%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO500^1.003 : 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 : n002.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 1.59s 1.32s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 68
% Syntax : Number of formulae : 188 ( 19 unt; 0 typ; 48 def)
% Number of atoms : 1188 ( 288 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 466 ( 42 ~; 238 |; 0 &; 149 @)
% ( 37 <=>; 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 : 55 ( 52 usr; 51 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(f299,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f94,f103,f116,f125,f134,f139,f144,f153,f158,f167,f172,f181,f186,f191,f192,f205,f214,f223,f228,f233,f234,f239,f240,f241,f242,f243,f244,f245,f246,f247,f248,f249,f250,f251,f252,f257,f258,f263,f264,f269,f274,f275,f276,f277,f278,f279,f280,f281,f282,f283,f284,f285,f286,f287,f288,f289,f290,f291,f292,f293,f294,f295,f296,f297,f298]) ).
thf(f298,plain,
( ( $true != sF3 )
| ( $false != sF3 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f297,plain,
( ( $true != sF8 )
| ( $false != sF8 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f296,plain,
( ( sF9 != $true )
| ( sF9 != $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f295,plain,
( ( x != $false )
| ( x != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f294,plain,
( ( sF5 != $false )
| ( sF5 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f293,plain,
( ( ( f2 @ $false )
!= $true )
| ( ( f2 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f292,plain,
( ( ( f2 @ $true )
!= $false )
| ( ( f2 @ $true )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f291,plain,
( ( $true != sF1 )
| ( $false != sF1 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f290,plain,
( ( $false != sF0 )
| ( $true != sF0 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f289,plain,
( ( $true != sF6 )
| ( $false != sF6 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f288,plain,
( ( sF7 != $false )
| ( sF7 != $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f287,plain,
( ( $true != sF4 )
| ( $false != sF4 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f286,plain,
( ( $true != sF10 )
| ( $false != sF10 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f285,plain,
( ( ( f0 @ $false )
!= $false )
| ( ( f0 @ $false )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f284,plain,
( ( $false
!= ( f0 @ $true ) )
| ( $true
!= ( f0 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f283,plain,
( ( ( f1 @ $false )
!= $true )
| ( ( f1 @ $false )
!= $false )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f282,plain,
( ( $false
!= ( f1 @ $true ) )
| ( $true
!= ( f1 @ $true ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f281,plain,
( ( $true != sF2 )
| ( $false != sF2 )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f280,plain,
( spl11_37
| spl11_19
| spl11_35 ),
inference(avatar_split_clause,[status(thm)],[f21,f260,f169,f271]) ).
thf(f271,definition,
( spl11_37
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl11_37])],[avatar_definition]) ).
thf(f169,definition,
( spl11_19
<=> ( ( f0 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl11_19])],[avatar_definition]) ).
thf(f260,definition,
( spl11_35
<=> ( sF9 = $true ) ),
introduced(definition,[new_symbols(naming,[spl11_35])],[avatar_definition]) ).
thf(f21,plain,
( ( ( f0 @ $false )
= $false )
| ( $true = sF8 )
| ( sF9 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( f0 @ $false )
= sF9 )
| ( $true = sF8 ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f15,definition,
( sF9
= ( f0 @ sF8 ) ),
introduced(definition,[],[function_definition]) ).
thf(f279,plain,
( spl11_37
| spl11_18
| spl11_34 ),
inference(avatar_split_clause,[status(thm)],[f20,f254,f164,f271]) ).
thf(f164,definition,
( spl11_18
<=> ( ( f0 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_18])],[avatar_definition]) ).
thf(f254,definition,
( spl11_34
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(naming,[spl11_34])],[avatar_definition]) ).
thf(f20,plain,
( ( sF9 = $false )
| ( ( f0 @ $false )
= $true )
| ( $true = sF8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f278,plain,
( spl11_15
| spl11_34
| spl11_36 ),
inference(avatar_split_clause,[status(thm)],[f23,f266,f254,f150]) ).
thf(f150,definition,
( spl11_15
<=> ( $true
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_15])],[avatar_definition]) ).
thf(f266,definition,
( spl11_36
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(naming,[spl11_36])],[avatar_definition]) ).
thf(f23,plain,
( ( sF9 = $false )
| ( $false = sF8 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false = sF8 )
| ( sF9
= ( f0 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f15]) ).
thf(f277,plain,
( spl11_35
| spl11_16
| spl11_36 ),
inference(avatar_split_clause,[status(thm)],[f22,f266,f155,f260]) ).
thf(f155,definition,
( spl11_16
<=> ( $false
= ( f0 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_16])],[avatar_definition]) ).
thf(f22,plain,
( ( sF9 = $true )
| ( $false = sF8 )
| ( $false
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f276,plain,
( spl11_37
| spl11_19
| spl11_20 ),
inference(avatar_split_clause,[status(thm)],[f27,f174,f169,f271]) ).
thf(f174,definition,
( spl11_20
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(naming,[spl11_20])],[avatar_definition]) ).
thf(f27,plain,
( ( sF7 = $true )
| ( $true = sF8 )
| ( ( f0 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sF7 = $true )
| ( ( f0 @ $false )
= sF8 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f14,definition,
( ( f0 @ sF7 )
= sF8 ),
introduced(definition,[],[function_definition]) ).
thf(f275,plain,
( spl11_36
| spl11_20
| spl11_18 ),
inference(avatar_split_clause,[status(thm)],[f26,f164,f174,f266]) ).
thf(f26,plain,
( ( ( f0 @ $false )
= $true )
| ( $false = sF8 )
| ( sF7 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f274,plain,
( spl11_16
| spl11_37
| spl11_22 ),
inference(avatar_split_clause,[status(thm)],[f29,f183,f271,f155]) ).
thf(f183,definition,
( spl11_22
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(naming,[spl11_22])],[avatar_definition]) ).
thf(f29,plain,
( ( sF7 = $false )
| ( $true = sF8 )
| ( $false
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( sF7 = $false )
| ( ( f0 @ $true )
= sF8 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
thf(f269,plain,
( spl11_22
| spl11_15
| spl11_36 ),
inference(avatar_split_clause,[status(thm)],[f28,f266,f150,f183]) ).
thf(f28,plain,
( ( $false = sF8 )
| ( $true
= ( f0 @ $true ) )
| ( sF7 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f264,plain,
( spl11_19
| spl11_35
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f33,f91,f260,f169]) ).
thf(f91,definition,
( spl11_2
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition]) ).
thf(f33,plain,
( ( sF9 = $true )
| ( $true = sF10 )
| ( ( f0 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( f0 @ $false )
= sF10 )
| ( sF9 = $true ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f16,definition,
( sF10
= ( f0 @ sF9 ) ),
introduced(definition,[],[function_definition]) ).
thf(f263,plain,
( spl11_18
| spl11_35
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f32,f100,f260,f164]) ).
thf(f100,definition,
( spl11_4
<=> ( $false = sF10 ) ),
introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition]) ).
thf(f32,plain,
( ( $false = sF10 )
| ( ( f0 @ $false )
= $true )
| ( sF9 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f258,plain,
( spl11_2
| spl11_34
| spl11_16 ),
inference(avatar_split_clause,[status(thm)],[f35,f155,f254,f91]) ).
thf(f35,plain,
( ( sF9 = $false )
| ( $true = sF10 )
| ( $false
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( sF9 = $false )
| ( ( f0 @ $true )
= sF10 ) ),
inference(cases_simplifying,[status(thm)],[f16]) ).
thf(f257,plain,
( spl11_34
| spl11_4
| spl11_15 ),
inference(avatar_split_clause,[status(thm)],[f34,f150,f100,f254]) ).
