%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN036^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.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 09:50:23 AM UTC 2026
% Result : Theorem 0.27s 1.36s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 59
% Syntax : Number of formulae : 240 ( 1 unt; 0 typ; 33 def)
% Number of atoms : 1863 ( 458 equ; 0 cnn)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 1472 ( 363 ~; 460 |; 42 &; 513 @)
% ( 68 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 56 con; 0-2 aty)
% Number of variables : 316 ( 0 ^; 220 !; 96 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(func_def_14,type,
sK9: $i > $i ).
thf(func_def_18,type,
sK13: $i > $i ).
thf(func_def_26,type,
sK21: $i > $i ).
thf(f643,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f106,f121,f136,f148,f156,f171,f176,f187,f207,f213,f218,f219,f220,f241,f258,f259,f260,f264,f267,f269,f271,f281,f283,f307,f314,f316,f324,f330,f336,f338,f344,f352,f358,f369,f379,f394,f400,f406,f462,f480,f498,f510,f583,f589,f605,f611,f636,f642]) ).
thf(f642,plain,
( ~ spl25_3
| ~ spl25_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f641]) ).
thf(f641,plain,
( $false
| ~ spl25_3
| ~ spl25_18 ),
inference(trivial_inequality_removal,[status(thm)],[f637]) ).
thf(f637,plain,
( ( $true = $false )
| ~ spl25_3
| ~ spl25_18 ),
inference(superposition,[status(thm)],[f97,f155]) ).
thf(f155,plain,
( ! [X19: $i] :
( $false
= ( cQ @ X19 ) )
| ~ spl25_18 ),
inference(avatar_component_clause,[status(thm)],[f154]) ).
thf(f154,definition,
( spl25_18
<=> ! [X19: $i] :
( $false
= ( cQ @ X19 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_18])],[avatar_definition]) ).
thf(f97,plain,
( ( $true
= ( cQ @ sK19 ) )
| ~ spl25_3 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl25_3
<=> ( $true
= ( cQ @ sK19 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition]) ).
thf(f636,plain,
( spl25_19
| ~ spl25_2
| ~ spl25_21 ),
inference(avatar_split_clause,[status(thm)],[f633,f165,f92,f158]) ).
thf(f158,definition,
( spl25_19
<=> ! [X22: $i] :
( $true
= ( cP @ X22 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_19])],[avatar_definition]) ).
thf(f92,definition,
( spl25_2
<=> ! [X16: $i] :
( ( $true
= ( cP @ X16 ) )
| ( $true
= ( cP @ ( sK21 @ X16 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition]) ).
thf(f165,definition,
( spl25_21
<=> ! [X19: $i] :
( $false
= ( cP @ X19 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_21])],[avatar_definition]) ).
thf(f633,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl25_2
| ~ spl25_21 ),
inference(trivial_inequality_removal,[status(thm)],[f631]) ).
thf(f631,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl25_2
| ~ spl25_21 ),
inference(superposition,[status(thm)],[f93,f166]) ).
thf(f166,plain,
( ! [X19: $i] :
( $false
= ( cP @ X19 ) )
| ~ spl25_21 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f93,plain,
( ! [X16: $i] :
( ( $true
= ( cP @ ( sK21 @ X16 ) ) )
| ( $true
= ( cP @ X16 ) ) )
| ~ spl25_2 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f611,plain,
( ~ spl25_28
| ~ spl25_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f610]) ).
thf(f610,plain,
( $false
| ~ spl25_28
| ~ spl25_29 ),
inference(trivial_inequality_removal,[status(thm)],[f607]) ).
thf(f607,plain,
( ( $true = $false )
| ~ spl25_28
| ~ spl25_29 ),
inference(superposition,[status(thm)],[f200,f205]) ).
thf(f205,plain,
( ( $false
= ( cQ @ sK4 ) )
| ~ spl25_29 ),
inference(avatar_component_clause,[status(thm)],[f203]) ).
thf(f203,definition,
( spl25_29
<=> ( $false
= ( cQ @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_29])],[avatar_definition]) ).
thf(f200,plain,
( ( $true
= ( cQ @ sK4 ) )
| ~ spl25_28 ),
inference(avatar_component_clause,[status(thm)],[f198]) ).
thf(f198,definition,
( spl25_28
<=> ( $true
= ( cQ @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_28])],[avatar_definition]) ).
thf(f605,plain,
( ~ spl25_21
| ~ spl25_35 ),
inference(avatar_contradiction_clause,[status(thm)],[f604]) ).
thf(f604,plain,
( $false
| ~ spl25_21
| ~ spl25_35 ),
inference(trivial_inequality_removal,[status(thm)],[f600]) ).
thf(f600,plain,
( ( $true = $false )
| ~ spl25_21
| ~ spl25_35 ),
inference(superposition,[status(thm)],[f240,f166]) ).
thf(f240,plain,
( ( $true
= ( cP @ sK3 ) )
| ~ spl25_35 ),
inference(avatar_component_clause,[status(thm)],[f238]) ).
thf(f238,definition,
( spl25_35
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_35])],[avatar_definition]) ).
thf(f589,plain,
( ~ spl25_20
| ~ spl25_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f588]) ).
thf(f588,plain,
( $false
| ~ spl25_20
| ~ spl25_23 ),
inference(trivial_inequality_removal,[status(thm)],[f585]) ).
thf(f585,plain,
( ( $true = $false )
| ~ spl25_20
| ~ spl25_23 ),
inference(superposition,[status(thm)],[f175,f163]) ).
thf(f163,plain,
( ( $true
= ( cP @ sK22 ) )
| ~ spl25_20 ),
inference(avatar_component_clause,[status(thm)],[f161]) ).
thf(f161,definition,
( spl25_20
<=> ( $true
= ( cP @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_20])],[avatar_definition]) ).
thf(f175,plain,
( ( $false
= ( cP @ sK22 ) )
| ~ spl25_23 ),
inference(avatar_component_clause,[status(thm)],[f173]) ).
thf(f173,definition,
( spl25_23
<=> ( $false
= ( cP @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_23])],[avatar_definition]) ).
thf(f583,plain,
( ~ spl25_10
| ~ spl25_37 ),
inference(avatar_contradiction_clause,[status(thm)],[f582]) ).
thf(f582,plain,
( $false
| ~ spl25_10
| ~ spl25_37 ),
inference(subsumption_resolution,[status(thm)],[f573,f124]) ).
thf(f124,plain,
( ! [X3: $i] :
( $true
!= ( cQ @ X3 ) )
| ~ spl25_10 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl25_10
<=> ! [X3: $i] :
( $true
!= ( cQ @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_10])],[avatar_definition]) ).
thf(f573,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ~ spl25_10
| ~ spl25_37 ),
inference(trivial_inequality_removal,[status(thm)],[f571]) ).
thf(f571,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl25_10
| ~ spl25_37 ),
inference(superposition,[status(thm)],[f124,f249]) ).
thf(f249,plain,
( ! [X16: $i] :
( ( $true
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $true
= ( cQ @ X16 ) ) )
| ~ spl25_37 ),
inference(avatar_component_clause,[status(thm)],[f248]) ).
thf(f248,definition,
( spl25_37
<=> ! [X16: $i] :
( ( $true
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $true
= ( cQ @ X16 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_37])],[avatar_definition]) ).
thf(f510,plain,
( spl25_19
| ~ spl25_11
| ~ spl25_21 ),
inference(avatar_split_clause,[status(thm)],[f505,f165,f126,f158]) ).
thf(f126,definition,
( spl25_11
<=> ! [X0: $i] :
( ( ( cP @ ( sK13 @ X0 ) )
= $true )
| ( ( cP @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl25_11])],[avatar_definition]) ).
thf(f505,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl25_11
| ~ spl25_21 ),
inference(trivial_inequality_removal,[status(thm)],[f502]) ).
thf(f502,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( cP @ X0 )
= $true ) )
| ~ spl25_11
| ~ spl25_21 ),
inference(superposition,[status(thm)],[f127,f166]) ).
thf(f127,plain,
( ! [X0: $i] :
( ( ( cP @ ( sK13 @ X0 ) )
= $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl25_11 ),
inference(avatar_component_clause,[status(thm)],[f126]) ).
thf(f498,plain,
( ~ spl25_21
| ~ spl25_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f497]) ).
thf(f497,plain,
( $false
| ~ spl25_21
| ~ spl25_36 ),
inference(trivial_inequality_removal,[status(thm)],[f493]) ).
thf(f493,plain,
( ( $true = $false )
| ~ spl25_21
| ~ spl25_36 ),
inference(superposition,[status(thm)],[f246,f166]) ).
thf(f246,plain,
( ( ( cP @ sK7 )
= $true )
| ~ spl25_36 ),
inference(avatar_component_clause,[status(thm)],[f244]) ).
thf(f244,definition,
( spl25_36
<=> ( ( cP @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_36])],[avatar_definition]) ).
thf(f480,plain,
( ~ spl25_18
| ~ spl25_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f479]) ).
thf(f479,plain,
( $false
| ~ spl25_18
| ~ spl25_25 ),
inference(trivial_inequality_removal,[status(thm)],[f447]) ).
thf(f447,plain,
( ( $true = $false )
| ~ spl25_18
| ~ spl25_25 ),
inference(superposition,[status(thm)],[f155,f186]) ).
