| ( sF14 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
sF14 != sF7,
inference(definition_folding,[status(thm)],[f5,f20,f19,f18,f17,f16,f15,f14,f6,f13,f12,f11,f10,f9,f8,f7,f6]) ).
thf(f7,definition,
( sF1
= ( f2 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f8,definition,
( sF2
= ( f2 @ sF1 ) ),
introduced(definition,[],[function_definition]) ).
thf(f9,definition,
( sF3
= ( f2 @ sF2 ) ),
introduced(definition,[],[function_definition]) ).
thf(f10,definition,
( ( f1 @ sF3 )
= sF4 ),
introduced(definition,[],[function_definition]) ).
thf(f11,definition,
( ( f0 @ sF4 )
= sF5 ),
introduced(definition,[],[function_definition]) ).
thf(f12,definition,
( sF6
= ( f0 @ sF5 ) ),
introduced(definition,[],[function_definition]) ).
thf(f13,definition,
( ( f0 @ sF6 )
= sF7 ),
introduced(definition,[],[function_definition]) ).
thf(f6,definition,
( ( f3 @ x )
= sF0 ),
introduced(definition,[],[function_definition]) ).
thf(f14,definition,
( ( f3 @ sF0 )
= sF8 ),
introduced(definition,[],[function_definition]) ).
thf(f15,definition,
( sF9
= ( f3 @ sF8 ) ),
introduced(definition,[],[function_definition]) ).
thf(f17,definition,
( ( f1 @ sF10 )
= sF11 ),
introduced(definition,[],[function_definition]) ).
thf(f18,definition,
( sF12
= ( f1 @ sF11 ) ),
introduced(definition,[],[function_definition]) ).
thf(f5,plain,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
!= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2t3FYJtR9W/DTF2THF_29759.p',kaminski4) ).
thf(f347,plain,
( spl15_32
| spl15_46 ),
inference(avatar_split_clause,[status(thm)],[f40,f344,f260]) ).
thf(f260,definition,
( spl15_32
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(naming,[spl15_32])],[avatar_definition]) ).
thf(f40,plain,
( ( $true = sF7 )
| ( $true = sF14 ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f342,plain,
( spl15_42
| spl15_40
| spl15_36 ),
inference(avatar_split_clause,[status(thm)],[f45,f283,f302,f316]) ).
thf(f316,definition,
( spl15_42
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(naming,[spl15_42])],[avatar_definition]) ).
thf(f283,definition,
( spl15_36
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_36])],[avatar_definition]) ).
thf(f45,plain,
( ( sF2 = $false )
| ( $true
= ( f2 @ $false ) )
| ( $true = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( sF2
= ( f2 @ $false ) )
| ( $true = sF1 ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f341,plain,
( spl15_42
| spl15_38
| spl15_39 ),
inference(avatar_split_clause,[status(thm)],[f44,f297,f293,f316]) ).
thf(f293,definition,
( spl15_38
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_38])],[avatar_definition]) ).
thf(f44,plain,
( ( ( f2 @ $false )
= $false )
| ( $true = sF1 )
| ( sF2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f340,plain,
( spl15_36
| spl15_43
| spl15_37 ),
inference(avatar_split_clause,[status(thm)],[f47,f288,f321,f283]) ).
thf(f321,definition,
( spl15_43
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_43])],[avatar_definition]) ).
thf(f47,plain,
( ( sF1 = $false )
| ( $true
= ( f2 @ $true ) )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( sF1 = $false )
| ( sF2
= ( f2 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f339,plain,
( spl15_38
| spl15_35
| spl15_43 ),
inference(avatar_split_clause,[status(thm)],[f46,f321,f279,f293]) ).
thf(f46,plain,
( ( sF1 = $false )
| ( $false
= ( f2 @ $true ) )
| ( sF2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f338,plain,
( spl15_45
| spl15_22
| spl15_33 ),
inference(avatar_split_clause,[status(thm)],[f51,f267,f214,f333]) ).
thf(f214,definition,
( spl15_22
<=> ( $true
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_22])],[avatar_definition]) ).
thf(f267,definition,
( spl15_33
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl15_33])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
= ( f3 @ $false ) )
| ( sF9 = $false )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( sF9
= ( f3 @ $false ) )
| ( $true = sF8 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f337,plain,
( spl15_33
| spl15_20
| spl15_44 ),
inference(avatar_split_clause,[status(thm)],[f50,f328,f205,f267]) ).
thf(f205,definition,
( spl15_20
<=> ( $false
= ( f3 @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl15_20])],[avatar_definition]) ).
thf(f50,plain,
( ( $false
= ( f3 @ $false ) )
| ( $true = sF9 )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f336,plain,
( spl15_19
| spl15_34
| spl15_45 ),
inference(avatar_split_clause,[status(thm)],[f53,f333,f272,f200]) ).
thf(f200,definition,
( spl15_19
<=> ( $true
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_19])],[avatar_definition]) ).
thf(f272,definition,
( spl15_34
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl15_34])],[avatar_definition]) ).
thf(f53,plain,
( ( $false = sF8 )
| ( sF9 = $false )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( sF9
= ( f3 @ $true ) )
| ( $false = sF8 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f331,plain,
( spl15_44
| spl15_15
| spl15_34 ),
inference(avatar_split_clause,[status(thm)],[f52,f272,f183,f328]) ).
thf(f183,definition,
( spl15_15
<=> ( $false
= ( f3 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl15_15])],[avatar_definition]) ).
thf(f52,plain,
( ( $false
= ( f3 @ $true ) )
| ( $true = sF9 )
| ( $false = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f326,plain,
( spl15_39
| spl15_42
| spl15_16 ),
inference(avatar_split_clause,[status(thm)],[f57,f187,f316,f297]) ).
thf(f187,definition,
( spl15_16
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_16])],[avatar_definition]) ).
thf(f57,plain,
( ( sF0 = $true )
| ( ( f2 @ $false )
= $false )
| ( $true = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( sF0 = $true )
| ( ( f2 @ $false )
= sF1 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f325,plain,
( spl15_16
| spl15_43
| spl15_40 ),
inference(avatar_split_clause,[status(thm)],[f56,f302,f321,f187]) ).
thf(f56,plain,
( ( sF0 = $true )
| ( $true
= ( f2 @ $false ) )
| ( sF1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f324,plain,
( spl15_37
| spl15_18
| spl15_43 ),
inference(avatar_split_clause,[status(thm)],[f59,f321,f196,f288]) ).
thf(f196,definition,
( spl15_18
<=> ( sF0 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_18])],[avatar_definition]) ).
thf(f59,plain,
( ( sF0 = $false )
| ( $true
= ( f2 @ $true ) )
| ( sF1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( sF1
= ( f2 @ $true ) )
| ( sF0 = $false ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f319,plain,
( spl15_35
| spl15_18
| spl15_42 ),
inference(avatar_split_clause,[status(thm)],[f58,f316,f196,f279]) ).
thf(f58,plain,
( ( $false
= ( f2 @ $true ) )
| ( sF0 = $false )
| ( $true = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f314,plain,
~ spl15_41,
inference(avatar_split_clause,[status(thm)],[f3,f311]) ).
thf(f311,definition,
( spl15_41
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_41])],[avatar_definition]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f309,plain,
( spl15_11
| spl15_29
| spl15_28 ),
inference(avatar_split_clause,[status(thm)],[f63,f241,f245,f163]) ).
thf(f163,definition,
( spl15_11
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl15_11])],[avatar_definition]) ).
thf(f241,definition,
( spl15_28
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl15_28])],[avatar_definition]) ).
thf(f63,plain,
( ( $true = sF4 )
| ( $false
= ( f0 @ $false ) )
| ( $true = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true = sF4 )
| ( ( f0 @ $false )
= sF5 ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f308,plain,
( spl15_30
| spl15_11
| spl15_25 ),
inference(avatar_split_clause,[status(thm)],[f62,f227,f163,f250]) ).
thf(f227,definition,
( spl15_25
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl15_25])],[avatar_definition]) ).
thf(f62,plain,
( ( $false = sF5 )
| ( $true = sF4 )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f307,plain,
( spl15_26
| spl15_13
| spl15_28 ),
inference(avatar_split_clause,[status(thm)],[f65,f241,f172,f232]) ).
thf(f172,definition,
( spl15_13
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl15_13])],[avatar_definition]) ).