thf(f34,plain,
( ( sF9 = $false )
| ( $false = sF10 )
| ( $true
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f252,plain,
( spl11_12
| spl11_11
| spl11_27 ),
inference(avatar_split_clause,[status(thm)],[f39,f207,f131,f136]) ).
thf(f136,definition,
( spl11_12
<=> ( ( f1 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl11_12])],[avatar_definition]) ).
thf(f131,definition,
( spl11_11
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(naming,[spl11_11])],[avatar_definition]) ).
thf(f207,definition,
( spl11_27
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl11_27])],[avatar_definition]) ).
thf(f39,plain,
( ( ( f1 @ $false )
= $false )
| ( $true = sF1 )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = sF0 )
| ( ( f1 @ $false )
= sF1 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f7,definition,
( sF1
= ( f1 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f251,plain,
( spl11_27
| spl11_7
| spl11_10 ),
inference(avatar_split_clause,[status(thm)],[f38,f127,f113,f207]) ).
thf(f113,definition,
( spl11_7
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition]) ).
thf(f127,definition,
( spl11_10
<=> ( ( f1 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_10])],[avatar_definition]) ).
thf(f38,plain,
( ( $true = sF0 )
| ( ( f1 @ $false )
= $true )
| ( $false = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f250,plain,
( spl11_11
| spl11_24
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f41,f122,f194,f131]) ).
thf(f194,definition,
( spl11_24
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(naming,[spl11_24])],[avatar_definition]) ).
thf(f122,definition,
( spl11_9
<=> ( $false
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition]) ).
thf(f41,plain,
( ( $true = sF1 )
| ( $false
= ( f1 @ $true ) )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false = sF0 )
| ( ( f1 @ $true )
= sF1 ) ),
inference(cases_simplifying,[status(thm)],[f7]) ).
thf(f249,plain,
( spl11_7
| spl11_24
| spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f40,f109,f194,f113]) ).
thf(f109,definition,
( spl11_6
<=> ( $true
= ( f1 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition]) ).
thf(f40,plain,
( ( $false = sF0 )
| ( $true
= ( f1 @ $true ) )
| ( $false = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f248,plain,
( spl11_27
| spl11_30
| spl11_32 ),
inference(avatar_split_clause,[status(thm)],[f45,f230,f220,f207]) ).
thf(f220,definition,
( spl11_30
<=> ( ( f2 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_30])],[avatar_definition]) ).
thf(f230,definition,
( spl11_32
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(naming,[spl11_32])],[avatar_definition]) ).
thf(f45,plain,
( ( ( f2 @ $false )
= $true )
| ( sF5 = $false )
| ( $true = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = sF0 )
| ( sF5
= ( f2 @ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f11,definition,
( sF5
= ( f2 @ sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f247,plain,
( spl11_27
| spl11_31
| spl11_33 ),
inference(avatar_split_clause,[status(thm)],[f44,f236,f225,f207]) ).
thf(f225,definition,
( spl11_31
<=> ( ( f2 @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl11_31])],[avatar_definition]) ).
thf(f236,definition,
( spl11_33
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(naming,[spl11_33])],[avatar_definition]) ).
thf(f44,plain,
( ( ( f2 @ $false )
= $false )
| ( $true = sF0 )
| ( sF5 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f246,plain,
( spl11_26
| spl11_32
| spl11_24 ),
inference(avatar_split_clause,[status(thm)],[f47,f194,f230,f202]) ).
thf(f202,definition,
( spl11_26
<=> ( ( f2 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_26])],[avatar_definition]) ).
thf(f47,plain,
( ( $false = sF0 )
| ( ( f2 @ $true )
= $true )
| ( sF5 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false = sF0 )
| ( sF5
= ( f2 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f11]) ).
thf(f245,plain,
( spl11_28
| spl11_33
| spl11_24 ),
inference(avatar_split_clause,[status(thm)],[f46,f194,f236,f211]) ).
thf(f211,definition,
( spl11_28
<=> ( ( f2 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl11_28])],[avatar_definition]) ).
thf(f46,plain,
( ( ( f2 @ $true )
= $false )
| ( sF5 = $true )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f244,plain,
( spl11_12
| spl11_8
| spl11_17 ),
inference(avatar_split_clause,[status(thm)],[f51,f160,f118,f136]) ).
thf(f118,definition,
( spl11_8
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition]) ).
thf(f160,definition,
( spl11_17
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl11_17])],[avatar_definition]) ).
thf(f51,plain,
( ( ( f1 @ $false )
= $false )
| ( $true = sF2 )
| ( $true = sF3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true = sF2 )
| ( ( f1 @ $false )
= sF3 ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f9,definition,
( ( f1 @ sF2 )
= sF3 ),
introduced(definition,[],[function_definition]) ).
thf(f243,plain,
( spl11_8
| spl11_14
| spl11_10 ),
inference(avatar_split_clause,[status(thm)],[f50,f127,f146,f118]) ).
thf(f146,definition,
( spl11_14
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(naming,[spl11_14])],[avatar_definition]) ).
thf(f50,plain,
( ( $true = sF2 )
| ( ( f1 @ $false )
= $true )
| ( $false = sF3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f242,plain,
( spl11_17
| spl11_9
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f53,f105,f122,f160]) ).
thf(f105,definition,
( spl11_5
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition]) ).
thf(f53,plain,
( ( $false = sF2 )
| ( $true = sF3 )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false = sF2 )
| ( ( f1 @ $true )
= sF3 ) ),
inference(cases_simplifying,[status(thm)],[f9]) ).
thf(f241,plain,
( spl11_6
| spl11_5
| spl11_14 ),
inference(avatar_split_clause,[status(thm)],[f52,f146,f105,f109]) ).
thf(f52,plain,
( ( $true
= ( f1 @ $true ) )
| ( $false = sF3 )
| ( $false = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f240,plain,
( spl11_23
| spl11_33
| spl11_31 ),
inference(avatar_split_clause,[status(thm)],[f57,f225,f236,f188]) ).
thf(f188,definition,
( spl11_23
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl11_23])],[avatar_definition]) ).
thf(f57,plain,
( ( $true = sF6 )
| ( ( f2 @ $false )
= $false )
| ( sF5 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( sF5 = $true )
| ( ( f2 @ $false )
= sF6 ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f12,definition,
( ( f2 @ sF5 )
= sF6 ),
introduced(definition,[],[function_definition]) ).
thf(f239,plain,
( spl11_30
| spl11_21
| spl11_33 ),
inference(avatar_split_clause,[status(thm)],[f56,f236,f178,f220]) ).
thf(f178,definition,
( spl11_21
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(naming,[spl11_21])],[avatar_definition]) ).
thf(f56,plain,
( ( $false = sF6 )
| ( sF5 = $true )
| ( ( f2 @ $false )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f234,plain,
( spl11_28
| spl11_32
| spl11_23 ),
inference(avatar_split_clause,[status(thm)],[f59,f188,f230,f211]) ).
thf(f59,plain,
( ( sF5 = $false )
| ( $true = sF6 )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( f2 @ $true )
= sF6 )
| ( sF5 = $false ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
thf(f233,plain,
( spl11_26
| spl11_21
| spl11_32 ),
inference(avatar_split_clause,[status(thm)],[f58,f230,f178,f202]) ).
thf(f58,plain,
( ( ( f2 @ $true )
= $true )
| ( sF5 = $false )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f228,plain,
( spl11_31
| spl11_27
| spl11_29 ),
inference(avatar_split_clause,[status(thm)],[f63,f216,f207,f225]) ).