thf(f186,plain,
( ( ( cQ @ sK15 )
= $true )
| ~ spl25_25 ),
inference(avatar_component_clause,[status(thm)],[f184]) ).
thf(f184,definition,
( spl25_25
<=> ( ( cQ @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_25])],[avatar_definition]) ).
thf(f462,plain,
( ~ spl25_18
| ~ spl25_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f461]) ).
thf(f461,plain,
( $false
| ~ spl25_18
| ~ spl25_22 ),
inference(trivial_inequality_removal,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $true = $false )
| ~ spl25_18
| ~ spl25_22 ),
inference(superposition,[status(thm)],[f170,f155]) ).
thf(f170,plain,
( ( $true
= ( cQ @ sK24 ) )
| ~ spl25_22 ),
inference(avatar_component_clause,[status(thm)],[f168]) ).
thf(f168,definition,
( spl25_22
<=> ( $true
= ( cQ @ sK24 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_22])],[avatar_definition]) ).
thf(f406,plain,
( spl25_21
| ~ spl25_13
| ~ spl25_19 ),
inference(avatar_split_clause,[status(thm)],[f403,f158,f134,f165]) ).
thf(f134,definition,
( spl25_13
<=> ! [X0: $i] :
( ( ( cP @ ( sK13 @ X0 ) )
= $false )
| ( ( cP @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl25_13])],[avatar_definition]) ).
thf(f403,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $false )
| ~ spl25_13
| ~ spl25_19 ),
inference(trivial_inequality_removal,[status(thm)],[f401]) ).
thf(f401,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl25_13
| ~ spl25_19 ),
inference(superposition,[status(thm)],[f135,f159]) ).
thf(f159,plain,
( ! [X22: $i] :
( $true
= ( cP @ X22 ) )
| ~ spl25_19 ),
inference(avatar_component_clause,[status(thm)],[f158]) ).
thf(f135,plain,
( ! [X0: $i] :
( ( ( cP @ ( sK13 @ X0 ) )
= $false )
| ( ( cP @ X0 )
= $false ) )
| ~ spl25_13 ),
inference(avatar_component_clause,[status(thm)],[f134]) ).
thf(f400,plain,
( spl25_21
| ~ spl25_5
| ~ spl25_19 ),
inference(avatar_split_clause,[status(thm)],[f397,f158,f104,f165]) ).
thf(f104,definition,
( spl25_5
<=> ! [X16: $i] :
( ( $false
= ( cP @ X16 ) )
| ( $false
= ( cP @ ( sK21 @ X16 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_5])],[avatar_definition]) ).
thf(f397,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $false )
| ~ spl25_5
| ~ spl25_19 ),
inference(trivial_inequality_removal,[status(thm)],[f395]) ).
thf(f395,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( cP @ X0 )
= $false ) )
| ~ spl25_5
| ~ spl25_19 ),
inference(superposition,[status(thm)],[f105,f159]) ).
thf(f105,plain,
( ! [X16: $i] :
( ( $false
= ( cP @ ( sK21 @ X16 ) ) )
| ( $false
= ( cP @ X16 ) ) )
| ~ spl25_5 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f394,plain,
( ~ spl25_19
| spl25_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f393]) ).
thf(f393,plain,
( $false
| ~ spl25_19
| spl25_36 ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ( $true != $true )
| ~ spl25_19
| spl25_36 ),
inference(superposition,[status(thm)],[f245,f159]) ).
thf(f245,plain,
( ( ( cP @ sK7 )
!= $true )
| spl25_36 ),
inference(avatar_component_clause,[status(thm)],[f244]) ).
thf(f379,plain,
( spl25_12
| ~ spl25_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f378]) ).
thf(f378,plain,
( $false
| spl25_12
| ~ spl25_19 ),
inference(trivial_inequality_removal,[status(thm)],[f361]) ).
thf(f361,plain,
( ( $true != $true )
| spl25_12
| ~ spl25_19 ),
inference(superposition,[status(thm)],[f131,f159]) ).
thf(f131,plain,
( ( $true
!= ( cP @ sK14 ) )
| spl25_12 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl25_12
<=> ( $true
= ( cP @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_12])],[avatar_definition]) ).
thf(f369,plain,
( spl25_4
| ~ spl25_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f368]) ).
thf(f368,plain,
( $false
| spl25_4
| ~ spl25_19 ),
inference(trivial_inequality_removal,[status(thm)],[f363]) ).
thf(f363,plain,
( ( $true != $true )
| spl25_4
| ~ spl25_19 ),
inference(superposition,[status(thm)],[f101,f159]) ).
thf(f101,plain,
( ( $true
!= ( cP @ sK20 ) )
| spl25_4 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl25_4
<=> ( $true
= ( cP @ sK20 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition]) ).
thf(f358,plain,
( ~ spl25_30
| ~ spl25_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f357]) ).
thf(f357,plain,
( $false
| ~ spl25_30
| ~ spl25_31 ),
inference(trivial_inequality_removal,[status(thm)],[f353]) ).
thf(f353,plain,
( ( $true = $false )
| ~ spl25_30
| ~ spl25_31 ),
inference(superposition,[status(thm)],[f217,f212]) ).
thf(f212,plain,
( ( $true
= ( cP @ sK16 ) )
| ~ spl25_30 ),
inference(avatar_component_clause,[status(thm)],[f210]) ).
thf(f210,definition,
( spl25_30
<=> ( $true
= ( cP @ sK16 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_30])],[avatar_definition]) ).
thf(f217,plain,
( ( $false
= ( cP @ sK16 ) )
| ~ spl25_31 ),
inference(avatar_component_clause,[status(thm)],[f215]) ).
thf(f215,definition,
( spl25_31
<=> ( $false
= ( cP @ sK16 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_31])],[avatar_definition]) ).
thf(f352,plain,
( ~ spl25_14
| ~ spl25_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f351]) ).
thf(f351,plain,
( $false
| ~ spl25_14
| ~ spl25_21 ),
inference(trivial_inequality_removal,[status(thm)],[f348]) ).
thf(f348,plain,
( ( $true = $false )
| ~ spl25_14
| ~ spl25_21 ),
inference(superposition,[status(thm)],[f166,f140]) ).
thf(f140,plain,
( ( $true
= ( cP @ sK12 ) )
| ~ spl25_14 ),
inference(avatar_component_clause,[status(thm)],[f138]) ).
thf(f138,definition,
( spl25_14
<=> ( $true
= ( cP @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_14])],[avatar_definition]) ).
thf(f344,plain,
( ~ spl25_16
| ~ spl25_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f343]) ).
thf(f343,plain,
( $false
| ~ spl25_16
| ~ spl25_17 ),
inference(trivial_inequality_removal,[status(thm)],[f340]) ).
thf(f340,plain,
( ( $true = $false )
| ~ spl25_16
| ~ spl25_17 ),
inference(superposition,[status(thm)],[f147,f152]) ).
thf(f152,plain,
( ( $true
= ( cQ @ sK10 ) )
| ~ spl25_17 ),
inference(avatar_component_clause,[status(thm)],[f150]) ).
thf(f150,definition,
( spl25_17
<=> ( $true
= ( cQ @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_17])],[avatar_definition]) ).
thf(f147,plain,
( ( $false
= ( cQ @ sK10 ) )
| ~ spl25_16 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl25_16
<=> ( $false
= ( cQ @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_16])],[avatar_definition]) ).
thf(f338,plain,
( ~ spl25_7
| ~ spl25_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f337]) ).
thf(f337,plain,
( $false
| ~ spl25_7
| ~ spl25_14 ),
inference(subsumption_resolution,[status(thm)],[f140,f112]) ).
thf(f112,plain,
( ! [X3: $i] :
( $true
!= ( cP @ X3 ) )
| ~ spl25_7 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f111,definition,
( spl25_7
<=> ! [X3: $i] :
( $true
!= ( cP @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_7])],[avatar_definition]) ).
thf(f336,plain,
( ~ spl25_15
| ~ spl25_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f335]) ).
thf(f335,plain,
( $false
| ~ spl25_15
| ~ spl25_18 ),
inference(trivial_inequality_removal,[status(thm)],[f332]) ).
thf(f332,plain,
( ( $true = $false )
| ~ spl25_15
| ~ spl25_18 ),
inference(superposition,[status(thm)],[f143,f155]) ).
thf(f143,plain,
( ! [X22: $i] :
( $true
= ( cQ @ X22 ) )
| ~ spl25_15 ),
inference(avatar_component_clause,[status(thm)],[f142]) ).
thf(f142,definition,
( spl25_15
<=> ! [X22: $i] :
( $true
= ( cQ @ X22 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_15])],[avatar_definition]) ).
thf(f330,plain,
( spl25_18
| ~ spl25_15
| ~ spl25_39 ),
inference(avatar_split_clause,[status(thm)],[f327,f256,f142,f154]) ).
thf(f256,definition,
( spl25_39
<=> ! [X16: $i] :
( ( $false
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_39])],[avatar_definition]) ).
thf(f327,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $false )
| ~ spl25_15
| ~ spl25_39 ),
inference(trivial_inequality_removal,[status(thm)],[f326]) ).