thf(f65,plain,
( ( ( f0 @ $true )
= $false )
| ( $false = sF4 )
| ( $true = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( f0 @ $true )
= sF5 )
| ( $false = sF4 ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f306,plain,
( spl15_13
| spl15_25
| spl15_24 ),
inference(avatar_split_clause,[status(thm)],[f64,f223,f227,f172]) ).
thf(f64,plain,
( ( $true
= ( f0 @ $true ) )
| ( $false = sF5 )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f305,plain,
( spl15_38
| spl15_12
| spl15_40 ),
inference(avatar_split_clause,[status(thm)],[f69,f302,f167,f293]) ).
thf(f167,definition,
( spl15_12
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_12])],[avatar_definition]) ).
thf(f69,plain,
( ( sF3 = $false )
| ( sF2 = $true )
| ( $true
= ( f2 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( sF2 = $true )
| ( sF3
= ( f2 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f300,plain,
( spl15_14
| spl15_38
| spl15_39 ),
inference(avatar_split_clause,[status(thm)],[f68,f297,f293,f177]) ).
thf(f177,definition,
( spl15_14
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_14])],[avatar_definition]) ).
thf(f68,plain,
( ( ( f2 @ $false )
= $false )
| ( sF2 = $true )
| ( sF3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f291,plain,
( spl15_12
| spl15_37
| spl15_36 ),
inference(avatar_split_clause,[status(thm)],[f71,f283,f288,f167]) ).
thf(f71,plain,
( ( sF3 = $false )
| ( sF2 = $false )
| ( $true
= ( f2 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( sF3
= ( f2 @ $true ) )
| ( sF2 = $false ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f286,plain,
( spl15_35
| spl15_36
| spl15_14 ),
inference(avatar_split_clause,[status(thm)],[f70,f177,f283,f279]) ).
thf(f70,plain,
( ( $false
= ( f2 @ $true ) )
| ( sF3 = $true )
| ( sF2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f277,plain,
( spl15_16
| spl15_22
| spl15_34 ),
inference(avatar_split_clause,[status(thm)],[f75,f272,f214,f187]) ).
thf(f75,plain,
( ( $false = sF8 )
| ( sF0 = $true )
| ( $true
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( sF0 = $true )
| ( sF8
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f276,plain,
( spl15_16
| spl15_20
| spl15_33 ),
inference(avatar_split_clause,[status(thm)],[f74,f267,f205,f187]) ).
thf(f74,plain,
( ( sF0 = $true )
| ( $false
= ( f3 @ $false ) )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f275,plain,
( spl15_18
| spl15_19
| spl15_34 ),
inference(avatar_split_clause,[status(thm)],[f77,f272,f200,f196]) ).
thf(f77,plain,
( ( $false = sF8 )
| ( sF0 = $false )
| ( $true
= ( f3 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( sF8
= ( f3 @ $true ) )
| ( sF0 = $false ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f270,plain,
( spl15_15
| spl15_33
| spl15_18 ),
inference(avatar_split_clause,[status(thm)],[f76,f196,f267,f183]) ).
thf(f76,plain,
( ( $false
= ( f3 @ $true ) )
| ( sF0 = $false )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f265,plain,
( spl15_29
| spl15_32
| spl15_27 ),
inference(avatar_split_clause,[status(thm)],[f81,f236,f260,f245]) ).
thf(f236,definition,
( spl15_27
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl15_27])],[avatar_definition]) ).
thf(f81,plain,
( ( $false
= ( f0 @ $false ) )
| ( $true = sF7 )
| ( $true = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( f0 @ $false )
= sF7 )
| ( $true = sF6 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f264,plain,
( spl15_30
| spl15_31
| spl15_27 ),
inference(avatar_split_clause,[status(thm)],[f80,f236,f255,f250]) ).
thf(f80,plain,
( ( $false = sF7 )
| ( $true = sF6 )
| ( $true
= ( f0 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f263,plain,
( spl15_32
| spl15_23
| spl15_26 ),
inference(avatar_split_clause,[status(thm)],[f83,f232,f219,f260]) ).
thf(f219,definition,
( spl15_23
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_23])],[avatar_definition]) ).
thf(f83,plain,
( ( sF6 = $false )
| ( $true = sF7 )
| ( ( f0 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( f0 @ $true )
= sF7 )
| ( sF6 = $false ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f258,plain,
( spl15_24
| spl15_31
| spl15_23 ),
inference(avatar_split_clause,[status(thm)],[f82,f219,f255,f223]) ).
thf(f82,plain,
( ( sF6 = $false )
| ( $false = sF7 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f253,plain,
( spl15_30
| spl15_28
| spl15_23 ),
inference(avatar_split_clause,[status(thm)],[f87,f219,f241,f250]) ).
thf(f87,plain,
( ( $true
= ( f0 @ $false ) )
| ( $true = sF5 )
| ( sF6 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( sF6
= ( f0 @ $false ) )
| ( $true = sF5 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f248,plain,
( spl15_28
| spl15_29
| spl15_27 ),
inference(avatar_split_clause,[status(thm)],[f86,f236,f245,f241]) ).
thf(f86,plain,
( ( $false
= ( f0 @ $false ) )
| ( $true = sF5 )
| ( $true = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f239,plain,
( spl15_25
| spl15_26
| spl15_27 ),
inference(avatar_split_clause,[status(thm)],[f89,f236,f232,f227]) ).
thf(f89,plain,
( ( ( f0 @ $true )
= $false )
| ( $true = sF6 )
| ( $false = sF5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $false = sF5 )
| ( ( f0 @ $true )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f230,plain,
( spl15_23
| spl15_24
| spl15_25 ),
inference(avatar_split_clause,[status(thm)],[f88,f227,f223,f219]) ).
thf(f88,plain,
( ( $false = sF5 )
| ( $true
= ( f0 @ $true ) )
| ( sF6 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f217,plain,
( spl15_22
| spl15_18
| spl15_21 ),
inference(avatar_split_clause,[status(thm)],[f93,f209,f196,f214]) ).
thf(f209,definition,
( spl15_21
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_21])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
= ( f3 @ $false ) )
| ( x = $true )
| ( sF0 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( x = $true )
| ( sF0
= ( f3 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f212,plain,
( spl15_16
| spl15_20
| spl15_21 ),
inference(avatar_split_clause,[status(thm)],[f92,f209,f205,f187]) ).
thf(f92,plain,
( ( x = $true )
| ( sF0 = $true )
| ( $false
= ( f3 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f203,plain,
( spl15_18
| spl15_17
| spl15_19 ),
inference(avatar_split_clause,[status(thm)],[f95,f200,f191,f196]) ).
thf(f191,definition,
( spl15_17
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl15_17])],[avatar_definition]) ).
thf(f95,plain,
( ( $true
= ( f3 @ $true ) )
| ( x = $false )
| ( sF0 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( sF0
= ( f3 @ $true ) )
| ( x = $false ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f194,plain,
( spl15_15
| spl15_16
| spl15_17 ),
inference(avatar_split_clause,[status(thm)],[f94,f191,f187,f183]) ).
thf(f94,plain,
( ( $false
= ( f3 @ $true ) )
| ( sF0 = $true )
| ( x = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f181,plain,
( spl15_6
| spl15_11
| spl15_14 ),
inference(avatar_split_clause,[status(thm)],[f99,f177,f163,f137]) ).
thf(f99,plain,
( ( $false
= ( f1 @ $false ) )
| ( $true = sF4 )
| ( sF3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( f1 @ $false )
= sF4 )
| ( sF3 = $true ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f180,plain,
( spl15_14
| spl15_8
| spl15_13 ),
inference(avatar_split_clause,[status(thm)],[f98,f172,f146,f177]) ).
thf(f98,plain,
( ( sF3 = $true )
| ( $true
= ( f1 @ $false ) )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f175,plain,
( spl15_5
| spl15_12
| spl15_13 ),
inference(avatar_split_clause,[status(thm)],[f101,f172,f167,f132]) ).
thf(f101,plain,
( ( sF3 = $false )
| ( $false = sF4 )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( sF4
= ( f1 @ $true ) )
| ( sF3 = $false ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f170,plain,
( spl15_2
| spl15_11
| spl15_12 ),
inference(avatar_split_clause,[status(thm)],[f100,f167,f163,f119]) ).