thf(f216,definition,
( spl11_29
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl11_29])],[avatar_definition]) ).
thf(f63,plain,
( ( x = $true )
| ( $true = sF0 )
| ( ( f2 @ $false )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( x = $true )
| ( ( f2 @ $false )
= sF0 ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f6,definition,
( ( f2 @ x )
= sF0 ),
introduced(definition,[],[function_definition]) ).
thf(f223,plain,
( spl11_29
| spl11_30
| spl11_24 ),
inference(avatar_split_clause,[status(thm)],[f62,f194,f220,f216]) ).
thf(f62,plain,
( ( $false = sF0 )
| ( ( f2 @ $false )
= $true )
| ( x = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f214,plain,
( spl11_27
| spl11_25
| spl11_28 ),
inference(avatar_split_clause,[status(thm)],[f65,f211,f198,f207]) ).
thf(f198,definition,
( spl11_25
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl11_25])],[avatar_definition]) ).
thf(f65,plain,
( ( $true = sF0 )
| ( x = $false )
| ( ( f2 @ $true )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( f2 @ $true )
= sF0 )
| ( x = $false ) ),
inference(cases_simplifying,[status(thm)],[f6]) ).
thf(f205,plain,
( spl11_24
| spl11_25
| spl11_26 ),
inference(avatar_split_clause,[status(thm)],[f64,f202,f198,f194]) ).
thf(f64,plain,
( ( x = $false )
| ( ( f2 @ $true )
= $true )
| ( $false = sF0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f192,plain,
( spl11_12
| spl11_23
| spl11_20 ),
inference(avatar_split_clause,[status(thm)],[f69,f174,f188,f136]) ).
thf(f69,plain,
( ( $true = sF6 )
| ( ( f1 @ $false )
= $false )
| ( sF7 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true = sF6 )
| ( ( f1 @ $false )
= sF7 ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f13,definition,
( ( f1 @ sF6 )
= sF7 ),
introduced(definition,[],[function_definition]) ).
thf(f191,plain,
( spl11_10
| spl11_22
| spl11_23 ),
inference(avatar_split_clause,[status(thm)],[f68,f188,f183,f127]) ).
thf(f68,plain,
( ( $true = sF6 )
| ( ( f1 @ $false )
= $true )
| ( sF7 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f186,plain,
( spl11_21
| spl11_22
| spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f71,f109,f183,f178]) ).
thf(f71,plain,
( ( $true
= ( f1 @ $true ) )
| ( sF7 = $false )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = sF6 )
| ( sF7
= ( f1 @ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f13]) ).
thf(f181,plain,
( spl11_20
| spl11_21
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f70,f122,f178,f174]) ).
thf(f70,plain,
( ( $false
= ( f1 @ $true ) )
| ( sF7 = $true )
| ( $false = sF6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f172,plain,
( spl11_1
| spl11_19
| spl11_17 ),
inference(avatar_split_clause,[status(thm)],[f75,f160,f169,f87]) ).
thf(f87,definition,
( spl11_1
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition]) ).
thf(f75,plain,
( ( ( f0 @ $false )
= $false )
| ( $true = sF3 )
| ( $true = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( f0 @ $false )
= sF4 )
| ( $true = sF3 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f10,definition,
( ( f0 @ sF3 )
= sF4 ),
introduced(definition,[],[function_definition]) ).
thf(f167,plain,
( spl11_3
| spl11_17
| spl11_18 ),
inference(avatar_split_clause,[status(thm)],[f74,f164,f160,f96]) ).
thf(f96,definition,
( spl11_3
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition]) ).
thf(f74,plain,
( ( $true = sF3 )
| ( ( f0 @ $false )
= $true )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f158,plain,
( spl11_1
| spl11_16
| spl11_14 ),
inference(avatar_split_clause,[status(thm)],[f77,f146,f155,f87]) ).
thf(f77,plain,
( ( $false = sF3 )
| ( $true = sF4 )
| ( $false
= ( f0 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( f0 @ $true )
= sF4 )
| ( $false = sF3 ) ),
inference(cases_simplifying,[status(thm)],[f10]) ).
thf(f153,plain,
( spl11_3
| spl11_14
| spl11_15 ),
inference(avatar_split_clause,[status(thm)],[f76,f150,f146,f96]) ).
thf(f76,plain,
( ( $true
= ( f0 @ $true ) )
| ( $false = sF3 )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f144,plain,
~ spl11_13,
inference(avatar_split_clause,[status(thm)],[f3,f141]) ).
thf(f141,definition,
( spl11_13
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl11_13])],[avatar_definition]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f139,plain,
( spl11_8
| spl11_11
| spl11_12 ),
inference(avatar_split_clause,[status(thm)],[f81,f136,f131,f118]) ).
thf(f81,plain,
( ( $true = sF1 )
| ( ( f1 @ $false )
= $false )
| ( $true = sF2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true = sF1 )
| ( ( f1 @ $false )
= sF2 ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f8,definition,
( ( f1 @ sF1 )
= sF2 ),
introduced(definition,[],[function_definition]) ).
thf(f134,plain,
( spl11_5
| spl11_10
| spl11_11 ),
inference(avatar_split_clause,[status(thm)],[f80,f131,f127,f105]) ).
thf(f80,plain,
( ( ( f1 @ $false )
= $true )
| ( $false = sF2 )
| ( $true = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f125,plain,
( spl11_8
| spl11_9
| spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f83,f113,f122,f118]) ).
thf(f83,plain,
( ( $false = sF1 )
| ( $true = sF2 )
| ( $false
= ( f1 @ $true ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $false = sF1 )
| ( ( f1 @ $true )
= sF2 ) ),
inference(cases_simplifying,[status(thm)],[f8]) ).
thf(f116,plain,
( spl11_5
| spl11_6
| spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f82,f113,f109,f105]) ).
thf(f82,plain,
( ( $false = sF2 )
| ( $true
= ( f1 @ $true ) )
| ( $false = sF1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f103,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f85,f100,f96]) ).
thf(f85,plain,
( ( $false = sF10 )
| ( $false = sF4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
sF4 != sF10,
inference(definition_folding,[status(thm)],[f5,f16,f15,f14,f13,f12,f11,f6,f10,f9,f8,f7,f6]) ).
thf(f5,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
!= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yCfNfVysf7/DTF2THF_6054.p',kaminski3) ).
thf(f94,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f84,f91,f87]) ).
thf(f84,plain,
( ( $true = sF4 )
| ( $true = sF10 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO500^1.003 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:32:48 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SYO500^1.003 : TPTP v9.2.1. Released v4.1.0.
% 0.29/0.47 % Domain : Syntactic
% 0.29/0.47 % Problem : Three function variant of the Kaminski equation
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : basic11 [Bro09]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.43 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, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0
% 0.29/0.47 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.29/0.47 % Number of atoms : 15 ( 1 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 1 ( 15 avg)
% 0.29/0.47 % Number of connectives : 12 ( 0 ~; 0 |; 0 &; 12 @)
% 0.29/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.29/0.47 % Number of types : 1 ( 0 usr)
% 0.29/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments :
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(x,type,
% 0.29/0.47 x: $o ).
% 0.29/0.47
% 0.29/0.47 thf(f0,type,
% 0.29/0.47 f0: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f1,type,
% 0.29/0.47 f1: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(f2,type,
% 0.29/0.47 f2: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(kaminski3,conjecture,
% 0.29/0.47 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
% 0.29/0.47 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 14:32:49 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yCfNfVysf7/DTF2DTF6054.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(x,type,
% 1.49/1.26 x: $o ).