thf(f326,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( cQ @ X0 )
= $false ) )
| ~ spl25_15
| ~ spl25_39 ),
inference(superposition,[status(thm)],[f143,f257]) ).
thf(f257,plain,
( ! [X16: $i] :
( ( $false
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) ) )
| ~ spl25_39 ),
inference(avatar_component_clause,[status(thm)],[f256]) ).
thf(f324,plain,
( spl25_18
| ~ spl25_9
| ~ spl25_15 ),
inference(avatar_split_clause,[status(thm)],[f321,f142,f119,f154]) ).
thf(f119,definition,
( spl25_9
<=> ! [X0: $i] :
( ( $false
= ( cQ @ ( sK1 @ X0 ) ) )
| ( ( cQ @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl25_9])],[avatar_definition]) ).
thf(f321,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $false )
| ~ spl25_9
| ~ spl25_15 ),
inference(trivial_inequality_removal,[status(thm)],[f320]) ).
thf(f320,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( cQ @ X0 )
= $false ) )
| ~ spl25_9
| ~ spl25_15 ),
inference(superposition,[status(thm)],[f143,f120]) ).
thf(f120,plain,
( ! [X0: $i] :
( ( $false
= ( cQ @ ( sK1 @ X0 ) ) )
| ( ( cQ @ X0 )
= $false ) )
| ~ spl25_9 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f316,plain,
( ~ spl25_15
| spl25_38 ),
inference(avatar_contradiction_clause,[status(thm)],[f315]) ).
thf(f315,plain,
( $false
| ~ spl25_15
| spl25_38 ),
inference(subsumption_resolution,[status(thm)],[f253,f143]) ).
thf(f253,plain,
( ( $true
!= ( cQ @ sK8 ) )
| spl25_38 ),
inference(avatar_component_clause,[status(thm)],[f251]) ).
thf(f251,definition,
( spl25_38
<=> ( $true
= ( cQ @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_38])],[avatar_definition]) ).
thf(f314,plain,
( ~ spl25_7
| ~ spl25_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f313]) ).
thf(f313,plain,
( $false
| ~ spl25_7
| ~ spl25_11 ),
inference(subsumption_resolution,[status(thm)],[f312,f112]) ).
thf(f312,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl25_7
| ~ spl25_11 ),
inference(subsumption_resolution,[status(thm)],[f127,f112]) ).
thf(f307,plain,
( ~ spl25_2
| ~ spl25_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f306]) ).
thf(f306,plain,
( $false
| ~ spl25_2
| ~ spl25_7 ),
inference(subsumption_resolution,[status(thm)],[f305,f112]) ).
thf(f305,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl25_2
| ~ spl25_7 ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl25_2
| ~ spl25_7 ),
inference(superposition,[status(thm)],[f112,f93]) ).
thf(f283,plain,
( spl25_8
| ~ spl25_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f282]) ).
thf(f282,plain,
( $false
| spl25_8
| ~ spl25_15 ),
inference(subsumption_resolution,[status(thm)],[f116,f143]) ).
thf(f116,plain,
( ( $true
!= ( cQ @ sK2 ) )
| spl25_8 ),
inference(avatar_component_clause,[status(thm)],[f114]) ).
thf(f114,definition,
( spl25_8
<=> ( $true
= ( cQ @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl25_8])],[avatar_definition]) ).
thf(f281,plain,
( ~ spl25_6
| ~ spl25_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f280]) ).
thf(f280,plain,
( $false
| ~ spl25_6
| ~ spl25_10 ),
inference(subsumption_resolution,[status(thm)],[f279,f124]) ).
thf(f279,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ~ spl25_6
| ~ spl25_10 ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ X0 )
= $true ) )
| ~ spl25_6
| ~ spl25_10 ),
inference(superposition,[status(thm)],[f124,f109]) ).
thf(f109,plain,
( ! [X0: $i] :
( ( $true
= ( cQ @ ( sK1 @ X0 ) ) )
| ( ( cQ @ X0 )
= $true ) )
| ~ spl25_6 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl25_6
<=> ! [X0: $i] :
( ( $true
= ( cQ @ ( sK1 @ X0 ) ) )
| ( ( cQ @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl25_6])],[avatar_definition]) ).
thf(f271,plain,
( ~ spl25_10
| ~ spl25_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f270]) ).
thf(f270,plain,
( $false
| ~ spl25_10
| ~ spl25_15 ),
inference(subsumption_resolution,[status(thm)],[f143,f124]) ).
thf(f269,plain,
( ~ spl25_7
| ~ spl25_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f268]) ).
thf(f268,plain,
( $false
| ~ spl25_7
| ~ spl25_20 ),
inference(subsumption_resolution,[status(thm)],[f163,f112]) ).
thf(f267,plain,
( ~ spl25_10
| ~ spl25_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f266]) ).
thf(f266,plain,
( $false
| ~ spl25_10
| ~ spl25_22 ),
inference(trivial_inequality_removal,[status(thm)],[f265]) ).
thf(f265,plain,
( ( $true != $true )
| ~ spl25_10
| ~ spl25_22 ),
inference(superposition,[status(thm)],[f124,f170]) ).
thf(f264,plain,
( ~ spl25_7
| ~ spl25_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f263]) ).
thf(f263,plain,
( $false
| ~ spl25_7
| ~ spl25_19 ),
inference(subsumption_resolution,[status(thm)],[f112,f159]) ).
thf(f260,plain,
( ~ spl25_1
| spl25_15
| spl25_7
| spl25_39 ),
inference(avatar_split_clause,[status(thm)],[f56,f256,f111,f142,f88]) ).
thf(f88,definition,
( spl25_1
<=> ( $true = sP0 ) ),
introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition]) ).
thf(f56,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( $false
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) )
| ( $true != sP0 )
| ( $true
!= ( cP @ X15 ) )
| ( $true
= ( cQ @ X14 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( $true
= ( cQ @ X14 ) )
| ( $true != sP0 )
| ( $true
!= ( cP @ X15 ) )
| ( ( cQ @ ( sK9 @ X16 ) )
!= ( cQ @ X16 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( $true = sP0 )
| ( ( ! [X0: $i] :
( ( cQ @ X0 )
!= ( cQ @ ( sK1 @ X0 ) ) )
| ( ( ( $true
!= ( cQ @ sK2 ) )
| ! [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X4: $i] :
( $true
= ( cQ @ X4 ) )
| ( $true
= ( cP @ sK3 ) ) ) ) )
& ( ! [X7: $i] :
( ( cQ @ sK4 )
= ( cQ @ X7 ) )
| ( ( ( ( cP @ sK5 )
= $true )
| ( $true
!= ( cQ @ sK6 ) ) )
& ( ! [X10: $i] :
( $true
= ( cQ @ X10 ) )
| ! [X11: $i] :
( $true
!= ( cP @ X11 ) ) ) ) ) ) )
& ( ( ( ( ( ( ( cP @ sK7 )
= $true )
| ( $true
!= ( cQ @ sK8 ) ) )
& ( ! [X14: $i] :
( $true
= ( cQ @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cP @ X15 ) ) ) )
| ! [X16: $i] :
( ( cQ @ ( sK9 @ X16 ) )
!= ( cQ @ X16 ) ) )
& ( ! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ sK10 ) )
| ( ( ( $true
!= ( cQ @ sK11 ) )
| ! [X21: $i] :
( $true
!= ( cP @ X21 ) ) )
& ( ! [X22: $i] :
( $true
= ( cQ @ X22 ) )
| ( $true
= ( cP @ sK12 ) ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f10,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11]) ).