thf(f100,plain,
( ( sF3 = $false )
| ( $true = sF4 )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f161,plain,
( spl15_7
| spl15_6
| spl15_10 ),
inference(avatar_split_clause,[status(thm)],[f105,f157,f137,f141]) ).
thf(f141,definition,
( spl15_7
<=> ( $true = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl15_7])],[avatar_definition]) ).
thf(f105,plain,
( ( $false
= ( f1 @ $false ) )
| ( $true = sF10 )
| ( $true = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( f1 @ $false )
= sF11 )
| ( $true = sF10 ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f160,plain,
( spl15_10
| spl15_1
| spl15_8 ),
inference(avatar_split_clause,[status(thm)],[f104,f146,f115,f157]) ).
thf(f115,definition,
( spl15_1
<=> ( $false = sF11 ) ),
introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition]) ).
thf(f104,plain,
( ( $true = sF10 )
| ( $false = sF11 )
| ( $true
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f155,plain,
( spl15_1
| spl15_9
| spl15_5 ),
inference(avatar_split_clause,[status(thm)],[f107,f132,f151,f115]) ).
thf(f107,plain,
( ( sF10 = $false )
| ( $false = sF11 )
| ( $true
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( sF11
= ( f1 @ $true ) )
| ( sF10 = $false ) ),
inference(cases_simplifying,[status(thm)],[f17]) ).
thf(f154,plain,
( spl15_9
| spl15_2
| spl15_7 ),
inference(avatar_split_clause,[status(thm)],[f106,f141,f119,f151]) ).
thf(f106,plain,
( ( $false
= ( f1 @ $true ) )
| ( $true = sF11 )
| ( sF10 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f149,plain,
( spl15_4
| spl15_8
| spl15_7 ),
inference(avatar_split_clause,[status(thm)],[f111,f141,f146,f128]) ).
thf(f111,plain,
( ( $true = sF11 )
| ( sF12 = $false )
| ( $true
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( sF12
= ( f1 @ $false ) )
| ( $true = sF11 ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f144,plain,
( spl15_6
| spl15_7
| spl15_3 ),
inference(avatar_split_clause,[status(thm)],[f110,f123,f141,f137]) ).
thf(f110,plain,
( ( $true = sF12 )
| ( $true = sF11 )
| ( $false
= ( f1 @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f135,plain,
( spl15_4
| spl15_5
| spl15_1 ),
inference(avatar_split_clause,[status(thm)],[f113,f115,f132,f128]) ).
thf(f113,plain,
( ( sF12 = $false )
| ( $true
= ( f1 @ $true ) )
| ( $false = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $false = sF11 )
| ( sF12
= ( f1 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f18]) ).
thf(f126,plain,
( spl15_1
| spl15_2
| spl15_3 ),
inference(avatar_split_clause,[status(thm)],[f112,f123,f119,f115]) ).
thf(f112,plain,
( ( $false
= ( f1 @ $true ) )
| ( $true = sF12 )
| ( $false = sF11 ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO500^1.004 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:33:19 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO500^1.004 : TPTP v9.2.1. Released v4.1.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : Four function variant of the Kaminski equation
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : basic12 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 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
% 0.18/0.45 % Syntax : Number of formulae : 6 ( 1 unt; 5 typ; 0 def)
% 0.18/0.45 % Number of atoms : 19 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 19 avg)
% 0.18/0.45 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 16 @)
% 0.18/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.18/0.45 % Number of types : 1 ( 0 usr)
% 0.18/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 6 ( 5 usr; 1 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(x,type,
% 0.18/0.45 x: $o ).
% 0.18/0.45
% 0.18/0.45 thf(f0,type,
% 0.18/0.45 f0: $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(f1,type,
% 0.18/0.45 f1: $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(f2,type,
% 0.18/0.45 f2: $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(f3,type,
% 0.18/0.45 f3: $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(kaminski4,conjecture,
% 0.18/0.45 ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
% 0.18/0.45 = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 14:33:20 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2t3FYJtR9W/DTF2DTF29759.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.30 thf(x,type,
% 1.46/1.30 x: $o ).
% 1.46/1.30
% 1.46/1.30 thf(f0,type,
% 1.46/1.30 f0: $o > $o ).
% 1.46/1.30
% 1.46/1.30 thf(f1,type,
% 1.46/1.30 f1: $o > $o ).
% 1.46/1.30
% 1.46/1.30 thf(f2,type,
% 1.46/1.30 f2: $o > $o ).
% 1.46/1.30
% 1.46/1.30 thf(f3,type,
% 1.46/1.30 f3: $o > $o ).
% 1.46/1.30
% 1.46/1.30 thf(kaminski4,conjecture,
% 1.46/1.30 ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
% 1.46/1.30 = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ) ).
% 1.46/1.30 ------------------------
% 1.64/1.32 % (29979)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29759 for (3000ds/2Mi)
% 1.64/1.32 % (29977)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_29759 for (3000ds/4Mi)
% 1.64/1.32 % (29976)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29759 for (3000ds/183Mi)
% 1.64/1.32 % (29980)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_29759 for (3000ds/2Mi)
% 1.64/1.32 % (29978)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_29759 for (3000ds/27Mi)
% 1.64/1.32 % (29981)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_29759 for (3000ds/275Mi)
% 1.64/1.32 % (29982)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29759 for (3000ds/18Mi)
% 1.64/1.32 % (29981)Refutation not found, incomplete strategy
% 1.64/1.32 % (29981)------------------------------
% 1.64/1.32 % (29981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29981)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.32
% 1.64/1.32
% 1.64/1.32 % (29981)Memory used [KB]: 5500
% 1.64/1.32 % (29981)Time elapsed: 0.003 s
% 1.64/1.32 % (29981)Instructions burned: 1 (million)
% 1.64/1.32 % (29981)------------------------------
% 1.64/1.32 % (29981)------------------------------
% 1.64/1.32 % (29979)Instruction limit reached!
% 1.64/1.32 % (29979)------------------------------
% 1.64/1.32 % (29979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29979)Termination reason: Unknown
% 1.64/1.32 % (29979)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (29979)Memory used [KB]: 5500
% 1.64/1.32 % (29979)Time elapsed: 0.004 s
% 1.64/1.32 % (29979)Instructions burned: 2 (million)
% 1.64/1.32 % (29979)------------------------------
% 1.64/1.32 % (29979)------------------------------
% 1.64/1.32 % (29980)Refutation not found, incomplete strategy
% 1.64/1.32 % (29980)------------------------------
% 1.64/1.32 % (29980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29980)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.32
% 1.64/1.32
% 1.64/1.32 % (29980)Memory used [KB]: 5500
% 1.64/1.32 % (29980)Time elapsed: 0.004 s
% 1.64/1.32 % (29980)Instructions burned: 1 (million)
% 1.64/1.32 % (29980)------------------------------
% 1.64/1.32 % (29980)------------------------------
% 1.64/1.32 % (29978)Refutation not found, incomplete strategy
% 1.64/1.32 % (29978)------------------------------
% 1.64/1.32 % (29978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29978)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.32
% 1.64/1.32
% 1.64/1.32 % (29978)Memory used [KB]: 5500
% 1.64/1.32 % (29978)Time elapsed: 0.004 s
% 1.64/1.32 % (29978)Instructions burned: 2 (million)
% 1.64/1.32 % (29978)------------------------------
% 1.64/1.32 % (29978)------------------------------
% 1.64/1.32 % (29977)Instruction limit reached!
% 1.64/1.32 % (29977)------------------------------
% 1.64/1.32 % (29977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29977)Termination reason: Unknown
% 1.64/1.32 % (29977)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (29977)Memory used [KB]: 5500
% 1.64/1.32 % (29977)Time elapsed: 0.005 s
% 1.64/1.32 % (29977)Instructions burned: 4 (million)
% 1.64/1.32 % (29977)------------------------------
% 1.64/1.32 % (29977)------------------------------
% 1.64/1.33 % (29982)Instruction limit reached!
% 1.64/1.33 % (29982)------------------------------
% 1.64/1.33 % (29982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29982)Termination reason: Unknown
% 1.64/1.33 % (29982)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (29982)Memory used [KB]: 5628
% 1.64/1.33 % (29982)Time elapsed: 0.014 s
% 1.64/1.33 % (29982)Instructions burned: 19 (million)
% 1.64/1.33 % (29982)------------------------------
% 1.64/1.33 % (29982)------------------------------
% 1.64/1.33 % (29985)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_29759 for (2999ds/15Mi)
% 1.64/1.33 % (29985)Instruction limit reached!