% 1.49/1.26
% 1.49/1.26 thf(f0,type,
% 1.49/1.26 f0: $o > $o ).
% 1.49/1.26
% 1.49/1.26 thf(f1,type,
% 1.49/1.26 f1: $o > $o ).
% 1.49/1.26
% 1.49/1.26 thf(f2,type,
% 1.49/1.26 f2: $o > $o ).
% 1.49/1.26
% 1.49/1.26 thf(kaminski3,conjecture,
% 1.49/1.26 ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ x ) ) ) ) )
% 1.49/1.26 = ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ x ) ) ) ) ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (6376)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_6054 for (2999ds/27Mi)
% 1.49/1.28 % (6375)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_6054 for (2999ds/4Mi)
% 1.49/1.28 % (6376)Refutation not found, incomplete strategy
% 1.49/1.28 % (6376)------------------------------
% 1.49/1.28 % (6376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (6376)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.28
% 1.49/1.28
% 1.49/1.28 % (6376)Memory used [KB]: 5500
% 1.49/1.28 % (6376)Time elapsed: 0.003 s
% 1.49/1.28 % (6376)Instructions burned: 1 (million)
% 1.49/1.28 % (6376)------------------------------
% 1.49/1.28 % (6376)------------------------------
% 1.49/1.28 % (6375)Instruction limit reached!
% 1.49/1.28 % (6375)------------------------------
% 1.49/1.28 % (6375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (6375)Termination reason: Unknown
% 1.49/1.28 % (6375)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (6375)Memory used [KB]: 5500
% 1.49/1.28 % (6375)Time elapsed: 0.003 s
% 1.49/1.28 % (6375)Instructions burned: 5 (million)
% 1.49/1.28 % (6375)------------------------------
% 1.49/1.28 % (6375)------------------------------
% 1.49/1.29 % (6374)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/183Mi)
% 1.49/1.29 % (6377)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/2Mi)
% 1.49/1.29 % (6378)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_6054 for (2999ds/2Mi)
% 1.49/1.29 % (6379)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_6054 for (2999ds/275Mi)
% 1.49/1.29 % (6380)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/18Mi)
% 1.49/1.29 % (6379)Refutation not found, incomplete strategy
% 1.49/1.29 % (6379)------------------------------
% 1.49/1.29 % (6379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6379)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (6379)Memory used [KB]: 5500
% 1.49/1.29 % (6379)Time elapsed: 0.003 s
% 1.49/1.29 % (6379)Instructions burned: 1 (million)
% 1.49/1.29 % (6379)------------------------------
% 1.49/1.29 % (6379)------------------------------
% 1.49/1.29 % (6378)Refutation not found, incomplete strategy
% 1.49/1.29 % (6378)------------------------------
% 1.49/1.29 % (6378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6378)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (6378)Memory used [KB]: 5500
% 1.49/1.29 % (6378)Time elapsed: 0.003 s
% 1.49/1.29 % (6378)Instructions burned: 1 (million)
% 1.49/1.29 % (6378)------------------------------
% 1.49/1.29 % (6378)------------------------------
% 1.49/1.29 % (6377)Refutation not found, incomplete strategy
% 1.49/1.29 % (6377)------------------------------
% 1.49/1.29 % (6377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6377)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (6377)Memory used [KB]: 5500
% 1.49/1.29 % (6377)Time elapsed: 0.004 s
% 1.49/1.29 % (6377)Instructions burned: 1 (million)
% 1.49/1.29 % (6377)------------------------------
% 1.49/1.29 % (6377)------------------------------
% 1.49/1.29 % (6381)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/3Mi)
% 1.49/1.29 % (6381)Refutation not found, incomplete strategy
% 1.49/1.29 % (6381)------------------------------
% 1.49/1.29 % (6381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6381)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (6381)Memory used [KB]: 5500
% 1.49/1.29 % (6381)Time elapsed: 0.001 s
% 1.49/1.29 % (6381)Instructions burned: 1 (million)
% 1.49/1.29 % (6381)------------------------------
% 1.49/1.29 % (6381)------------------------------
% 1.49/1.29 % (6382)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_6054 for (2999ds/37Mi)
% 1.59/1.30 % (6380)Instruction limit reached!
% 1.59/1.30 % (6380)------------------------------
% 1.59/1.30 % (6380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (6380)Termination reason: Unknown
% 1.59/1.30 % (6380)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (6380)Memory used [KB]: 5628
% 1.59/1.30 % (6380)Time elapsed: 0.014 s
% 1.59/1.30 % (6380)Instructions burned: 19 (million)
% 1.59/1.30 % (6380)------------------------------
% 1.59/1.30 % (6380)------------------------------
% 1.59/1.30 % (6382)Instruction limit reached!
% 1.59/1.30 % (6382)------------------------------
% 1.59/1.30 % (6382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (6382)Termination reason: Unknown
% 1.59/1.30 % (6382)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (6382)Memory used [KB]: 5628
% 1.59/1.30 % (6382)Time elapsed: 0.015 s
% 1.59/1.30 % (6382)Instructions burned: 37 (million)
% 1.59/1.30 % (6382)------------------------------
% 1.59/1.30 % (6382)------------------------------
% 1.59/1.31 % (6383)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_6054 for (2999ds/15Mi)
% 1.59/1.31 % (6385)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_6054 for (2999ds/1041Mi)
% 1.59/1.31 % (6384)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_6054 for (2999ds/3Mi)
% 1.59/1.31 % (6384)Refutation not found, incomplete strategy
% 1.59/1.31 % (6384)------------------------------
% 1.59/1.31 % (6384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (6384)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.31
% 1.59/1.31
% 1.59/1.31 % (6384)Memory used [KB]: 5373
% 1.59/1.31 % (6384)Time elapsed: 0.003 s
% 1.59/1.31 % (6384)Instructions burned: 1 (million)
% 1.59/1.31 % (6384)------------------------------
% 1.59/1.31 % (6384)------------------------------
% 1.59/1.31 % (6386)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/7Mi)
% 1.59/1.31 % (6385)Refutation not found, incomplete strategy
% 1.59/1.31 % (6385)------------------------------
% 1.59/1.31 % (6385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (6385)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.31
% 1.59/1.31
% 1.59/1.31 % (6385)Memory used [KB]: 5500
% 1.59/1.31 % (6385)Time elapsed: 0.005 s
% 1.59/1.31 % (6385)Instructions burned: 4 (million)
% 1.59/1.31 % (6385)------------------------------
% 1.59/1.31 % (6385)------------------------------
% 1.59/1.31 % (6386)Instruction limit reached!
% 1.59/1.31 % (6386)------------------------------
% 1.59/1.31 % (6386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (6386)Termination reason: Unknown
% 1.59/1.31 % (6386)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (6386)Memory used [KB]: 1023
% 1.59/1.31 % (6386)Time elapsed: 0.007 s
% 1.59/1.31 % (6386)Instructions burned: 8 (million)
% 1.59/1.31 % (6386)------------------------------
% 1.59/1.31 % (6386)------------------------------
% 1.59/1.31 % (6388)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_6054 for (2999ds/3Mi)
% 1.59/1.32 % (6388)Refutation not found, incomplete strategy
% 1.59/1.32 % (6388)------------------------------
% 1.59/1.32 % (6388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6388)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.32
% 1.59/1.32
% 1.59/1.32 % (6388)Memory used [KB]: 5500
% 1.59/1.32 % (6388)Time elapsed: 0.002 s
% 1.59/1.32 % (6388)Instructions burned: 1 (million)
% 1.59/1.32 % (6388)------------------------------
% 1.59/1.32 % (6388)------------------------------
% 1.59/1.32 % (6387)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6054 for (2999ds/16Mi)
% 1.59/1.32 % (6383)Instruction limit reached!