thf(f11,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cQ @ X0 )
!= ( cQ @ X1 ) )
=> ( ( cQ @ X0 )
!= ( cQ @ ( sK1 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( $true
!= ( cQ @ X2 ) )
=> ( $true
!= ( cQ @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X5: $i] :
( $true
= ( cP @ X5 ) )
=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) )
=> ! [X7: $i] :
( ( cQ @ sK4 )
= ( cQ @ X7 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X8: $i] :
( $true
= ( cP @ X8 ) )
=> ( ( cP @ sK5 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X9: $i] :
( $true
!= ( cQ @ X9 ) )
=> ( $true
!= ( cQ @ sK6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X12: $i] :
( ( cP @ X12 )
= $true )
=> ( ( cP @ sK7 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X13: $i] :
( $true
!= ( cQ @ X13 ) )
=> ( $true
!= ( cQ @ sK8 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X16: $i] :
( ? [X17: $i] :
( ( cQ @ X17 )
!= ( cQ @ X16 ) )
=> ( ( cQ @ ( sK9 @ X16 ) )
!= ( cQ @ X16 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X18: $i] :
! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ X18 ) )
=> ! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ sK10 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X20: $i] :
( $true
!= ( cQ @ X20 ) )
=> ( $true
!= ( cQ @ sK11 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X23: $i] :
( $true
= ( cP @ X23 ) )
=> ( $true
= ( cP @ sK12 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( ( $true = sP0 )
| ( ( ! [X0: $i] :
? [X1: $i] :
( ( cQ @ X0 )
!= ( cQ @ X1 ) )
| ( ( ? [X2: $i] :
( $true
!= ( cQ @ X2 ) )
| ! [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X4: $i] :
( $true
= ( cQ @ X4 ) )
| ? [X5: $i] :
( $true
= ( cP @ X5 ) ) ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) )
| ( ( ? [X8: $i] :
( $true
= ( cP @ X8 ) )
| ? [X9: $i] :
( $true
!= ( cQ @ X9 ) ) )
& ( ! [X10: $i] :
( $true
= ( cQ @ X10 ) )
| ! [X11: $i] :
( $true
!= ( cP @ X11 ) ) ) ) ) ) )
& ( ( ( ( ( ? [X12: $i] :
( ( cP @ X12 )
= $true )
| ? [X13: $i] :
( $true
!= ( cQ @ X13 ) ) )
& ( ! [X14: $i] :
( $true
= ( cQ @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cP @ X15 ) ) ) )
| ! [X16: $i] :
? [X17: $i] :
( ( cQ @ X17 )
!= ( cQ @ X16 ) ) )
& ( ? [X18: $i] :
! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ X18 ) )
| ( ( ? [X20: $i] :
( $true
!= ( cQ @ X20 ) )
| ! [X21: $i] :
( $true
!= ( cP @ X21 ) ) )
& ( ! [X22: $i] :
( $true
= ( cQ @ X22 ) )
| ? [X23: $i] :
( $true
= ( cP @ X23 ) ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( $true = sP0 )
| ( ( ! [X6: $i] :
? [X7: $i] :
( ( cQ @ X6 )
!= ( cQ @ X7 ) )
| ( ( ? [X5: $i] :
( $true
!= ( cQ @ X5 ) )
| ! [X4: $i] :
( $true
!= ( cP @ X4 ) ) )
& ( ! [X5: $i] :
( $true
= ( cQ @ X5 ) )
| ? [X4: $i] :
( $true
= ( cP @ X4 ) ) ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) )
| ( ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
!= ( cQ @ X5 ) ) )
& ( ! [X5: $i] :
( $true
= ( cQ @ X5 ) )
| ! [X4: $i] :
( $true
!= ( cP @ X4 ) ) ) ) ) ) )
& ( ( ( ( ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
!= ( cQ @ X5 ) ) )
& ( ! [X5: $i] :
( $true
= ( cQ @ X5 ) )
| ! [X4: $i] :
( $true
!= ( cP @ X4 ) ) ) )
| ! [X6: $i] :
? [X7: $i] :
( ( cQ @ X6 )
!= ( cQ @ X7 ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) )
| ( ( ? [X5: $i] :
( $true
!= ( cQ @ X5 ) )
| ! [X4: $i] :
( $true
!= ( cP @ X4 ) ) )
& ( ! [X5: $i] :
( $true
= ( cQ @ X5 ) )
| ? [X4: $i] :
( $true
= ( cP @ X4 ) ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( $true = sP0 )
<=> ( ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
<=> ! [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
<=> ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f259,plain,
( ~ spl25_1
| spl25_37
| spl25_7
| spl25_15 ),
inference(avatar_split_clause,[status(thm)],[f55,f142,f111,f248,f88]) ).
thf(f55,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( $true
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $true
!= ( cP @ X15 ) )
| ( $true
= ( cQ @ X16 ) )
| ( $true
= ( cQ @ X14 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f258,plain,
( spl25_36
| spl25_39
| ~ spl25_1
| ~ spl25_38 ),
inference(avatar_split_clause,[status(thm)],[f58,f251,f88,f256,f244]) ).
thf(f58,plain,
! [X16: $i] :
( ( $false
= ( cQ @ ( sK9 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) )
| ( $true
!= ( cQ @ sK8 ) )
| ( ( cP @ sK7 )
= $true )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X16: $i] :
( ( ( cP @ sK7 )
= $true )
| ( $true != sP0 )
| ( ( cQ @ ( sK9 @ X16 ) )
!= ( cQ @ X16 ) )
| ( $true
!= ( cQ @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f241,plain,
( spl25_1
| spl25_35
| spl25_6
| spl25_15 ),
inference(avatar_split_clause,[status(thm)],[f59,f142,f108,f238,f88]) ).
thf(f59,plain,
! [X0: $i,X4: $i] :
( ( ( cQ @ X0 )
= $true )
| ( $true
= ( cP @ sK3 ) )
| ( $true = sP0 )
| ( $true
= ( cQ @ ( sK1 @ X0 ) ) )
| ( $true
= ( cQ @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i,X4: $i] :
( ( $true
= ( cP @ sK3 ) )
| ( ( cQ @ X0 )
!= ( cQ @ ( sK1 @ X0 ) ) )
| ( $true
= ( cQ @ X4 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f220,plain,
( spl25_15
| spl25_1
| spl25_15
| spl25_29
| spl25_7 ),
inference(avatar_split_clause,[status(thm)],[f66,f111,f203,f142,f88,f142]) ).
thf(f66,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( $true = sP0 )
| ( $false
= ( cQ @ sK4 ) )
| ( $true
= ( cQ @ X10 ) )
| ( $true
= ( cQ @ X7 ) )
| ( $true
!= ( cP @ X11 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( ( cQ @ sK4 )
= ( cQ @ X7 ) )
| ( $true
!= ( cP @ X11 ) )
| ( $true
= ( cQ @ X10 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f219,plain,
( spl25_18
| spl25_15
| spl25_28
| spl25_1
| spl25_7 ),
inference(avatar_split_clause,[status(thm)],[f65,f111,f88,f198,f142,f154]) ).
thf(f65,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( $true
!= ( cP @ X11 ) )
| ( $true
= ( cQ @ X10 ) )
| ( $false
= ( cQ @ X7 ) )
| ( $true
= ( cQ @ sK4 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f218,plain,
( spl25_31
| ~ spl25_1
| spl25_19
| spl25_10
| spl25_19 ),
inference(avatar_split_clause,[status(thm)],[f68,f158,f123,f158,f88,f215]) ).
thf(f68,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( $false
= ( cP @ sK16 ) )
| ( $true != sP0 )
| ( ( cP @ X10 )
= $true )
| ( ( cQ @ X11 )
!= $true )
| ( $true
= ( cP @ X7 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( ( cP @ sK16 )
= ( cP @ X7 ) )
| ( ( cQ @ X11 )
!= $true )
| ( ( cP @ X10 )
= $true )
| ( $true != sP0 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= ( cP @ ( sK13 @ X0 ) ) )
| ( ( ( $true
!= ( cP @ sK14 ) )
| ! [X3: $i] :
( $true
!= ( cQ @ X3 ) ) )
& ( ! [X4: $i] :
( $true
= ( cP @ X4 ) )
| ( ( cQ @ sK15 )
= $true ) ) ) )
& ( ! [X7: $i] :
( ( cP @ sK16 )
= ( cP @ X7 ) )
| ( ( ( $true
= ( cQ @ sK17 ) )
| ( $true
!= ( cP @ sK18 ) ) )
& ( ! [X10: $i] :
( ( cP @ X10 )
= $true )
| ! [X11: $i] :
( ( cQ @ X11 )
!= $true ) ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ( ( ( $true
= ( cQ @ sK19 ) )
| ( $true
!= ( cP @ sK20 ) ) )
& ( ! [X14: $i] :
( $true
= ( cP @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cQ @ X15 ) ) ) )
| ! [X16: $i] :
( ( cP @ ( sK21 @ X16 ) )
!= ( cP @ X16 ) ) )
& ( ! [X19: $i] :
( ( cP @ sK22 )
= ( cP @ X19 ) )
| ( ( ( $true
!= ( cP @ sK23 ) )
| ! [X21: $i] :
( ( cQ @ X21 )
!= $true ) )
& ( ! [X22: $i] :
( $true
= ( cP @ X22 ) )
| ( $true
= ( cQ @ sK24 ) ) ) ) ) )
| ( $true = sP0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24])],[f25,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26]) ).