% 1.64/1.33 % (29985)------------------------------
% 1.64/1.33 % (29985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29985)Termination reason: Unknown
% 1.64/1.33 % (29985)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (29985)Memory used [KB]: 5756
% 1.64/1.33 % (29985)Time elapsed: 0.008 s
% 1.64/1.33 % (29985)Instructions burned: 17 (million)
% 1.64/1.33 % (29985)------------------------------
% 1.64/1.33 % (29985)------------------------------
% 1.64/1.34 % (29983)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29759 for (2999ds/3Mi)
% 1.64/1.34 % (29984)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_29759 for (2999ds/37Mi)
% 1.64/1.34 % (29986)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_29759 for (2999ds/3Mi)
% 1.64/1.34 % (29987)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_29759 for (2999ds/1041Mi)
% 1.64/1.34 % (29983)Refutation not found, incomplete strategy
% 1.64/1.34 % (29983)------------------------------
% 1.64/1.34 % (29983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29983)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.34
% 1.64/1.34
% 1.64/1.34 % (29983)Memory used [KB]: 5500
% 1.64/1.34 % (29983)Time elapsed: 0.003 s
% 1.64/1.34 % (29983)Instructions burned: 2 (million)
% 1.64/1.34 % (29983)------------------------------
% 1.64/1.34 % (29983)------------------------------
% 1.64/1.34 % (29986)Refutation not found, incomplete strategy
% 1.64/1.34 % (29986)------------------------------
% 1.64/1.34 % (29986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29986)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.34
% 1.64/1.34
% 1.64/1.34 % (29986)Memory used [KB]: 5500
% 1.64/1.34 % (29986)Time elapsed: 0.003 s
% 1.64/1.34 % (29986)Instructions burned: 2 (million)
% 1.64/1.34 % (29986)------------------------------
% 1.64/1.34 % (29986)------------------------------
% 1.64/1.34 % (29987)Refutation not found, incomplete strategy
% 1.64/1.34 % (29987)------------------------------
% 1.64/1.34 % (29987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29987)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.34
% 1.64/1.34
% 1.64/1.34 % (29987)Memory used [KB]: 5500
% 1.64/1.34 % (29987)Time elapsed: 0.006 s
% 1.64/1.34 % (29987)Instructions burned: 6 (million)
% 1.64/1.34 % (29987)------------------------------
% 1.64/1.34 % (29987)------------------------------
% 1.64/1.34 % (29989)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29759 for (2999ds/16Mi)
% 1.64/1.35 % (29988)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29759 for (2999ds/7Mi)
% 1.64/1.35 % (29989)First to succeed.
% 1.64/1.35 % (29988)Instruction limit reached!
% 1.64/1.35 % (29988)------------------------------
% 1.64/1.35 % (29988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (29988)Termination reason: Unknown
% 1.64/1.35 % (29988)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (29988)Memory used [KB]: 1023
% 1.64/1.35 % (29988)Time elapsed: 0.006 s
% 1.64/1.35 % (29988)Instructions burned: 7 (million)
% 1.64/1.35 % (29988)------------------------------
% 1.64/1.35 % (29988)------------------------------
% 1.64/1.35 % (29989)Refutation found. Thanks to Tanya!
% 1.64/1.35 % SZS status Theorem for DTF2THF_29759
% 1.64/1.35 % SZS output start Proof for DTF2THF_29759
% 1.64/1.35 thf(func_def_1, type, f0: $o > $o).
% 1.64/1.35 thf(func_def_2, type, f1: $o > $o).
% 1.64/1.35 thf(func_def_3, type, f2: $o > $o).
% 1.64/1.35 thf(func_def_4, type, f3: $o > $o).
% 1.64/1.35 thf(f397,plain,(
% 1.64/1.35 $false),
% 1.64/1.35 inference(avatar_sat_refutation,[status(thm)],[f126,f135,f144,f149,f154,f155,f160,f161,f170,f175,f180,f181,f194,f203,f212,f217,f230,f239,f248,f253,f258,f263,f264,f265,f270,f275,f276,f277,f286,f291,f300,f305,f306,f307,f308,f309,f314,f319,f324,f325,f326,f331,f336,f337,f338,f339,f340,f341,f342,f347,f352,f357,f362,f363,f364,f365,f366,f367,f368,f369,f370,f371,f372,f373,f374,f375,f376,f377,f378,f379,f380,f381,f382,f383,f384,f385,f386,f387,f388,f389,f390,f391,f392,f393,f394,f395,f396])).
% 1.64/1.35 thf(f396,plain,(
% 1.64/1.35 ($true != sF6) | (sF6 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f395,plain,(
% 1.64/1.35 ($true != sF12) | (sF12 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f394,plain,(
% 1.64/1.35 ($true != sF4) | ($false != sF4) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f393,plain,(
% 1.64/1.35 ($true != sF1) | (sF1 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f392,plain,(
% 1.64/1.35 ($true != (f2 @ $false)) | ((f2 @ $false) != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f391,plain,(
% 1.64/1.35 (x != $true) | (x != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f390,plain,(
% 1.64/1.35 ($true != sF8) | ($false != sF8) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f389,plain,(
% 1.64/1.35 (sF9 != $false) | ($true != sF9) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f388,plain,(
% 1.64/1.35 ($true != sF11) | ($false != sF11) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f387,plain,(
% 1.64/1.35 ($false != sF13) | ($true != sF13) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f386,plain,(
% 1.64/1.35 (sF14 != $false) | ($true != sF14) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f385,plain,(
% 1.64/1.35 (sF3 != $true) | (sF3 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f384,plain,(
% 1.64/1.35 ($true != (f2 @ $true)) | ($false != (f2 @ $true)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f383,plain,(
% 1.64/1.35 (sF2 != $true) | (sF2 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f382,plain,(
% 1.64/1.35 ($true != sF7) | ($false != sF7) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f381,plain,(
% 1.64/1.35 ($true != sF5) | ($false != sF5) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f380,plain,(
% 1.64/1.35 ($true != (f0 @ $false)) | ($false != (f0 @ $false)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f379,plain,(
% 1.64/1.35 ($true != (f0 @ $true)) | ((f0 @ $true) != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f378,plain,(
% 1.64/1.35 ($true != (f3 @ $false)) | ($false != (f3 @ $false)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f377,plain,(
% 1.64/1.35 ($true != (f3 @ $true)) | ($false != (f3 @ $true)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f376,plain,(
% 1.64/1.35 (sF0 != $true) | (sF0 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f375,plain,(
% 1.64/1.35 ($true != sF10) | (sF10 != $false) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f374,plain,(
% 1.64/1.35 ($true != (f1 @ $false)) | ($false != (f1 @ $false)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f373,plain,(
% 1.64/1.35 ($true != (f1 @ $true)) | ($false != (f1 @ $true)) | ($true = $false)),
% 1.64/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.64/1.35 thf(f372,plain,(
% 1.64/1.35 spl15_48 | spl15_30 | spl15_47),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f25,f349,f250,f354])).
% 1.64/1.35 thf(f354,definition,(
% 1.64/1.35 spl15_48 <=> ($true = sF13)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_48])],[avatar_definition])).
% 1.64/1.35 thf(f250,definition,(
% 1.64/1.35 spl15_30 <=> ($true = (f0 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_30])],[avatar_definition])).
% 1.64/1.35 thf(f349,definition,(
% 1.64/1.35 spl15_47 <=> (sF14 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_47])],[avatar_definition])).
% 1.64/1.35 thf(f25,plain,(
% 1.64/1.35 ($true = sF13) | ($true = (f0 @ $false)) | (sF14 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.64/1.35 thf(f23,plain,(
% 1.64/1.35 (sF14 = (f0 @ $false)) | ($true = sF13)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f20])).
% 1.64/1.35 thf(f20,definition,(
% 1.64/1.35 ((f0 @ sF13) = sF14)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f371,plain,(
% 1.64/1.35 spl15_46 | spl15_29 | spl15_48),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f24,f354,f245,f344])).
% 1.64/1.35 thf(f344,definition,(
% 1.64/1.35 spl15_46 <=> ($true = sF14)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_46])],[avatar_definition])).
% 1.64/1.35 thf(f245,definition,(
% 1.64/1.35 spl15_29 <=> ($false = (f0 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_29])],[avatar_definition])).