% 1.59/1.32 % (6383)------------------------------
% 1.59/1.32 % (6383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6383)Termination reason: Unknown
% 1.59/1.32 % (6383)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (6383)Memory used [KB]: 5628
% 1.59/1.32 % (6383)Time elapsed: 0.012 s
% 1.59/1.32 % (6383)Instructions burned: 16 (million)
% 1.59/1.32 % (6383)------------------------------
% 1.59/1.32 % (6383)------------------------------
% 1.59/1.32 % (6387)First to succeed.
% 1.59/1.32 % (6387)Refutation found. Thanks to Tanya!
% 1.59/1.32 % SZS status Theorem for DTF2THF_6054
% 1.59/1.32 % SZS output start Proof for DTF2THF_6054
% 1.59/1.32 thf(func_def_1, type, f0: $o > $o).
% 1.59/1.32 thf(func_def_2, type, f1: $o > $o).
% 1.59/1.32 thf(func_def_3, type, f2: $o > $o).
% 1.59/1.32 thf(f299,plain,(
% 1.59/1.32 $false),
% 1.59/1.32 inference(avatar_sat_refutation,[status(thm)],[f94,f103,f116,f125,f134,f139,f144,f153,f158,f167,f172,f181,f186,f191,f192,f205,f214,f223,f228,f233,f234,f239,f240,f241,f242,f243,f244,f245,f246,f247,f248,f249,f250,f251,f252,f257,f258,f263,f264,f269,f274,f275,f276,f277,f278,f279,f280,f281,f282,f283,f284,f285,f286,f287,f288,f289,f290,f291,f292,f293,f294,f295,f296,f297,f298])).
% 1.59/1.32 thf(f298,plain,(
% 1.59/1.32 ($true != sF3) | ($false != sF3) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f297,plain,(
% 1.59/1.32 ($true != sF8) | ($false != sF8) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f296,plain,(
% 1.59/1.32 (sF9 != $true) | (sF9 != $false) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f295,plain,(
% 1.59/1.32 (x != $false) | (x != $true) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f294,plain,(
% 1.59/1.32 (sF5 != $false) | (sF5 != $true) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f293,plain,(
% 1.59/1.32 ((f2 @ $false) != $true) | ((f2 @ $false) != $false) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f292,plain,(
% 1.59/1.32 ((f2 @ $true) != $false) | ((f2 @ $true) != $true) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f291,plain,(
% 1.59/1.32 ($true != sF1) | ($false != sF1) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f290,plain,(
% 1.59/1.32 ($false != sF0) | ($true != sF0) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f289,plain,(
% 1.59/1.32 ($true != sF6) | ($false != sF6) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f288,plain,(
% 1.59/1.32 (sF7 != $false) | (sF7 != $true) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f287,plain,(
% 1.59/1.32 ($true != sF4) | ($false != sF4) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f286,plain,(
% 1.59/1.32 ($true != sF10) | ($false != sF10) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f285,plain,(
% 1.59/1.32 ((f0 @ $false) != $false) | ((f0 @ $false) != $true) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f284,plain,(
% 1.59/1.32 ($false != (f0 @ $true)) | ($true != (f0 @ $true)) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f283,plain,(
% 1.59/1.32 ((f1 @ $false) != $true) | ((f1 @ $false) != $false) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f282,plain,(
% 1.59/1.32 ($false != (f1 @ $true)) | ($true != (f1 @ $true)) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f281,plain,(
% 1.59/1.32 ($true != sF2) | ($false != sF2) | ($true = $false)),
% 1.59/1.32 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.32 thf(f280,plain,(
% 1.59/1.32 spl11_37 | spl11_19 | spl11_35),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f21,f260,f169,f271])).
% 1.59/1.32 thf(f271,definition,(
% 1.59/1.32 spl11_37 <=> ($true = sF8)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_37])],[avatar_definition])).
% 1.59/1.32 thf(f169,definition,(
% 1.59/1.32 spl11_19 <=> ((f0 @ $false) = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_19])],[avatar_definition])).
% 1.59/1.32 thf(f260,definition,(
% 1.59/1.32 spl11_35 <=> (sF9 = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_35])],[avatar_definition])).
% 1.59/1.32 thf(f21,plain,(
% 1.59/1.32 ((f0 @ $false) = $false) | ($true = sF8) | (sF9 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.59/1.32 thf(f19,plain,(
% 1.59/1.32 ((f0 @ $false) = sF9) | ($true = sF8)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f15])).
% 1.59/1.32 thf(f15,definition,(
% 1.59/1.32 (sF9 = (f0 @ sF8))),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f279,plain,(
% 1.59/1.32 spl11_37 | spl11_18 | spl11_34),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f20,f254,f164,f271])).
% 1.59/1.32 thf(f164,definition,(
% 1.59/1.32 spl11_18 <=> ((f0 @ $false) = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_18])],[avatar_definition])).
% 1.59/1.32 thf(f254,definition,(
% 1.59/1.32 spl11_34 <=> (sF9 = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_34])],[avatar_definition])).
% 1.59/1.32 thf(f20,plain,(
% 1.59/1.32 (sF9 = $false) | ((f0 @ $false) = $true) | ($true = sF8)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.59/1.32 thf(f278,plain,(
% 1.59/1.32 spl11_15 | spl11_34 | spl11_36),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f23,f266,f254,f150])).
% 1.59/1.32 thf(f150,definition,(
% 1.59/1.32 spl11_15 <=> ($true = (f0 @ $true))),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_15])],[avatar_definition])).
% 1.59/1.32 thf(f266,definition,(
% 1.59/1.32 spl11_36 <=> ($false = sF8)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_36])],[avatar_definition])).
% 1.59/1.32 thf(f23,plain,(
% 1.59/1.32 (sF9 = $false) | ($false = sF8) | ($true = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.59/1.32 thf(f18,plain,(
% 1.59/1.32 ($false = sF8) | (sF9 = (f0 @ $true))),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f15])).
% 1.59/1.32 thf(f277,plain,(
% 1.59/1.32 spl11_35 | spl11_16 | spl11_36),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f22,f266,f155,f260])).
% 1.59/1.32 thf(f155,definition,(
% 1.59/1.32 spl11_16 <=> ($false = (f0 @ $true))),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_16])],[avatar_definition])).
% 1.59/1.32 thf(f22,plain,(
% 1.59/1.32 (sF9 = $true) | ($false = sF8) | ($false = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.59/1.32 thf(f276,plain,(
% 1.59/1.32 spl11_37 | spl11_19 | spl11_20),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f27,f174,f169,f271])).
% 1.59/1.32 thf(f174,definition,(
% 1.59/1.32 spl11_20 <=> (sF7 = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_20])],[avatar_definition])).
% 1.59/1.32 thf(f27,plain,(
% 1.59/1.32 (sF7 = $true) | ($true = sF8) | ((f0 @ $false) = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.59/1.32 thf(f25,plain,(
% 1.59/1.32 (sF7 = $true) | ((f0 @ $false) = sF8)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f14])).
% 1.59/1.32 thf(f14,definition,(
% 1.59/1.32 ((f0 @ sF7) = sF8)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f275,plain,(
% 1.59/1.32 spl11_36 | spl11_20 | spl11_18),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f26,f164,f174,f266])).