thf(f26,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cP @ X0 )
!= ( cP @ X1 ) )
=> ( ( cP @ X0 )
!= ( cP @ ( sK13 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
=> ( $true
!= ( cP @ sK14 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X5: $i] :
( $true
= ( cQ @ X5 ) )
=> ( ( cQ @ sK15 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X6: $i] :
! [X7: $i] :
( ( cP @ X6 )
= ( cP @ X7 ) )
=> ! [X7: $i] :
( ( cP @ sK16 )
= ( cP @ X7 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X8: $i] :
( $true
= ( cQ @ X8 ) )
=> ( $true
= ( cQ @ sK17 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X9: $i] :
( $true
!= ( cP @ X9 ) )
=> ( $true
!= ( cP @ sK18 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X12: $i] :
( $true
= ( cQ @ X12 ) )
=> ( $true
= ( cQ @ sK19 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X13: $i] :
( $true
!= ( cP @ X13 ) )
=> ( $true
!= ( cP @ sK20 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
! [X16: $i] :
( ? [X17: $i] :
( ( cP @ X16 )
!= ( cP @ X17 ) )
=> ( ( cP @ ( sK21 @ X16 ) )
!= ( cP @ X16 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X18: $i] :
! [X19: $i] :
( ( cP @ X18 )
= ( cP @ X19 ) )
=> ! [X19: $i] :
( ( cP @ sK22 )
= ( cP @ X19 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X20: $i] :
( ( cP @ X20 )
!= $true )
=> ( $true
!= ( cP @ sK23 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X23: $i] :
( $true
= ( cQ @ X23 ) )
=> ( $true
= ( cQ @ sK24 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 )
!= ( cP @ X1 ) )
| ( ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ! [X3: $i] :
( $true
!= ( cQ @ X3 ) ) )
& ( ! [X4: $i] :
( $true
= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
= ( cQ @ X5 ) ) ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cP @ X6 )
= ( cP @ X7 ) )
| ( ( ? [X8: $i] :
( $true
= ( cQ @ X8 ) )
| ? [X9: $i] :
( $true
!= ( cP @ X9 ) ) )
& ( ! [X10: $i] :
( ( cP @ X10 )
= $true )
| ! [X11: $i] :
( ( cQ @ X11 )
!= $true ) ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ( ( ? [X12: $i] :
( $true
= ( cQ @ X12 ) )
| ? [X13: $i] :
( $true
!= ( cP @ X13 ) ) )
& ( ! [X14: $i] :
( $true
= ( cP @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cQ @ X15 ) ) ) )
| ! [X16: $i] :
? [X17: $i] :
( ( cP @ X16 )
!= ( cP @ X17 ) ) )
& ( ? [X18: $i] :
! [X19: $i] :
( ( cP @ X18 )
= ( cP @ X19 ) )
| ( ( ? [X20: $i] :
( ( cP @ X20 )
!= $true )
| ! [X21: $i] :
( ( cQ @ X21 )
!= $true ) )
& ( ! [X22: $i] :
( $true
= ( cP @ X22 ) )
| ? [X23: $i] :
( $true
= ( cQ @ X23 ) ) ) ) ) )
| ( $true = sP0 ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ( ! [X2: $i] :
? [X3: $i] :
( ( cP @ X3 )
!= ( cP @ X2 ) )
| ( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ? [X1: $i] :
( ( cQ @ X1 )
= $true ) ) ) )
& ( ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) )
| ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
| ? [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
| ? [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) ) )
| ! [X2: $i] :
? [X3: $i] :
( ( cP @ X3 )
!= ( cP @ X2 ) ) )
& ( ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) )
| ( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ? [X1: $i] :
( ( cQ @ X1 )
= $true ) ) ) ) )
| ( $true = sP0 ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( $true = sP0 )
<~> ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) )
<=> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) ) ) ),
inference(definition_folding,[status(thm)],[f6,f7]) ).
thf(f6,plain,
( ( ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
<=> ! [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
<=> ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) ) )
<~> ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) )
<=> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
<=> ! [X5: $i] :
( $true
= ( cQ @ X5 ) ) )
<=> ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X6 )
= ( cQ @ X7 ) ) )
<=> ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) )
<=> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cQ @ X1 ) )
<=> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X2 )
<=> ( cP @ X3 ) ) )
<=> ( ( ? [X4: $i] : ( cP @ X4 )
<=> ! [X5: $i] : ( cQ @ X5 ) )
<=> ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X7 )
<=> ( cQ @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [X1: $i] : ( cP @ X1 )
<=> ? [X0: $i] : ( cQ @ X0 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
<=> ( cP @ X1 ) ) )
<=> ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cQ @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cQ @ X1 )
<=> ( cQ @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ! [X1: $i] : ( cP @ X1 )
<=> ? [X0: $i] : ( cQ @ X0 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
<=> ( cP @ X1 ) ) )
<=> ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cQ @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cQ @ X1 )
<=> ( cQ @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BL3uNYjvsH/DTF2THF_13477.p',cX2129) ).
thf(f213,plain,
( spl25_19
| spl25_10
| spl25_21
| ~ spl25_1
| spl25_30 ),
inference(avatar_split_clause,[status(thm)],[f67,f210,f88,f165,f123,f158]) ).
thf(f67,plain,
! [X10: $i,X11: $i,X7: $i] :
( ( ( cQ @ X11 )
!= $true )
| ( $false
= ( cP @ X7 ) )
| ( ( cP @ X10 )
= $true )
| ( $true
= ( cP @ sK16 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f207,plain,
( spl25_2
| spl25_1
| spl25_19
| spl25_10 ),
inference(avatar_split_clause,[status(thm)],[f69,f123,f158,f88,f92]) ).
thf(f69,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( $true
!= ( cQ @ X15 ) )
| ( $true
= ( cP @ X14 ) )
| ( $true
= ( cP @ X16 ) )
| ( $true
= ( cP @ ( sK21 @ X16 ) ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( $true = sP0 )
| ( ( cP @ ( sK21 @ X16 ) )
!= ( cP @ X16 ) )
| ( $true
= ( cP @ X14 ) )
| ( $true
!= ( cQ @ X15 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f187,plain,
( spl25_11
| spl25_19
| spl25_25
| ~ spl25_1 ),
inference(avatar_split_clause,[status(thm)],[f73,f88,f184,f158,f126]) ).
thf(f73,plain,
! [X0: $i,X4: $i] :
( ( ( cP @ X0 )
= $true )
| ( ( cQ @ sK15 )
= $true )
| ( ( cP @ ( sK13 @ X0 ) )
= $true )
| ( $true
= ( cP @ X4 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: $i,X4: $i] :
( ( ( cQ @ sK15 )
= $true )
| ( $true
= ( cP @ X4 ) )
| ( $true != sP0 )
| ( ( cP @ X0 )
!= ( cP @ ( sK13 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f176,plain,
( spl25_1
| spl25_23
| spl25_19
| spl25_22
| spl25_19 ),
inference(avatar_split_clause,[status(thm)],[f78,f158,f168,f158,f173,f88]) ).
thf(f78,plain,
! [X19: $i,X22: $i] :
( ( $true
= ( cQ @ sK24 ) )
| ( $true
= ( cP @ X22 ) )
| ( $false
= ( cP @ sK22 ) )
| ( $true
= ( cP @ X19 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X19: $i,X22: $i] :
( ( ( cP @ sK22 )
= ( cP @ X19 ) )
| ( $true
= ( cP @ X22 ) )
| ( $true = sP0 )
| ( $true
= ( cQ @ sK24 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f171,plain,
( spl25_19
| spl25_20
| spl25_1
| spl25_21
| spl25_22 ),
inference(avatar_split_clause,[status(thm)],[f77,f168,f165,f88,f161,f158]) ).
thf(f77,plain,
! [X19: $i,X22: $i] :
( ( $true = sP0 )
| ( $true
= ( cP @ sK22 ) )
| ( $false
= ( cP @ X19 ) )
| ( $true
= ( cQ @ sK24 ) )
| ( $true
= ( cP @ X22 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f156,plain,
( spl25_17
| spl25_14
| spl25_15
| spl25_18
| ~ spl25_1 ),
inference(avatar_split_clause,[status(thm)],[f80,f88,f154,f142,f138,f150]) ).
thf(f80,plain,
! [X19: $i,X22: $i] :
( ( $false
= ( cQ @ X19 ) )
| ( $true
= ( cQ @ sK10 ) )
| ( $true
= ( cP @ sK12 ) )
| ( $true != sP0 )
| ( $true
= ( cQ @ X22 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X19: $i,X22: $i] :
( ( $true != sP0 )
| ( $true
= ( cP @ sK12 ) )
| ( ( cQ @ X19 )
= ( cQ @ sK10 ) )
| ( $true
= ( cQ @ X22 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f148,plain,
( spl25_14
| spl25_15
| spl25_15
| ~ spl25_1
| spl25_16 ),
inference(avatar_split_clause,[status(thm)],[f79,f145,f88,f142,f142,f138]) ).
thf(f79,plain,
! [X19: $i,X22: $i] :
( ( $true
= ( cQ @ X22 ) )
| ( $false
= ( cQ @ sK10 ) )
| ( $true
= ( cQ @ X19 ) )
| ( $true != sP0 )
| ( $true
= ( cP @ sK12 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f136,plain,
( spl25_13
| spl25_10
| ~ spl25_12
| ~ spl25_1 ),
inference(avatar_split_clause,[status(thm)],[f82,f88,f129,f123,f134]) ).
thf(f82,plain,
! [X3: $i,X0: $i] :
( ( $true
!= ( cP @ sK14 ) )
| ( ( cP @ ( sK13 @ X0 ) )
= $false )
| ( $true
!= ( cQ @ X3 ) )
| ( $true != sP0 )
| ( ( cP @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X3: $i,X0: $i] :
( ( ( cP @ X0 )
!= ( cP @ ( sK13 @ X0 ) ) )
| ( $true
!= ( cQ @ X3 ) )
| ( $true
!= ( cP @ sK14 ) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f121,plain,
( spl25_1
| ~ spl25_8
| spl25_9
| spl25_7 ),
inference(avatar_split_clause,[status(thm)],[f84,f111,f119,f114,f88]) ).
thf(f84,plain,
! [X3: $i,X0: $i] :
( ( $false
= ( cQ @ ( sK1 @ X0 ) ) )
| ( $true = sP0 )
| ( ( cQ @ X0 )
= $false )
| ( $true
!= ( cP @ X3 ) )
| ( $true
!= ( cQ @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X3: $i,X0: $i] :
( ( $true
!= ( cQ @ sK2 ) )
| ( $true
!= ( cP @ X3 ) )
| ( $true = sP0 )
| ( ( cQ @ X0 )
!= ( cQ @ ( sK1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f106,plain,
( spl25_1
| spl25_5
| spl25_3
| ~ spl25_4 ),
inference(avatar_split_clause,[status(thm)],[f86,f99,f95,f104,f88]) ).