% 1.64/1.35 thf(f24,plain,(
% 1.64/1.35 ($false = (f0 @ $false)) | ($true = sF13) | ($true = sF14)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.64/1.35 thf(f370,plain,(
% 1.64/1.35 spl15_49 | spl15_26 | spl15_46),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f27,f344,f232,f359])).
% 1.64/1.35 thf(f359,definition,(
% 1.64/1.35 spl15_49 <=> ($false = sF13)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_49])],[avatar_definition])).
% 1.64/1.35 thf(f232,definition,(
% 1.64/1.35 spl15_26 <=> ((f0 @ $true) = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_26])],[avatar_definition])).
% 1.64/1.35 thf(f27,plain,(
% 1.64/1.35 ($true = sF14) | ($false = sF13) | ((f0 @ $true) = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.35 thf(f22,plain,(
% 1.64/1.35 ($false = sF13) | ((f0 @ $true) = sF14)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f20])).
% 1.64/1.35 thf(f369,plain,(
% 1.64/1.35 spl15_24 | spl15_47 | spl15_49),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f26,f359,f349,f223])).
% 1.64/1.35 thf(f223,definition,(
% 1.64/1.35 spl15_24 <=> ($true = (f0 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_24])],[avatar_definition])).
% 1.64/1.35 thf(f26,plain,(
% 1.64/1.35 (sF14 = $false) | ($false = sF13) | ($true = (f0 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.35 thf(f368,plain,(
% 1.64/1.35 spl15_39 | spl15_10 | spl15_44),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f31,f328,f157,f297])).
% 1.64/1.35 thf(f297,definition,(
% 1.64/1.35 spl15_39 <=> ((f2 @ $false) = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_39])],[avatar_definition])).
% 1.64/1.35 thf(f157,definition,(
% 1.64/1.35 spl15_10 <=> ($true = sF10)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_10])],[avatar_definition])).
% 1.64/1.35 thf(f328,definition,(
% 1.64/1.35 spl15_44 <=> ($true = sF9)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_44])],[avatar_definition])).
% 1.64/1.35 thf(f31,plain,(
% 1.64/1.35 ((f2 @ $false) = $false) | ($true = sF10) | ($true = sF9)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.64/1.35 thf(f29,plain,(
% 1.64/1.35 ((f2 @ $false) = sF10) | ($true = sF9)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f16])).
% 1.64/1.35 thf(f16,definition,(
% 1.64/1.35 (sF10 = (f2 @ sF9))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f367,plain,(
% 1.64/1.35 spl15_9 | spl15_44 | spl15_40),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f30,f302,f328,f151])).
% 1.64/1.35 thf(f151,definition,(
% 1.64/1.35 spl15_9 <=> (sF10 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_9])],[avatar_definition])).
% 1.64/1.35 thf(f302,definition,(
% 1.64/1.35 spl15_40 <=> ($true = (f2 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_40])],[avatar_definition])).
% 1.64/1.35 thf(f30,plain,(
% 1.64/1.35 (sF10 = $false) | ($true = sF9) | ($true = (f2 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.64/1.35 thf(f366,plain,(
% 1.64/1.35 spl15_37 | spl15_9 | spl15_45),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f33,f333,f151,f288])).
% 1.64/1.35 thf(f288,definition,(
% 1.64/1.35 spl15_37 <=> ($true = (f2 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_37])],[avatar_definition])).
% 1.64/1.35 thf(f333,definition,(
% 1.64/1.35 spl15_45 <=> (sF9 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_45])],[avatar_definition])).
% 1.64/1.35 thf(f33,plain,(
% 1.64/1.35 (sF9 = $false) | (sF10 = $false) | ($true = (f2 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.64/1.35 thf(f28,plain,(
% 1.64/1.35 (sF9 = $false) | (sF10 = (f2 @ $true))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f16])).
% 1.64/1.35 thf(f365,plain,(
% 1.64/1.35 spl15_10 | spl15_35 | spl15_45),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f32,f333,f279,f157])).
% 1.64/1.35 thf(f279,definition,(
% 1.64/1.35 spl15_35 <=> ($false = (f2 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_35])],[avatar_definition])).
% 1.64/1.35 thf(f32,plain,(
% 1.64/1.35 (sF9 = $false) | ($false = (f2 @ $true)) | ($true = sF10)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.64/1.35 thf(f364,plain,(
% 1.64/1.35 spl15_3 | spl15_6 | spl15_48),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f37,f354,f137,f123])).
% 1.64/1.35 thf(f123,definition,(
% 1.64/1.35 spl15_3 <=> ($true = sF12)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_3])],[avatar_definition])).
% 1.64/1.35 thf(f137,definition,(
% 1.64/1.35 spl15_6 <=> ($false = (f1 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_6])],[avatar_definition])).
% 1.64/1.35 thf(f37,plain,(
% 1.64/1.35 ($false = (f1 @ $false)) | ($true = sF12) | ($true = sF13)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.64/1.35 thf(f35,plain,(
% 1.64/1.35 ((f1 @ $false) = sF13) | ($true = sF12)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f19])).
% 1.64/1.35 thf(f19,definition,(
% 1.64/1.35 ((f1 @ sF12) = sF13)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f363,plain,(
% 1.64/1.35 spl15_49 | spl15_3 | spl15_8),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f36,f146,f123,f359])).
% 1.64/1.35 thf(f146,definition,(
% 1.64/1.35 spl15_8 <=> ($true = (f1 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_8])],[avatar_definition])).
% 1.64/1.35 thf(f36,plain,(
% 1.64/1.35 ($true = (f1 @ $false)) | ($false = sF13) | ($true = sF12)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.64/1.35 thf(f362,plain,(
% 1.64/1.35 spl15_4 | spl15_49 | spl15_5),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f39,f132,f359,f128])).
% 1.64/1.35 thf(f128,definition,(
% 1.64/1.35 spl15_4 <=> (sF12 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_4])],[avatar_definition])).
% 1.64/1.35 thf(f132,definition,(
% 1.64/1.35 spl15_5 <=> ($true = (f1 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_5])],[avatar_definition])).
% 1.64/1.35 thf(f39,plain,(
% 1.64/1.35 (sF12 = $false) | ($false = sF13) | ($true = (f1 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.64/1.35 thf(f34,plain,(
% 1.64/1.35 (sF12 = $false) | (sF13 = (f1 @ $true))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f19])).
% 1.64/1.35 thf(f357,plain,(
% 1.64/1.35 spl15_48 | spl15_2 | spl15_4),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f38,f128,f119,f354])).
% 1.64/1.35 thf(f119,definition,(
% 1.64/1.35 spl15_2 <=> ($false = (f1 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition])).
% 1.64/1.35 thf(f38,plain,(
% 1.64/1.35 ($false = (f1 @ $true)) | (sF12 = $false) | ($true = sF13)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.64/1.35 thf(f352,plain,(
% 1.64/1.35 spl15_47 | spl15_31),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f41,f255,f349])).
% 1.64/1.35 thf(f255,definition,(
% 1.64/1.35 spl15_31 <=> ($false = sF7)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_31])],[avatar_definition])).
% 1.64/1.35 thf(f41,plain,(
% 1.64/1.35 ($false = sF7) | (sF14 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.64/1.35 thf(f21,plain,(
% 1.64/1.35 (sF14 != sF7)),
% 1.64/1.35 inference(definition_folding,[status(thm)],[f5,f20,f19,f18,f17,f16,f15,f14,f6,f13,f12,f11,f10,f9,f8,f7,f6])).
% 1.64/1.35 thf(f7,definition,(
% 1.64/1.35 (sF1 = (f2 @ sF0))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f8,definition,(
% 1.64/1.35 (sF2 = (f2 @ sF1))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f9,definition,(
% 1.64/1.35 (sF3 = (f2 @ sF2))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f10,definition,(
% 1.64/1.35 ((f1 @ sF3) = sF4)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f11,definition,(
% 1.64/1.35 ((f0 @ sF4) = sF5)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f12,definition,(
% 1.64/1.35 (sF6 = (f0 @ sF5))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f13,definition,(
% 1.64/1.35 ((f0 @ sF6) = sF7)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f6,definition,(
% 1.64/1.35 ((f3 @ x) = sF0)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f14,definition,(
% 1.64/1.35 ((f3 @ sF0) = sF8)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f15,definition,(
% 1.64/1.35 (sF9 = (f3 @ sF8))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f17,definition,(
% 1.64/1.35 ((f1 @ sF10) = sF11)),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f18,definition,(
% 1.64/1.35 (sF12 = (f1 @ sF11))),
% 1.64/1.35 introduced(definition,[],[function_definition])).