% 1.59/1.32 thf(f26,plain,(
% 1.59/1.32 ((f0 @ $false) = $true) | ($false = sF8) | (sF7 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.59/1.32 thf(f274,plain,(
% 1.59/1.32 spl11_16 | spl11_37 | spl11_22),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f29,f183,f271,f155])).
% 1.59/1.32 thf(f183,definition,(
% 1.59/1.32 spl11_22 <=> (sF7 = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_22])],[avatar_definition])).
% 1.59/1.32 thf(f29,plain,(
% 1.59/1.32 (sF7 = $false) | ($true = sF8) | ($false = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.59/1.32 thf(f24,plain,(
% 1.59/1.32 (sF7 = $false) | ((f0 @ $true) = sF8)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f14])).
% 1.59/1.32 thf(f269,plain,(
% 1.59/1.32 spl11_22 | spl11_15 | spl11_36),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f28,f266,f150,f183])).
% 1.59/1.32 thf(f28,plain,(
% 1.59/1.32 ($false = sF8) | ($true = (f0 @ $true)) | (sF7 = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.59/1.32 thf(f264,plain,(
% 1.59/1.32 spl11_19 | spl11_35 | spl11_2),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f33,f91,f260,f169])).
% 1.59/1.32 thf(f91,definition,(
% 1.59/1.32 spl11_2 <=> ($true = sF10)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.59/1.32 thf(f33,plain,(
% 1.59/1.32 (sF9 = $true) | ($true = sF10) | ((f0 @ $false) = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.59/1.32 thf(f31,plain,(
% 1.59/1.32 ((f0 @ $false) = sF10) | (sF9 = $true)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f16])).
% 1.59/1.32 thf(f16,definition,(
% 1.59/1.32 (sF10 = (f0 @ sF9))),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f263,plain,(
% 1.59/1.32 spl11_18 | spl11_35 | spl11_4),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f32,f100,f260,f164])).
% 1.59/1.32 thf(f100,definition,(
% 1.59/1.32 spl11_4 <=> ($false = sF10)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.59/1.32 thf(f32,plain,(
% 1.59/1.32 ($false = sF10) | ((f0 @ $false) = $true) | (sF9 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.59/1.32 thf(f258,plain,(
% 1.59/1.32 spl11_2 | spl11_34 | spl11_16),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f35,f155,f254,f91])).
% 1.59/1.32 thf(f35,plain,(
% 1.59/1.32 (sF9 = $false) | ($true = sF10) | ($false = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.59/1.32 thf(f30,plain,(
% 1.59/1.32 (sF9 = $false) | ((f0 @ $true) = sF10)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f16])).
% 1.59/1.32 thf(f257,plain,(
% 1.59/1.32 spl11_34 | spl11_4 | spl11_15),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f34,f150,f100,f254])).
% 1.59/1.32 thf(f34,plain,(
% 1.59/1.32 (sF9 = $false) | ($false = sF10) | ($true = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.59/1.32 thf(f252,plain,(
% 1.59/1.32 spl11_12 | spl11_11 | spl11_27),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f39,f207,f131,f136])).
% 1.59/1.32 thf(f136,definition,(
% 1.59/1.32 spl11_12 <=> ((f1 @ $false) = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_12])],[avatar_definition])).
% 1.59/1.32 thf(f131,definition,(
% 1.59/1.32 spl11_11 <=> ($true = sF1)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_11])],[avatar_definition])).
% 1.59/1.32 thf(f207,definition,(
% 1.59/1.32 spl11_27 <=> ($true = sF0)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_27])],[avatar_definition])).
% 1.59/1.32 thf(f39,plain,(
% 1.59/1.32 ((f1 @ $false) = $false) | ($true = sF1) | ($true = sF0)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.59/1.32 thf(f37,plain,(
% 1.59/1.32 ($true = sF0) | ((f1 @ $false) = sF1)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f7])).
% 1.59/1.32 thf(f7,definition,(
% 1.59/1.32 (sF1 = (f1 @ sF0))),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f251,plain,(
% 1.59/1.32 spl11_27 | spl11_7 | spl11_10),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f38,f127,f113,f207])).
% 1.59/1.32 thf(f113,definition,(
% 1.59/1.32 spl11_7 <=> ($false = sF1)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition])).
% 1.59/1.32 thf(f127,definition,(
% 1.59/1.32 spl11_10 <=> ((f1 @ $false) = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_10])],[avatar_definition])).
% 1.59/1.32 thf(f38,plain,(
% 1.59/1.32 ($true = sF0) | ((f1 @ $false) = $true) | ($false = sF1)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.59/1.32 thf(f250,plain,(
% 1.59/1.32 spl11_11 | spl11_24 | spl11_9),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f41,f122,f194,f131])).
% 1.59/1.32 thf(f194,definition,(
% 1.59/1.32 spl11_24 <=> ($false = sF0)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_24])],[avatar_definition])).
% 1.59/1.32 thf(f122,definition,(
% 1.59/1.32 spl11_9 <=> ($false = (f1 @ $true))),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition])).
% 1.59/1.32 thf(f41,plain,(
% 1.59/1.32 ($true = sF1) | ($false = (f1 @ $true)) | ($false = sF0)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.59/1.32 thf(f36,plain,(
% 1.59/1.32 ($false = sF0) | ((f1 @ $true) = sF1)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f7])).
% 1.59/1.32 thf(f249,plain,(
% 1.59/1.32 spl11_7 | spl11_24 | spl11_6),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f40,f109,f194,f113])).
% 1.59/1.32 thf(f109,definition,(
% 1.59/1.32 spl11_6 <=> ($true = (f1 @ $true))),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.59/1.32 thf(f40,plain,(
% 1.59/1.32 ($false = sF0) | ($true = (f1 @ $true)) | ($false = sF1)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.59/1.32 thf(f248,plain,(
% 1.59/1.32 spl11_27 | spl11_30 | spl11_32),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f45,f230,f220,f207])).
% 1.59/1.32 thf(f220,definition,(
% 1.59/1.32 spl11_30 <=> ((f2 @ $false) = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_30])],[avatar_definition])).
% 1.59/1.32 thf(f230,definition,(
% 1.59/1.32 spl11_32 <=> (sF5 = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_32])],[avatar_definition])).
% 1.59/1.32 thf(f45,plain,(
% 1.59/1.32 ((f2 @ $false) = $true) | (sF5 = $false) | ($true = sF0)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.59/1.32 thf(f43,plain,(
% 1.59/1.32 ($true = sF0) | (sF5 = (f2 @ $false))),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f11])).
% 1.59/1.32 thf(f11,definition,(
% 1.59/1.32 (sF5 = (f2 @ sF0))),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f247,plain,(
% 1.59/1.32 spl11_27 | spl11_31 | spl11_33),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f44,f236,f225,f207])).
% 1.59/1.32 thf(f225,definition,(
% 1.59/1.32 spl11_31 <=> ((f2 @ $false) = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_31])],[avatar_definition])).
% 1.59/1.32 thf(f236,definition,(
% 1.59/1.32 spl11_33 <=> (sF5 = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_33])],[avatar_definition])).
% 1.59/1.32 thf(f44,plain,(
% 1.59/1.32 ((f2 @ $false) = $false) | ($true = sF0) | (sF5 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.59/1.32 thf(f246,plain,(
% 1.59/1.32 spl11_26 | spl11_32 | spl11_24),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f47,f194,f230,f202])).
% 1.59/1.32 thf(f202,definition,(
% 1.59/1.32 spl11_26 <=> ((f2 @ $true) = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_26])],[avatar_definition])).