thf(f86,plain,
! [X16: $i] :
( ( $false
= ( cP @ X16 ) )
| ( $false
= ( cP @ ( sK21 @ X16 ) ) )
| ( $true
= ( cQ @ sK19 ) )
| ( $true
!= ( cP @ sK20 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X16: $i] :
( ( $true
!= ( cP @ sK20 ) )
| ( ( cP @ ( sK21 @ X16 ) )
!= ( cP @ X16 ) )
| ( $true
= ( cQ @ sK19 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN036^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.31 % Computer : n022.cluster.edu
% 0.15/0.31 % Model : x86_64 x86_64
% 0.15/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.31 % Memory : 8042.1875MB
% 0.15/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Tue Feb 24 13:50:51 EST 2026
% 0.15/0.31 % CPUTime :
% 0.15/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SYN036^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.44 % Domain : Syntactic
% 0.16/0.44 % Problem : TPS problem X2129
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Bro09]
% 0.16/0.44 % Names : tps_0554 [Bro09]
% 0.16/0.44 % : THM57 [TPS]
% 0.16/0.44 % : X2129 [TPS]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.16/0.44 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.44 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 8 ( 8 avg)
% 0.16/0.44 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 8 @)
% 0.16/0.44 % ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.44 % Number of types : 2 ( 0 usr)
% 0.16/0.44 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.16/0.44 % Number of variables : 8 ( 0 ^; 4 !; 4 ?; 8 :)
% 0.16/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.44 % : This was an early Challenge Problem given by Peter Andrews in
% 0.16/0.44 % 1979 or 1980.
% 0.16/0.44 % :
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(cQ,type,
% 0.16/0.44 cQ: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(cP,type,
% 0.16/0.44 cP: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(cX2129,conjecture,
% 0.16/0.44 ( ( ? [Xx: $i] :
% 0.16/0.44 ! [Xy: $i] :
% 0.16/0.44 ( ( cP @ Xx )
% 0.16/0.44 <=> ( cP @ Xy ) )
% 0.16/0.44 <=> ( ? [Xx: $i] : ( cQ @ Xx )
% 0.16/0.44 <=> ! [Xy: $i] : ( cP @ Xy ) ) )
% 0.16/0.44 <=> ( ? [Xx: $i] :
% 0.16/0.44 ! [Xy: $i] :
% 0.16/0.44 ( ( cQ @ Xx )
% 0.16/0.44 <=> ( cQ @ Xy ) )
% 0.16/0.44 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 0.16/0.44 <=> ! [Xy: $i] : ( cQ @ Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 0.27/1.30 ---- Embedded in THF ---
% 0.27/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.27/1.30 %%% Generated on Tue Feb 24 13:50:52 EST 2026
% 0.27/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.27/1.30 %%% Logic specification used:
% 0.27/1.30 %%% thf(spec, logic, $$dhol).
% 0.27/1.30
% 0.27/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BL3uNYjvsH/DTF2DTF13477.p
% See solution above
% 0.27/1.30 ------------------------
% 0.27/1.31 ---- Cleaned THF ---
% 0.27/1.31 thf(cQ,type,
% 0.27/1.31 cQ: $i > $o ).
% 0.27/1.31
% 0.27/1.31 thf(cP,type,
% 0.27/1.31 cP: $i > $o ).
% 0.27/1.31
% 0.27/1.31 thf(cX2129,conjecture,
% 0.27/1.31 ( ( ? [Xx: $i] :
% 0.27/1.31 ! [Xy: $i] :
% 0.27/1.31 ( ( cP @ Xx )
% 0.27/1.31 <=> ( cP @ Xy ) )
% 0.27/1.31 <=> ( ? [Xx: $i] : ( cQ @ Xx )
% 0.27/1.31 <=> ! [Xy: $i] : ( cP @ Xy ) ) )
% 0.27/1.31 <=> ( ? [Xx: $i] :
% 0.27/1.31 ! [Xy: $i] :
% 0.27/1.31 ( ( cQ @ Xx )
% 0.27/1.31 <=> ( cQ @ Xy ) )
% 0.27/1.31 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 0.27/1.31 <=> ! [Xy: $i] : ( cQ @ Xy ) ) ) ) ).
% 0.27/1.31 ------------------------
% 0.27/1.33 % (13725)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_13477 for (2999ds/275Mi)
% 0.27/1.33 % (13725)Refutation not found, incomplete strategy
% 0.27/1.33 % (13725)------------------------------
% 0.27/1.33 % (13725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.33 % (13725)Termination reason: Refutation not found, incomplete strategy
% 0.27/1.33
% 0.27/1.33
% 0.27/1.33 % (13725)Memory used [KB]: 5628
% 0.27/1.33 % (13725)Time elapsed: 0.004 s
% 0.27/1.33 % (13725)Instructions burned: 8 (million)
% 0.27/1.33 % (13725)------------------------------
% 0.27/1.33 % (13725)------------------------------
% 0.27/1.33 % (13720)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13477 for (2999ds/183Mi)
% 0.27/1.33 % (13721)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_13477 for (2999ds/4Mi)
% 0.27/1.33 % (13722)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_13477 for (2999ds/27Mi)
% 0.27/1.33 % (13723)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13477 for (2999ds/2Mi)
% 0.27/1.33 % (13724)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_13477 for (2999ds/2Mi)
% 0.27/1.33 % (13726)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13477 for (2999ds/18Mi)
% 0.27/1.33 % (13723)Instruction limit reached!
% 0.27/1.33 % (13723)------------------------------
% 0.27/1.33 % (13723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.33 % (13723)Termination reason: Unknown
% 0.27/1.33 % (13723)Termination phase: Preprocessing 3
% 0.27/1.33
% 0.27/1.33 % (13723)Memory used [KB]: 1023
% 0.27/1.33 % (13723)Time elapsed: 0.003 s
% 0.27/1.33 % (13723)Instructions burned: 2 (million)
% 0.27/1.33 % (13723)------------------------------
% 0.27/1.33 % (13723)------------------------------
% 0.27/1.33 % (13724)Instruction limit reached!
% 0.27/1.33 % (13724)------------------------------
% 0.27/1.33 % (13724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.33 % (13724)Termination reason: Unknown
% 0.27/1.33 % (13724)Termination phase: Saturation
% 0.27/1.33
% 0.27/1.33 % (13724)Memory used [KB]: 895
% 0.27/1.33 % (13724)Time elapsed: 0.003 s
% 0.27/1.33 % (13724)Instructions burned: 2 (million)
% 0.27/1.33 % (13724)------------------------------
% 0.27/1.33 % (13724)------------------------------
% 0.27/1.34 % (13721)Instruction limit reached!
% 0.27/1.34 % (13721)------------------------------
% 0.27/1.34 % (13721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.34 % (13721)Termination reason: Unknown
% 0.27/1.34 % (13721)Termination phase: Saturation
% 0.27/1.34
% 0.27/1.34 % (13721)Memory used [KB]: 5500
% 0.27/1.34 % (13721)Time elapsed: 0.005 s
% 0.27/1.34 % (13721)Instructions burned: 5 (million)
% 0.27/1.34 % (13721)------------------------------
% 0.27/1.34 % (13721)------------------------------
% 0.27/1.34 % (13727)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13477 for (2999ds/3Mi)
% 0.27/1.34 % (13727)Instruction limit reached!
% 0.27/1.34 % (13727)------------------------------
% 0.27/1.34 % (13727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.34 % (13727)Termination reason: Unknown
% 0.27/1.34 % (13727)Termination phase: Saturation
% 0.27/1.34
% 0.27/1.34 % (13727)Memory used [KB]: 5500
% 0.27/1.34 % (13727)Time elapsed: 0.003 s
% 0.27/1.34 % (13727)Instructions burned: 4 (million)
% 0.27/1.34 % (13727)------------------------------
% 0.27/1.34 % (13727)------------------------------
% 0.27/1.35 % (13726)Instruction limit reached!
% 0.27/1.35 % (13726)------------------------------
% 0.27/1.35 % (13726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.35 % (13726)Termination reason: Unknown
% 0.27/1.35 % (13726)Termination phase: Saturation
% 0.27/1.35
% 0.27/1.35 % (13726)Memory used [KB]: 5756
% 0.27/1.35 % (13726)Time elapsed: 0.014 s
% 0.27/1.35 % (13726)Instructions burned: 18 (million)
% 0.27/1.35 % (13726)------------------------------
% 0.27/1.35 % (13726)------------------------------
% 0.27/1.35 % (13722)Instruction limit reached!
% 0.27/1.35 % (13722)------------------------------
% 0.27/1.35 % (13722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.35 % (13722)Termination reason: Unknown
% 0.27/1.35 % (13722)Termination phase: Saturation
% 0.27/1.35
% 0.27/1.35 % (13722)Memory used [KB]: 5756
% 0.27/1.35 % (13722)Time elapsed: 0.018 s
% 0.27/1.35 % (13722)Instructions burned: 27 (million)
% 0.27/1.35 % (13722)------------------------------
% 0.27/1.35 % (13722)------------------------------
% 0.27/1.35 % (13729)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_13477 for (2999ds/15Mi)
% 0.27/1.35 % (13728)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_13477 for (2999ds/37Mi)
% 0.27/1.35 % (13731)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_13477 for (2999ds/1041Mi)
% 0.27/1.35 % (13730)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_13477 for (2999ds/3Mi)
% 0.27/1.36 % (13720)First to succeed.