% 1.64/1.35 thf(f5,plain,(
% 1.64/1.35 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ x)))))))) != (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ x)))))))))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f4])).
% 1.64/1.35 thf(f4,plain,(
% 1.64/1.35 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ x)))))))) != (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ x)))))))))),
% 1.64/1.35 inference(flattening,[status(thm)],[f2])).
% 1.64/1.35 thf(f2,negated_conjecture,(
% 1.64/1.35 ~((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ x)))))))) = (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ x)))))))))),
% 1.64/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.35 thf(f1,conjecture,(
% 1.64/1.35 ((f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ (f3 @ x)))))))) = (f0 @ (f1 @ (f1 @ (f1 @ (f2 @ (f3 @ (f3 @ (f3 @ x)))))))))),
% 1.64/1.35 file('/export/starexec/sandbox2/tmp/tmp.2t3FYJtR9W/DTF2THF_29759.p',kaminski4)).
% 1.64/1.35 thf(f347,plain,(
% 1.64/1.35 spl15_32 | spl15_46),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f40,f344,f260])).
% 1.64/1.35 thf(f260,definition,(
% 1.64/1.35 spl15_32 <=> ($true = sF7)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_32])],[avatar_definition])).
% 1.64/1.35 thf(f40,plain,(
% 1.64/1.35 ($true = sF7) | ($true = sF14)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.64/1.35 thf(f342,plain,(
% 1.64/1.35 spl15_42 | spl15_40 | spl15_36),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f45,f283,f302,f316])).
% 1.64/1.35 thf(f316,definition,(
% 1.64/1.35 spl15_42 <=> ($true = sF1)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_42])],[avatar_definition])).
% 1.64/1.35 thf(f283,definition,(
% 1.64/1.35 spl15_36 <=> (sF2 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_36])],[avatar_definition])).
% 1.64/1.35 thf(f45,plain,(
% 1.64/1.35 (sF2 = $false) | ($true = (f2 @ $false)) | ($true = sF1)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.64/1.35 thf(f43,plain,(
% 1.64/1.35 (sF2 = (f2 @ $false)) | ($true = sF1)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f8])).
% 1.64/1.35 thf(f341,plain,(
% 1.64/1.35 spl15_42 | spl15_38 | spl15_39),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f44,f297,f293,f316])).
% 1.64/1.35 thf(f293,definition,(
% 1.64/1.35 spl15_38 <=> (sF2 = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_38])],[avatar_definition])).
% 1.64/1.35 thf(f44,plain,(
% 1.64/1.35 ((f2 @ $false) = $false) | ($true = sF1) | (sF2 = $true)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.64/1.35 thf(f340,plain,(
% 1.64/1.35 spl15_36 | spl15_43 | spl15_37),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f47,f288,f321,f283])).
% 1.64/1.35 thf(f321,definition,(
% 1.64/1.35 spl15_43 <=> (sF1 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_43])],[avatar_definition])).
% 1.64/1.35 thf(f47,plain,(
% 1.64/1.35 (sF1 = $false) | ($true = (f2 @ $true)) | (sF2 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.64/1.35 thf(f42,plain,(
% 1.64/1.35 (sF1 = $false) | (sF2 = (f2 @ $true))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f8])).
% 1.64/1.35 thf(f339,plain,(
% 1.64/1.35 spl15_38 | spl15_35 | spl15_43),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f46,f321,f279,f293])).
% 1.64/1.35 thf(f46,plain,(
% 1.64/1.35 (sF1 = $false) | ($false = (f2 @ $true)) | (sF2 = $true)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.64/1.35 thf(f338,plain,(
% 1.64/1.35 spl15_45 | spl15_22 | spl15_33),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f51,f267,f214,f333])).
% 1.64/1.35 thf(f214,definition,(
% 1.64/1.35 spl15_22 <=> ($true = (f3 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_22])],[avatar_definition])).
% 1.64/1.35 thf(f267,definition,(
% 1.64/1.35 spl15_33 <=> ($true = sF8)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_33])],[avatar_definition])).
% 1.64/1.35 thf(f51,plain,(
% 1.64/1.35 ($true = (f3 @ $false)) | (sF9 = $false) | ($true = sF8)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.64/1.35 thf(f49,plain,(
% 1.64/1.35 (sF9 = (f3 @ $false)) | ($true = sF8)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f15])).
% 1.64/1.35 thf(f337,plain,(
% 1.64/1.35 spl15_33 | spl15_20 | spl15_44),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f50,f328,f205,f267])).
% 1.64/1.35 thf(f205,definition,(
% 1.64/1.35 spl15_20 <=> ($false = (f3 @ $false))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_20])],[avatar_definition])).
% 1.64/1.35 thf(f50,plain,(
% 1.64/1.35 ($false = (f3 @ $false)) | ($true = sF9) | ($true = sF8)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.64/1.35 thf(f336,plain,(
% 1.64/1.35 spl15_19 | spl15_34 | spl15_45),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f53,f333,f272,f200])).
% 1.64/1.35 thf(f200,definition,(
% 1.64/1.35 spl15_19 <=> ($true = (f3 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_19])],[avatar_definition])).
% 1.64/1.35 thf(f272,definition,(
% 1.64/1.35 spl15_34 <=> ($false = sF8)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_34])],[avatar_definition])).
% 1.64/1.35 thf(f53,plain,(
% 1.64/1.35 ($false = sF8) | (sF9 = $false) | ($true = (f3 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.64/1.35 thf(f48,plain,(
% 1.64/1.35 (sF9 = (f3 @ $true)) | ($false = sF8)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f15])).
% 1.64/1.35 thf(f331,plain,(
% 1.64/1.35 spl15_44 | spl15_15 | spl15_34),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f52,f272,f183,f328])).
% 1.64/1.35 thf(f183,definition,(
% 1.64/1.35 spl15_15 <=> ($false = (f3 @ $true))),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_15])],[avatar_definition])).
% 1.64/1.35 thf(f52,plain,(
% 1.64/1.35 ($false = (f3 @ $true)) | ($true = sF9) | ($false = sF8)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.64/1.35 thf(f326,plain,(
% 1.64/1.35 spl15_39 | spl15_42 | spl15_16),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f57,f187,f316,f297])).
% 1.64/1.35 thf(f187,definition,(
% 1.64/1.35 spl15_16 <=> (sF0 = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_16])],[avatar_definition])).
% 1.64/1.35 thf(f57,plain,(
% 1.64/1.35 (sF0 = $true) | ((f2 @ $false) = $false) | ($true = sF1)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.64/1.35 thf(f55,plain,(
% 1.64/1.35 (sF0 = $true) | ((f2 @ $false) = sF1)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f7])).
% 1.64/1.35 thf(f325,plain,(
% 1.64/1.35 spl15_16 | spl15_43 | spl15_40),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f56,f302,f321,f187])).
% 1.64/1.35 thf(f56,plain,(
% 1.64/1.35 (sF0 = $true) | ($true = (f2 @ $false)) | (sF1 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.64/1.35 thf(f324,plain,(
% 1.64/1.35 spl15_37 | spl15_18 | spl15_43),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f59,f321,f196,f288])).
% 1.64/1.35 thf(f196,definition,(
% 1.64/1.35 spl15_18 <=> (sF0 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_18])],[avatar_definition])).
% 1.64/1.35 thf(f59,plain,(
% 1.64/1.35 (sF0 = $false) | ($true = (f2 @ $true)) | (sF1 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.64/1.35 thf(f54,plain,(
% 1.64/1.35 (sF1 = (f2 @ $true)) | (sF0 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f7])).
% 1.64/1.35 thf(f319,plain,(
% 1.64/1.35 spl15_35 | spl15_18 | spl15_42),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f58,f316,f196,f279])).
% 1.64/1.35 thf(f58,plain,(
% 1.64/1.35 ($false = (f2 @ $true)) | (sF0 = $false) | ($true = sF1)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.64/1.35 thf(f314,plain,(
% 1.64/1.35 ~spl15_41),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f3,f311])).
% 1.64/1.35 thf(f311,definition,(
% 1.64/1.35 spl15_41 <=> ($true = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_41])],[avatar_definition])).