% 1.59/1.32 thf(f47,plain,(
% 1.59/1.32 ($false = sF0) | ((f2 @ $true) = $true) | (sF5 = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.59/1.32 thf(f42,plain,(
% 1.59/1.32 ($false = sF0) | (sF5 = (f2 @ $true))),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f11])).
% 1.59/1.32 thf(f245,plain,(
% 1.59/1.32 spl11_28 | spl11_33 | spl11_24),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f46,f194,f236,f211])).
% 1.59/1.32 thf(f211,definition,(
% 1.59/1.32 spl11_28 <=> ((f2 @ $true) = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_28])],[avatar_definition])).
% 1.59/1.32 thf(f46,plain,(
% 1.59/1.32 ((f2 @ $true) = $false) | (sF5 = $true) | ($false = sF0)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.59/1.32 thf(f244,plain,(
% 1.59/1.32 spl11_12 | spl11_8 | spl11_17),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f51,f160,f118,f136])).
% 1.59/1.32 thf(f118,definition,(
% 1.59/1.32 spl11_8 <=> ($true = sF2)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition])).
% 1.59/1.32 thf(f160,definition,(
% 1.59/1.32 spl11_17 <=> ($true = sF3)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_17])],[avatar_definition])).
% 1.59/1.32 thf(f51,plain,(
% 1.59/1.32 ((f1 @ $false) = $false) | ($true = sF2) | ($true = sF3)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.59/1.32 thf(f49,plain,(
% 1.59/1.32 ($true = sF2) | ((f1 @ $false) = sF3)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f9])).
% 1.59/1.32 thf(f9,definition,(
% 1.59/1.32 ((f1 @ sF2) = sF3)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f243,plain,(
% 1.59/1.32 spl11_8 | spl11_14 | spl11_10),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f50,f127,f146,f118])).
% 1.59/1.32 thf(f146,definition,(
% 1.59/1.32 spl11_14 <=> ($false = sF3)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_14])],[avatar_definition])).
% 1.59/1.32 thf(f50,plain,(
% 1.59/1.32 ($true = sF2) | ((f1 @ $false) = $true) | ($false = sF3)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.59/1.32 thf(f242,plain,(
% 1.59/1.32 spl11_17 | spl11_9 | spl11_5),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f53,f105,f122,f160])).
% 1.59/1.32 thf(f105,definition,(
% 1.59/1.32 spl11_5 <=> ($false = sF2)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.59/1.32 thf(f53,plain,(
% 1.59/1.32 ($false = sF2) | ($true = sF3) | ($false = (f1 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.59/1.32 thf(f48,plain,(
% 1.59/1.32 ($false = sF2) | ((f1 @ $true) = sF3)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f9])).
% 1.59/1.32 thf(f241,plain,(
% 1.59/1.32 spl11_6 | spl11_5 | spl11_14),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f52,f146,f105,f109])).
% 1.59/1.32 thf(f52,plain,(
% 1.59/1.32 ($true = (f1 @ $true)) | ($false = sF3) | ($false = sF2)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.59/1.32 thf(f240,plain,(
% 1.59/1.32 spl11_23 | spl11_33 | spl11_31),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f57,f225,f236,f188])).
% 1.59/1.32 thf(f188,definition,(
% 1.59/1.32 spl11_23 <=> ($true = sF6)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_23])],[avatar_definition])).
% 1.59/1.32 thf(f57,plain,(
% 1.59/1.32 ($true = sF6) | ((f2 @ $false) = $false) | (sF5 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.59/1.32 thf(f55,plain,(
% 1.59/1.32 (sF5 = $true) | ((f2 @ $false) = sF6)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f12])).
% 1.59/1.32 thf(f12,definition,(
% 1.59/1.32 ((f2 @ sF5) = sF6)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f239,plain,(
% 1.59/1.32 spl11_30 | spl11_21 | spl11_33),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f56,f236,f178,f220])).
% 1.59/1.32 thf(f178,definition,(
% 1.59/1.32 spl11_21 <=> ($false = sF6)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_21])],[avatar_definition])).
% 1.59/1.32 thf(f56,plain,(
% 1.59/1.32 ($false = sF6) | (sF5 = $true) | ((f2 @ $false) = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.59/1.32 thf(f234,plain,(
% 1.59/1.32 spl11_28 | spl11_32 | spl11_23),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f59,f188,f230,f211])).
% 1.59/1.32 thf(f59,plain,(
% 1.59/1.32 (sF5 = $false) | ($true = sF6) | ((f2 @ $true) = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.59/1.32 thf(f54,plain,(
% 1.59/1.32 ((f2 @ $true) = sF6) | (sF5 = $false)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f12])).
% 1.59/1.32 thf(f233,plain,(
% 1.59/1.32 spl11_26 | spl11_21 | spl11_32),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f58,f230,f178,f202])).
% 1.59/1.32 thf(f58,plain,(
% 1.59/1.32 ((f2 @ $true) = $true) | (sF5 = $false) | ($false = sF6)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.59/1.32 thf(f228,plain,(
% 1.59/1.32 spl11_31 | spl11_27 | spl11_29),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f63,f216,f207,f225])).
% 1.59/1.32 thf(f216,definition,(
% 1.59/1.32 spl11_29 <=> (x = $true)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_29])],[avatar_definition])).
% 1.59/1.32 thf(f63,plain,(
% 1.59/1.32 (x = $true) | ($true = sF0) | ((f2 @ $false) = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.59/1.32 thf(f61,plain,(
% 1.59/1.32 (x = $true) | ((f2 @ $false) = sF0)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f6])).
% 1.59/1.32 thf(f6,definition,(
% 1.59/1.32 ((f2 @ x) = sF0)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f223,plain,(
% 1.59/1.32 spl11_29 | spl11_30 | spl11_24),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f62,f194,f220,f216])).
% 1.59/1.32 thf(f62,plain,(
% 1.59/1.32 ($false = sF0) | ((f2 @ $false) = $true) | (x = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.59/1.32 thf(f214,plain,(
% 1.59/1.32 spl11_27 | spl11_25 | spl11_28),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f65,f211,f198,f207])).
% 1.59/1.32 thf(f198,definition,(
% 1.59/1.32 spl11_25 <=> (x = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_25])],[avatar_definition])).
% 1.59/1.32 thf(f65,plain,(
% 1.59/1.32 ($true = sF0) | (x = $false) | ((f2 @ $true) = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.59/1.32 thf(f60,plain,(
% 1.59/1.32 ((f2 @ $true) = sF0) | (x = $false)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f6])).
% 1.59/1.32 thf(f205,plain,(
% 1.59/1.32 spl11_24 | spl11_25 | spl11_26),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f64,f202,f198,f194])).
% 1.59/1.32 thf(f64,plain,(
% 1.59/1.32 (x = $false) | ((f2 @ $true) = $true) | ($false = sF0)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.59/1.32 thf(f192,plain,(
% 1.59/1.32 spl11_12 | spl11_23 | spl11_20),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f69,f174,f188,f136])).
% 1.59/1.32 thf(f69,plain,(
% 1.59/1.32 ($true = sF6) | ((f1 @ $false) = $false) | (sF7 = $true)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.59/1.32 thf(f67,plain,(
% 1.59/1.32 ($true = sF6) | ((f1 @ $false) = sF7)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f13])).
% 1.59/1.32 thf(f13,definition,(
% 1.59/1.32 ((f1 @ sF6) = sF7)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f191,plain,(
% 1.59/1.32 spl11_10 | spl11_22 | spl11_23),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f68,f188,f183,f127])).