% 0.27/1.36 % (13730)Instruction limit reached!
% 0.27/1.36 % (13730)------------------------------
% 0.27/1.36 % (13730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.36 % (13730)Termination reason: Unknown
% 0.27/1.36 % (13730)Termination phase: Saturation
% 0.27/1.36
% 0.27/1.36 % (13730)Memory used [KB]: 5500
% 0.27/1.36 % (13730)Time elapsed: 0.004 s
% 0.27/1.36 % (13730)Instructions burned: 4 (million)
% 0.27/1.36 % (13730)------------------------------
% 0.27/1.36 % (13730)------------------------------
% 0.27/1.36 % (13729)Instruction limit reached!
% 0.27/1.36 % (13729)------------------------------
% 0.27/1.36 % (13729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.36 % (13729)Termination reason: Unknown
% 0.27/1.36 % (13729)Termination phase: Saturation
% 0.27/1.36
% 0.27/1.36 % (13729)Memory used [KB]: 5628
% 0.27/1.36 % (13729)Time elapsed: 0.009 s
% 0.27/1.36 % (13729)Instructions burned: 17 (million)
% 0.27/1.36 % (13729)------------------------------
% 0.27/1.36 % (13729)------------------------------
% 0.27/1.36 % (13720)Refutation found. Thanks to Tanya!
% 0.27/1.36 % SZS status Theorem for DTF2THF_13477
% 0.27/1.36 % SZS output start Proof for DTF2THF_13477
% 0.27/1.36 thf(func_def_0, type, cQ: $i > $o).
% 0.27/1.36 thf(func_def_1, type, cP: $i > $o).
% 0.27/1.36 thf(func_def_6, type, sK1: $i > $i).
% 0.27/1.36 thf(func_def_14, type, sK9: $i > $i).
% 0.27/1.36 thf(func_def_18, type, sK13: $i > $i).
% 0.27/1.36 thf(func_def_26, type, sK21: $i > $i).
% 0.27/1.36 thf(f643,plain,(
% 0.27/1.36 $false),
% 0.27/1.36 inference(avatar_sat_refutation,[status(thm)],[f106,f121,f136,f148,f156,f171,f176,f187,f207,f213,f218,f219,f220,f241,f258,f259,f260,f264,f267,f269,f271,f281,f283,f307,f314,f316,f324,f330,f336,f338,f344,f352,f358,f369,f379,f394,f400,f406,f462,f480,f498,f510,f583,f589,f605,f611,f636,f642])).
% 0.27/1.36 thf(f642,plain,(
% 0.27/1.36 ~spl25_3 | ~spl25_18),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f641])).
% 0.27/1.36 thf(f641,plain,(
% 0.27/1.36 $false | (~spl25_3 | ~spl25_18)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f637])).
% 0.27/1.36 thf(f637,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_3 | ~spl25_18)),
% 0.27/1.36 inference(superposition,[status(thm)],[f97,f155])).
% 0.27/1.36 thf(f155,plain,(
% 0.27/1.36 ( ! [X19 : $i] : (($false = (cQ @ X19))) ) | ~spl25_18),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f154])).
% 0.27/1.36 thf(f154,definition,(
% 0.27/1.36 spl25_18 <=> ! [X19 : $i] : ($false = (cQ @ X19))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_18])],[avatar_definition])).
% 0.27/1.36 thf(f97,plain,(
% 0.27/1.36 ($true = (cQ @ sK19)) | ~spl25_3),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f95])).
% 0.27/1.36 thf(f95,definition,(
% 0.27/1.36 spl25_3 <=> ($true = (cQ @ sK19))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition])).
% 0.27/1.36 thf(f636,plain,(
% 0.27/1.36 spl25_19 | ~spl25_2 | ~spl25_21),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f633,f165,f92,f158])).
% 0.27/1.36 thf(f158,definition,(
% 0.27/1.36 spl25_19 <=> ! [X22 : $i] : ($true = (cP @ X22))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_19])],[avatar_definition])).
% 0.27/1.36 thf(f92,definition,(
% 0.27/1.36 spl25_2 <=> ! [X16 : $i] : (($true = (cP @ X16)) | ($true = (cP @ (sK21 @ X16))))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition])).
% 0.27/1.36 thf(f165,definition,(
% 0.27/1.36 spl25_21 <=> ! [X19 : $i] : ($false = (cP @ X19))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_21])],[avatar_definition])).
% 0.27/1.36 thf(f633,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl25_2 | ~spl25_21)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f631])).
% 0.27/1.36 thf(f631,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $true) | ($true = $false)) ) | (~spl25_2 | ~spl25_21)),
% 0.27/1.36 inference(superposition,[status(thm)],[f93,f166])).
% 0.27/1.36 thf(f166,plain,(
% 0.27/1.36 ( ! [X19 : $i] : (($false = (cP @ X19))) ) | ~spl25_21),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f165])).
% 0.27/1.36 thf(f93,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($true = (cP @ (sK21 @ X16))) | ($true = (cP @ X16))) ) | ~spl25_2),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f92])).
% 0.27/1.36 thf(f611,plain,(
% 0.27/1.36 ~spl25_28 | ~spl25_29),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f610])).
% 0.27/1.36 thf(f610,plain,(
% 0.27/1.36 $false | (~spl25_28 | ~spl25_29)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f607])).
% 0.27/1.36 thf(f607,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_28 | ~spl25_29)),
% 0.27/1.36 inference(superposition,[status(thm)],[f200,f205])).
% 0.27/1.36 thf(f205,plain,(
% 0.27/1.36 ($false = (cQ @ sK4)) | ~spl25_29),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f203])).
% 0.27/1.36 thf(f203,definition,(
% 0.27/1.36 spl25_29 <=> ($false = (cQ @ sK4))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_29])],[avatar_definition])).
% 0.27/1.36 thf(f200,plain,(
% 0.27/1.36 ($true = (cQ @ sK4)) | ~spl25_28),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f198])).
% 0.27/1.36 thf(f198,definition,(
% 0.27/1.36 spl25_28 <=> ($true = (cQ @ sK4))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_28])],[avatar_definition])).
% 0.27/1.36 thf(f605,plain,(
% 0.27/1.36 ~spl25_21 | ~spl25_35),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f604])).
% 0.27/1.36 thf(f604,plain,(
% 0.27/1.36 $false | (~spl25_21 | ~spl25_35)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f600])).
% 0.27/1.36 thf(f600,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_21 | ~spl25_35)),
% 0.27/1.36 inference(superposition,[status(thm)],[f240,f166])).
% 0.27/1.36 thf(f240,plain,(
% 0.27/1.36 ($true = (cP @ sK3)) | ~spl25_35),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f238])).
% 0.27/1.36 thf(f238,definition,(
% 0.27/1.36 spl25_35 <=> ($true = (cP @ sK3))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_35])],[avatar_definition])).
% 0.27/1.36 thf(f589,plain,(
% 0.27/1.36 ~spl25_20 | ~spl25_23),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f588])).
% 0.27/1.36 thf(f588,plain,(
% 0.27/1.36 $false | (~spl25_20 | ~spl25_23)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f585])).
% 0.27/1.36 thf(f585,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_20 | ~spl25_23)),
% 0.27/1.36 inference(superposition,[status(thm)],[f175,f163])).
% 0.27/1.36 thf(f163,plain,(
% 0.27/1.36 ($true = (cP @ sK22)) | ~spl25_20),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f161])).
% 0.27/1.36 thf(f161,definition,(
% 0.27/1.36 spl25_20 <=> ($true = (cP @ sK22))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_20])],[avatar_definition])).
% 0.27/1.36 thf(f175,plain,(
% 0.27/1.36 ($false = (cP @ sK22)) | ~spl25_23),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f173])).
% 0.27/1.36 thf(f173,definition,(
% 0.27/1.36 spl25_23 <=> ($false = (cP @ sK22))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_23])],[avatar_definition])).
% 0.27/1.36 thf(f583,plain,(
% 0.27/1.36 ~spl25_10 | ~spl25_37),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f582])).
% 0.27/1.36 thf(f582,plain,(
% 0.27/1.36 $false | (~spl25_10 | ~spl25_37)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f573,f124])).
% 0.27/1.36 thf(f124,plain,(
% 0.27/1.36 ( ! [X3 : $i] : (($true != (cQ @ X3))) ) | ~spl25_10),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f123])).
% 0.27/1.36 thf(f123,definition,(
% 0.27/1.36 spl25_10 <=> ! [X3 : $i] : ($true != (cQ @ X3))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_10])],[avatar_definition])).
% 0.27/1.36 thf(f573,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cQ @ X0) = $true)) ) | (~spl25_10 | ~spl25_37)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f571])).
% 0.27/1.36 thf(f571,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cQ @ X0) = $true) | ($true != $true)) ) | (~spl25_10 | ~spl25_37)),
% 0.27/1.36 inference(superposition,[status(thm)],[f124,f249])).