% 1.64/1.35 thf(f3,plain,(
% 1.64/1.35 ($true != $false)),
% 1.64/1.35 introduced(definition,[],[fool_axiom])).
% 1.64/1.35 thf(f309,plain,(
% 1.64/1.35 spl15_11 | spl15_29 | spl15_28),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f63,f241,f245,f163])).
% 1.64/1.35 thf(f163,definition,(
% 1.64/1.35 spl15_11 <=> ($true = sF4)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_11])],[avatar_definition])).
% 1.64/1.35 thf(f241,definition,(
% 1.64/1.35 spl15_28 <=> ($true = sF5)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_28])],[avatar_definition])).
% 1.64/1.35 thf(f63,plain,(
% 1.64/1.35 ($true = sF4) | ($false = (f0 @ $false)) | ($true = sF5)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.64/1.35 thf(f61,plain,(
% 1.64/1.35 ($true = sF4) | ((f0 @ $false) = sF5)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f11])).
% 1.64/1.35 thf(f308,plain,(
% 1.64/1.35 spl15_30 | spl15_11 | spl15_25),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f62,f227,f163,f250])).
% 1.64/1.35 thf(f227,definition,(
% 1.64/1.35 spl15_25 <=> ($false = sF5)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_25])],[avatar_definition])).
% 1.64/1.35 thf(f62,plain,(
% 1.64/1.35 ($false = sF5) | ($true = sF4) | ($true = (f0 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.64/1.35 thf(f307,plain,(
% 1.64/1.35 spl15_26 | spl15_13 | spl15_28),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f65,f241,f172,f232])).
% 1.64/1.35 thf(f172,definition,(
% 1.64/1.35 spl15_13 <=> ($false = sF4)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_13])],[avatar_definition])).
% 1.64/1.35 thf(f65,plain,(
% 1.64/1.35 ((f0 @ $true) = $false) | ($false = sF4) | ($true = sF5)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.64/1.35 thf(f60,plain,(
% 1.64/1.35 ((f0 @ $true) = sF5) | ($false = sF4)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f11])).
% 1.64/1.35 thf(f306,plain,(
% 1.64/1.35 spl15_13 | spl15_25 | spl15_24),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f64,f223,f227,f172])).
% 1.64/1.35 thf(f64,plain,(
% 1.64/1.35 ($true = (f0 @ $true)) | ($false = sF5) | ($false = sF4)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.64/1.35 thf(f305,plain,(
% 1.64/1.35 spl15_38 | spl15_12 | spl15_40),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f69,f302,f167,f293])).
% 1.64/1.35 thf(f167,definition,(
% 1.64/1.35 spl15_12 <=> (sF3 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_12])],[avatar_definition])).
% 1.64/1.35 thf(f69,plain,(
% 1.64/1.35 (sF3 = $false) | (sF2 = $true) | ($true = (f2 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.64/1.35 thf(f67,plain,(
% 1.64/1.35 (sF2 = $true) | (sF3 = (f2 @ $false))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f9])).
% 1.64/1.35 thf(f300,plain,(
% 1.64/1.35 spl15_14 | spl15_38 | spl15_39),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f68,f297,f293,f177])).
% 1.64/1.35 thf(f177,definition,(
% 1.64/1.35 spl15_14 <=> (sF3 = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_14])],[avatar_definition])).
% 1.64/1.35 thf(f68,plain,(
% 1.64/1.35 ((f2 @ $false) = $false) | (sF2 = $true) | (sF3 = $true)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.64/1.35 thf(f291,plain,(
% 1.64/1.35 spl15_12 | spl15_37 | spl15_36),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f71,f283,f288,f167])).
% 1.64/1.35 thf(f71,plain,(
% 1.64/1.35 (sF3 = $false) | (sF2 = $false) | ($true = (f2 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.64/1.35 thf(f66,plain,(
% 1.64/1.35 (sF3 = (f2 @ $true)) | (sF2 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f9])).
% 1.64/1.35 thf(f286,plain,(
% 1.64/1.35 spl15_35 | spl15_36 | spl15_14),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f70,f177,f283,f279])).
% 1.64/1.35 thf(f70,plain,(
% 1.64/1.35 ($false = (f2 @ $true)) | (sF3 = $true) | (sF2 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.64/1.35 thf(f277,plain,(
% 1.64/1.35 spl15_16 | spl15_22 | spl15_34),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f75,f272,f214,f187])).
% 1.64/1.35 thf(f75,plain,(
% 1.64/1.35 ($false = sF8) | (sF0 = $true) | ($true = (f3 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.64/1.35 thf(f73,plain,(
% 1.64/1.35 (sF0 = $true) | (sF8 = (f3 @ $false))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f14])).
% 1.64/1.35 thf(f276,plain,(
% 1.64/1.35 spl15_16 | spl15_20 | spl15_33),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f74,f267,f205,f187])).
% 1.64/1.35 thf(f74,plain,(
% 1.64/1.35 (sF0 = $true) | ($false = (f3 @ $false)) | ($true = sF8)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.64/1.35 thf(f275,plain,(
% 1.64/1.35 spl15_18 | spl15_19 | spl15_34),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f77,f272,f200,f196])).
% 1.64/1.35 thf(f77,plain,(
% 1.64/1.35 ($false = sF8) | (sF0 = $false) | ($true = (f3 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.64/1.35 thf(f72,plain,(
% 1.64/1.35 (sF8 = (f3 @ $true)) | (sF0 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f14])).
% 1.64/1.35 thf(f270,plain,(
% 1.64/1.35 spl15_15 | spl15_33 | spl15_18),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f76,f196,f267,f183])).
% 1.64/1.35 thf(f76,plain,(
% 1.64/1.35 ($false = (f3 @ $true)) | (sF0 = $false) | ($true = sF8)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.64/1.35 thf(f265,plain,(
% 1.64/1.35 spl15_29 | spl15_32 | spl15_27),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f81,f236,f260,f245])).
% 1.64/1.35 thf(f236,definition,(
% 1.64/1.35 spl15_27 <=> ($true = sF6)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_27])],[avatar_definition])).
% 1.64/1.35 thf(f81,plain,(
% 1.64/1.35 ($false = (f0 @ $false)) | ($true = sF7) | ($true = sF6)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.64/1.35 thf(f79,plain,(
% 1.64/1.35 ((f0 @ $false) = sF7) | ($true = sF6)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f13])).
% 1.64/1.35 thf(f264,plain,(
% 1.64/1.35 spl15_30 | spl15_31 | spl15_27),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f80,f236,f255,f250])).
% 1.64/1.35 thf(f80,plain,(
% 1.64/1.35 ($false = sF7) | ($true = sF6) | ($true = (f0 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.64/1.35 thf(f263,plain,(
% 1.64/1.35 spl15_32 | spl15_23 | spl15_26),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f83,f232,f219,f260])).
% 1.64/1.35 thf(f219,definition,(
% 1.64/1.35 spl15_23 <=> (sF6 = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_23])],[avatar_definition])).
% 1.64/1.35 thf(f83,plain,(
% 1.64/1.35 (sF6 = $false) | ($true = sF7) | ((f0 @ $true) = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.64/1.35 thf(f78,plain,(
% 1.64/1.35 ((f0 @ $true) = sF7) | (sF6 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f13])).
% 1.64/1.35 thf(f258,plain,(
% 1.64/1.35 spl15_24 | spl15_31 | spl15_23),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f82,f219,f255,f223])).
% 1.64/1.35 thf(f82,plain,(
% 1.64/1.35 (sF6 = $false) | ($false = sF7) | ($true = (f0 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.64/1.35 thf(f253,plain,(
% 1.64/1.35 spl15_30 | spl15_28 | spl15_23),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f87,f219,f241,f250])).
% 1.64/1.35 thf(f87,plain,(
% 1.64/1.35 ($true = (f0 @ $false)) | ($true = sF5) | (sF6 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.64/1.35 thf(f85,plain,(
% 1.64/1.35 (sF6 = (f0 @ $false)) | ($true = sF5)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f12])).
% 1.64/1.35 thf(f248,plain,(
% 1.64/1.35 spl15_28 | spl15_29 | spl15_27),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f86,f236,f245,f241])).