% 1.59/1.32 thf(f68,plain,(
% 1.59/1.32 ($true = sF6) | ((f1 @ $false) = $true) | (sF7 = $false)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.59/1.32 thf(f186,plain,(
% 1.59/1.32 spl11_21 | spl11_22 | spl11_6),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f71,f109,f183,f178])).
% 1.59/1.32 thf(f71,plain,(
% 1.59/1.32 ($true = (f1 @ $true)) | (sF7 = $false) | ($false = sF6)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.59/1.32 thf(f66,plain,(
% 1.59/1.32 ($false = sF6) | (sF7 = (f1 @ $true))),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f13])).
% 1.59/1.32 thf(f181,plain,(
% 1.59/1.32 spl11_20 | spl11_21 | spl11_9),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f70,f122,f178,f174])).
% 1.59/1.32 thf(f70,plain,(
% 1.59/1.32 ($false = (f1 @ $true)) | (sF7 = $true) | ($false = sF6)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.59/1.32 thf(f172,plain,(
% 1.59/1.32 spl11_1 | spl11_19 | spl11_17),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f75,f160,f169,f87])).
% 1.59/1.32 thf(f87,definition,(
% 1.59/1.32 spl11_1 <=> ($true = sF4)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 1.59/1.32 thf(f75,plain,(
% 1.59/1.32 ((f0 @ $false) = $false) | ($true = sF3) | ($true = sF4)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.59/1.32 thf(f73,plain,(
% 1.59/1.32 ((f0 @ $false) = sF4) | ($true = sF3)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f10])).
% 1.59/1.32 thf(f10,definition,(
% 1.59/1.32 ((f0 @ sF3) = sF4)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f167,plain,(
% 1.59/1.32 spl11_3 | spl11_17 | spl11_18),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f74,f164,f160,f96])).
% 1.59/1.32 thf(f96,definition,(
% 1.59/1.32 spl11_3 <=> ($false = sF4)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.59/1.32 thf(f74,plain,(
% 1.59/1.32 ($true = sF3) | ((f0 @ $false) = $true) | ($false = sF4)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.59/1.32 thf(f158,plain,(
% 1.59/1.32 spl11_1 | spl11_16 | spl11_14),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f77,f146,f155,f87])).
% 1.59/1.32 thf(f77,plain,(
% 1.59/1.32 ($false = sF3) | ($true = sF4) | ($false = (f0 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.59/1.32 thf(f72,plain,(
% 1.59/1.32 ((f0 @ $true) = sF4) | ($false = sF3)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f10])).
% 1.59/1.32 thf(f153,plain,(
% 1.59/1.32 spl11_3 | spl11_14 | spl11_15),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f76,f150,f146,f96])).
% 1.59/1.32 thf(f76,plain,(
% 1.59/1.32 ($true = (f0 @ $true)) | ($false = sF3) | ($false = sF4)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.59/1.32 thf(f144,plain,(
% 1.59/1.32 ~spl11_13),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f3,f141])).
% 1.59/1.32 thf(f141,definition,(
% 1.59/1.32 spl11_13 <=> ($true = $false)),
% 1.59/1.32 introduced(definition,[new_symbols(naming,[spl11_13])],[avatar_definition])).
% 1.59/1.32 thf(f3,plain,(
% 1.59/1.32 ($true != $false)),
% 1.59/1.32 introduced(definition,[],[fool_axiom])).
% 1.59/1.32 thf(f139,plain,(
% 1.59/1.32 spl11_8 | spl11_11 | spl11_12),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f81,f136,f131,f118])).
% 1.59/1.32 thf(f81,plain,(
% 1.59/1.32 ($true = sF1) | ((f1 @ $false) = $false) | ($true = sF2)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.59/1.32 thf(f79,plain,(
% 1.59/1.32 ($true = sF1) | ((f1 @ $false) = sF2)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f8])).
% 1.59/1.32 thf(f8,definition,(
% 1.59/1.32 ((f1 @ sF1) = sF2)),
% 1.59/1.32 introduced(definition,[],[function_definition])).
% 1.59/1.32 thf(f134,plain,(
% 1.59/1.32 spl11_5 | spl11_10 | spl11_11),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f80,f131,f127,f105])).
% 1.59/1.32 thf(f80,plain,(
% 1.59/1.32 ((f1 @ $false) = $true) | ($false = sF2) | ($true = sF1)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.59/1.32 thf(f125,plain,(
% 1.59/1.32 spl11_8 | spl11_9 | spl11_7),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f83,f113,f122,f118])).
% 1.59/1.32 thf(f83,plain,(
% 1.59/1.32 ($false = sF1) | ($true = sF2) | ($false = (f1 @ $true))),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.59/1.32 thf(f78,plain,(
% 1.59/1.32 ($false = sF1) | ((f1 @ $true) = sF2)),
% 1.59/1.32 inference(cases_simplifying,[status(thm)],[f8])).
% 1.59/1.32 thf(f116,plain,(
% 1.59/1.32 spl11_5 | spl11_6 | spl11_7),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f82,f113,f109,f105])).
% 1.59/1.32 thf(f82,plain,(
% 1.59/1.32 ($false = sF2) | ($true = (f1 @ $true)) | ($false = sF1)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.59/1.32 thf(f103,plain,(
% 1.59/1.32 spl11_3 | spl11_4),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f85,f100,f96])).
% 1.59/1.32 thf(f85,plain,(
% 1.59/1.32 ($false = sF10) | ($false = sF4)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.59/1.32 thf(f17,plain,(
% 1.59/1.32 (sF4 != sF10)),
% 1.59/1.32 inference(definition_folding,[status(thm)],[f5,f16,f15,f14,f13,f12,f11,f6,f10,f9,f8,f7,f6])).
% 1.59/1.32 thf(f5,plain,(
% 1.59/1.32 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ x))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ x))))))))),
% 1.59/1.32 inference(cnf_transformation,[status(thm)],[f4])).
% 1.59/1.32 thf(f4,plain,(
% 1.59/1.32 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ x))))) != (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ x))))))))),
% 1.59/1.32 inference(flattening,[status(thm)],[f2])).
% 1.59/1.32 thf(f2,negated_conjecture,(
% 1.59/1.32 ~((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ x))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ x))))))))),
% 1.59/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.32 thf(f1,conjecture,(
% 1.59/1.32 ((f0 @ (f1 @ (f1 @ (f1 @ (f2 @ x))))) = (f0 @ (f0 @ (f0 @ (f1 @ (f2 @ (f2 @ (f2 @ x))))))))),
% 1.59/1.32 file('/export/starexec/sandbox/tmp/tmp.yCfNfVysf7/DTF2THF_6054.p',kaminski3)).
% 1.59/1.32 thf(f94,plain,(
% 1.59/1.32 spl11_1 | spl11_2),
% 1.59/1.32 inference(avatar_split_clause,[status(thm)],[f84,f91,f87])).
% 1.59/1.32 thf(f84,plain,(
% 1.59/1.32 ($true = sF4) | ($true = sF10)),
% 1.59/1.32 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.59/1.32 % SZS output end Proof for DTF2THF_6054
% 1.59/1.32 % (6387)------------------------------
% 1.59/1.32 % (6387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6387)Termination reason: Refutation
% 1.59/1.32
% 1.59/1.32 % (6387)Memory used [KB]: 5628
% 1.59/1.32 % (6387)Time elapsed: 0.007 s
% 1.59/1.32 % (6387)Instructions burned: 5 (million)
% 1.59/1.32 % (6387)------------------------------
% 1.59/1.32 % (6387)------------------------------
% 1.59/1.32 % (6373)Success in time 0.047 s
%------------------------------------------------------------------------------