% 1.64/1.35 thf(f86,plain,(
% 1.64/1.35 ($false = (f0 @ $false)) | ($true = sF5) | ($true = sF6)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.64/1.35 thf(f239,plain,(
% 1.64/1.35 spl15_25 | spl15_26 | spl15_27),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f89,f236,f232,f227])).
% 1.64/1.35 thf(f89,plain,(
% 1.64/1.35 ((f0 @ $true) = $false) | ($true = sF6) | ($false = sF5)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.64/1.35 thf(f84,plain,(
% 1.64/1.35 ($false = sF5) | ((f0 @ $true) = sF6)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f12])).
% 1.64/1.35 thf(f230,plain,(
% 1.64/1.35 spl15_23 | spl15_24 | spl15_25),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f88,f227,f223,f219])).
% 1.64/1.35 thf(f88,plain,(
% 1.64/1.35 ($false = sF5) | ($true = (f0 @ $true)) | (sF6 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.64/1.35 thf(f217,plain,(
% 1.64/1.35 spl15_22 | spl15_18 | spl15_21),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f93,f209,f196,f214])).
% 1.64/1.35 thf(f209,definition,(
% 1.64/1.35 spl15_21 <=> (x = $true)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_21])],[avatar_definition])).
% 1.64/1.35 thf(f93,plain,(
% 1.64/1.35 ($true = (f3 @ $false)) | (x = $true) | (sF0 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.64/1.35 thf(f91,plain,(
% 1.64/1.35 (x = $true) | (sF0 = (f3 @ $false))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f6])).
% 1.64/1.35 thf(f212,plain,(
% 1.64/1.35 spl15_16 | spl15_20 | spl15_21),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f92,f209,f205,f187])).
% 1.64/1.35 thf(f92,plain,(
% 1.64/1.35 (x = $true) | (sF0 = $true) | ($false = (f3 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.64/1.35 thf(f203,plain,(
% 1.64/1.35 spl15_18 | spl15_17 | spl15_19),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f95,f200,f191,f196])).
% 1.64/1.35 thf(f191,definition,(
% 1.64/1.35 spl15_17 <=> (x = $false)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_17])],[avatar_definition])).
% 1.64/1.35 thf(f95,plain,(
% 1.64/1.35 ($true = (f3 @ $true)) | (x = $false) | (sF0 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.64/1.35 thf(f90,plain,(
% 1.64/1.35 (sF0 = (f3 @ $true)) | (x = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f6])).
% 1.64/1.35 thf(f194,plain,(
% 1.64/1.35 spl15_15 | spl15_16 | spl15_17),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f94,f191,f187,f183])).
% 1.64/1.35 thf(f94,plain,(
% 1.64/1.35 ($false = (f3 @ $true)) | (sF0 = $true) | (x = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.64/1.35 thf(f181,plain,(
% 1.64/1.35 spl15_6 | spl15_11 | spl15_14),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f99,f177,f163,f137])).
% 1.64/1.35 thf(f99,plain,(
% 1.64/1.35 ($false = (f1 @ $false)) | ($true = sF4) | (sF3 = $true)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.64/1.35 thf(f97,plain,(
% 1.64/1.35 ((f1 @ $false) = sF4) | (sF3 = $true)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f10])).
% 1.64/1.35 thf(f180,plain,(
% 1.64/1.35 spl15_14 | spl15_8 | spl15_13),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f98,f172,f146,f177])).
% 1.64/1.35 thf(f98,plain,(
% 1.64/1.35 (sF3 = $true) | ($true = (f1 @ $false)) | ($false = sF4)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.64/1.35 thf(f175,plain,(
% 1.64/1.35 spl15_5 | spl15_12 | spl15_13),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f101,f172,f167,f132])).
% 1.64/1.35 thf(f101,plain,(
% 1.64/1.35 (sF3 = $false) | ($false = sF4) | ($true = (f1 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.64/1.35 thf(f96,plain,(
% 1.64/1.35 (sF4 = (f1 @ $true)) | (sF3 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f10])).
% 1.64/1.35 thf(f170,plain,(
% 1.64/1.35 spl15_2 | spl15_11 | spl15_12),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f100,f167,f163,f119])).
% 1.64/1.35 thf(f100,plain,(
% 1.64/1.35 (sF3 = $false) | ($true = sF4) | ($false = (f1 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.64/1.35 thf(f161,plain,(
% 1.64/1.35 spl15_7 | spl15_6 | spl15_10),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f105,f157,f137,f141])).
% 1.64/1.35 thf(f141,definition,(
% 1.64/1.35 spl15_7 <=> ($true = sF11)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_7])],[avatar_definition])).
% 1.64/1.35 thf(f105,plain,(
% 1.64/1.35 ($false = (f1 @ $false)) | ($true = sF10) | ($true = sF11)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.64/1.35 thf(f103,plain,(
% 1.64/1.35 ((f1 @ $false) = sF11) | ($true = sF10)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f17])).
% 1.64/1.35 thf(f160,plain,(
% 1.64/1.35 spl15_10 | spl15_1 | spl15_8),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f104,f146,f115,f157])).
% 1.64/1.35 thf(f115,definition,(
% 1.64/1.35 spl15_1 <=> ($false = sF11)),
% 1.64/1.35 introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition])).
% 1.64/1.35 thf(f104,plain,(
% 1.64/1.35 ($true = sF10) | ($false = sF11) | ($true = (f1 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.64/1.35 thf(f155,plain,(
% 1.64/1.35 spl15_1 | spl15_9 | spl15_5),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f107,f132,f151,f115])).
% 1.64/1.35 thf(f107,plain,(
% 1.64/1.35 (sF10 = $false) | ($false = sF11) | ($true = (f1 @ $true))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.64/1.35 thf(f102,plain,(
% 1.64/1.35 (sF11 = (f1 @ $true)) | (sF10 = $false)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f17])).
% 1.64/1.35 thf(f154,plain,(
% 1.64/1.35 spl15_9 | spl15_2 | spl15_7),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f106,f141,f119,f151])).
% 1.64/1.35 thf(f106,plain,(
% 1.64/1.35 ($false = (f1 @ $true)) | ($true = sF11) | (sF10 = $false)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.64/1.35 thf(f149,plain,(
% 1.64/1.35 spl15_4 | spl15_8 | spl15_7),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f111,f141,f146,f128])).
% 1.64/1.35 thf(f111,plain,(
% 1.64/1.35 ($true = sF11) | (sF12 = $false) | ($true = (f1 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.64/1.35 thf(f109,plain,(
% 1.64/1.35 (sF12 = (f1 @ $false)) | ($true = sF11)),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f18])).
% 1.64/1.35 thf(f144,plain,(
% 1.64/1.35 spl15_6 | spl15_7 | spl15_3),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f110,f123,f141,f137])).
% 1.64/1.35 thf(f110,plain,(
% 1.64/1.35 ($true = sF12) | ($true = sF11) | ($false = (f1 @ $false))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.64/1.35 thf(f135,plain,(
% 1.64/1.35 spl15_4 | spl15_5 | spl15_1),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f113,f115,f132,f128])).
% 1.64/1.35 thf(f113,plain,(
% 1.64/1.35 (sF12 = $false) | ($true = (f1 @ $true)) | ($false = sF11)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.64/1.35 thf(f108,plain,(
% 1.64/1.35 ($false = sF11) | (sF12 = (f1 @ $true))),
% 1.64/1.35 inference(cases_simplifying,[status(thm)],[f18])).
% 1.64/1.35 thf(f126,plain,(
% 1.64/1.35 spl15_1 | spl15_2 | spl15_3),
% 1.64/1.35 inference(avatar_split_clause,[status(thm)],[f112,f123,f119,f115])).
% 1.64/1.35 thf(f112,plain,(
% 1.64/1.35 ($false = (f1 @ $true)) | ($true = sF12) | ($false = sF11)),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.64/1.35 % SZS output end Proof for DTF2THF_29759
% 1.64/1.35 % (29989)------------------------------
% 1.64/1.35 % (29989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (29989)Termination reason: Refutation
% 1.64/1.35
% 1.64/1.35 % (29989)Memory used [KB]: 5628
% 1.64/1.35 % (29989)Time elapsed: 0.006 s
% 1.64/1.35 % (29989)Instructions burned: 7 (million)
% 1.64/1.35 % (29989)------------------------------
% 1.64/1.35 % (29989)------------------------------
% 1.64/1.35 % (29975)Success in time 0.046 s
%------------------------------------------------------------------------------