% 0.27/1.36 thf(f249,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($true = (cQ @ (sK9 @ X16))) | ($true = (cQ @ X16))) ) | ~spl25_37),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f248])).
% 0.27/1.36 thf(f248,definition,(
% 0.27/1.36 spl25_37 <=> ! [X16 : $i] : (($true = (cQ @ (sK9 @ X16))) | ($true = (cQ @ X16)))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_37])],[avatar_definition])).
% 0.27/1.36 thf(f510,plain,(
% 0.27/1.36 spl25_19 | ~spl25_11 | ~spl25_21),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f505,f165,f126,f158])).
% 0.27/1.36 thf(f126,definition,(
% 0.27/1.36 spl25_11 <=> ! [X0 : $i] : (((cP @ (sK13 @ X0)) = $true) | ((cP @ X0) = $true))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_11])],[avatar_definition])).
% 0.27/1.36 thf(f505,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl25_11 | ~spl25_21)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f502])).
% 0.27/1.36 thf(f502,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true = $false) | ((cP @ X0) = $true)) ) | (~spl25_11 | ~spl25_21)),
% 0.27/1.36 inference(superposition,[status(thm)],[f127,f166])).
% 0.27/1.36 thf(f127,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ (sK13 @ X0)) = $true) | ((cP @ X0) = $true)) ) | ~spl25_11),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f126])).
% 0.27/1.36 thf(f498,plain,(
% 0.27/1.36 ~spl25_21 | ~spl25_36),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f497])).
% 0.27/1.36 thf(f497,plain,(
% 0.27/1.36 $false | (~spl25_21 | ~spl25_36)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f493])).
% 0.27/1.36 thf(f493,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_21 | ~spl25_36)),
% 0.27/1.36 inference(superposition,[status(thm)],[f246,f166])).
% 0.27/1.36 thf(f246,plain,(
% 0.27/1.36 ((cP @ sK7) = $true) | ~spl25_36),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f244])).
% 0.27/1.36 thf(f244,definition,(
% 0.27/1.36 spl25_36 <=> ((cP @ sK7) = $true)),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_36])],[avatar_definition])).
% 0.27/1.36 thf(f480,plain,(
% 0.27/1.36 ~spl25_18 | ~spl25_25),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f479])).
% 0.27/1.36 thf(f479,plain,(
% 0.27/1.36 $false | (~spl25_18 | ~spl25_25)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f447])).
% 0.27/1.36 thf(f447,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_18 | ~spl25_25)),
% 0.27/1.36 inference(superposition,[status(thm)],[f155,f186])).
% 0.27/1.36 thf(f186,plain,(
% 0.27/1.36 ((cQ @ sK15) = $true) | ~spl25_25),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f184])).
% 0.27/1.36 thf(f184,definition,(
% 0.27/1.36 spl25_25 <=> ((cQ @ sK15) = $true)),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_25])],[avatar_definition])).
% 0.27/1.36 thf(f462,plain,(
% 0.27/1.36 ~spl25_18 | ~spl25_22),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f461])).
% 0.27/1.36 thf(f461,plain,(
% 0.27/1.36 $false | (~spl25_18 | ~spl25_22)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f456])).
% 0.27/1.36 thf(f456,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_18 | ~spl25_22)),
% 0.27/1.36 inference(superposition,[status(thm)],[f170,f155])).
% 0.27/1.36 thf(f170,plain,(
% 0.27/1.36 ($true = (cQ @ sK24)) | ~spl25_22),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f168])).
% 0.27/1.36 thf(f168,definition,(
% 0.27/1.36 spl25_22 <=> ($true = (cQ @ sK24))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_22])],[avatar_definition])).
% 0.27/1.36 thf(f406,plain,(
% 0.27/1.36 spl25_21 | ~spl25_13 | ~spl25_19),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f403,f158,f134,f165])).
% 0.27/1.36 thf(f134,definition,(
% 0.27/1.36 spl25_13 <=> ! [X0 : $i] : (((cP @ (sK13 @ X0)) = $false) | ((cP @ X0) = $false))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_13])],[avatar_definition])).
% 0.27/1.36 thf(f403,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $false)) ) | (~spl25_13 | ~spl25_19)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f401])).
% 0.27/1.36 thf(f401,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $false) | ($true = $false)) ) | (~spl25_13 | ~spl25_19)),
% 0.27/1.36 inference(superposition,[status(thm)],[f135,f159])).
% 0.27/1.36 thf(f159,plain,(
% 0.27/1.36 ( ! [X22 : $i] : (($true = (cP @ X22))) ) | ~spl25_19),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f158])).
% 0.27/1.36 thf(f135,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ (sK13 @ X0)) = $false) | ((cP @ X0) = $false)) ) | ~spl25_13),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f134])).
% 0.27/1.36 thf(f400,plain,(
% 0.27/1.36 spl25_21 | ~spl25_5 | ~spl25_19),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f397,f158,f104,f165])).
% 0.27/1.36 thf(f104,definition,(
% 0.27/1.36 spl25_5 <=> ! [X16 : $i] : (($false = (cP @ X16)) | ($false = (cP @ (sK21 @ X16))))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_5])],[avatar_definition])).
% 0.27/1.36 thf(f397,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $false)) ) | (~spl25_5 | ~spl25_19)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f395])).
% 0.27/1.36 thf(f395,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true = $false) | ((cP @ X0) = $false)) ) | (~spl25_5 | ~spl25_19)),
% 0.27/1.36 inference(superposition,[status(thm)],[f105,f159])).
% 0.27/1.36 thf(f105,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($false = (cP @ (sK21 @ X16))) | ($false = (cP @ X16))) ) | ~spl25_5),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f104])).
% 0.27/1.36 thf(f394,plain,(
% 0.27/1.36 ~spl25_19 | spl25_36),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f393])).
% 0.27/1.36 thf(f393,plain,(
% 0.27/1.36 $false | (~spl25_19 | spl25_36)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 0.27/1.36 thf(f392,plain,(
% 0.27/1.36 ($true != $true) | (~spl25_19 | spl25_36)),
% 0.27/1.36 inference(superposition,[status(thm)],[f245,f159])).
% 0.27/1.36 thf(f245,plain,(
% 0.27/1.36 ((cP @ sK7) != $true) | spl25_36),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f244])).
% 0.27/1.36 thf(f379,plain,(
% 0.27/1.36 spl25_12 | ~spl25_19),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f378])).
% 0.27/1.36 thf(f378,plain,(
% 0.27/1.36 $false | (spl25_12 | ~spl25_19)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f361])).
% 0.27/1.36 thf(f361,plain,(
% 0.27/1.36 ($true != $true) | (spl25_12 | ~spl25_19)),
% 0.27/1.36 inference(superposition,[status(thm)],[f131,f159])).
% 0.27/1.36 thf(f131,plain,(
% 0.27/1.36 ($true != (cP @ sK14)) | spl25_12),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f129])).
% 0.27/1.36 thf(f129,definition,(
% 0.27/1.36 spl25_12 <=> ($true = (cP @ sK14))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_12])],[avatar_definition])).
% 0.27/1.36 thf(f369,plain,(
% 0.27/1.36 spl25_4 | ~spl25_19),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f368])).
% 0.27/1.36 thf(f368,plain,(
% 0.27/1.36 $false | (spl25_4 | ~spl25_19)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f363])).
% 0.27/1.36 thf(f363,plain,(
% 0.27/1.36 ($true != $true) | (spl25_4 | ~spl25_19)),
% 0.27/1.36 inference(superposition,[status(thm)],[f101,f159])).
% 0.27/1.36 thf(f101,plain,(
% 0.27/1.36 ($true != (cP @ sK20)) | spl25_4),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f99])).
% 0.27/1.36 thf(f99,definition,(
% 0.27/1.36 spl25_4 <=> ($true = (cP @ sK20))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition])).
% 0.27/1.36 thf(f358,plain,(
% 0.27/1.36 ~spl25_30 | ~spl25_31),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f357])).
% 0.27/1.36 thf(f357,plain,(
% 0.27/1.36 $false | (~spl25_30 | ~spl25_31)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 0.27/1.36 thf(f353,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_30 | ~spl25_31)),
% 0.27/1.36 inference(superposition,[status(thm)],[f217,f212])).
% 0.27/1.36 thf(f212,plain,(
% 0.27/1.36 ($true = (cP @ sK16)) | ~spl25_30),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f210])).
% 0.27/1.36 thf(f210,definition,(
% 0.27/1.36 spl25_30 <=> ($true = (cP @ sK16))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_30])],[avatar_definition])).
% 0.27/1.36 thf(f217,plain,(
% 0.27/1.36 ($false = (cP @ sK16)) | ~spl25_31),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f215])).
% 0.27/1.36 thf(f215,definition,(
% 0.27/1.36 spl25_31 <=> ($false = (cP @ sK16))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_31])],[avatar_definition])).
% 0.27/1.36 thf(f352,plain,(
% 0.27/1.36 ~spl25_14 | ~spl25_21),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f351])).
% 0.27/1.36 thf(f351,plain,(
% 0.27/1.36 $false | (~spl25_14 | ~spl25_21)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f348])).
% 0.27/1.36 thf(f348,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_14 | ~spl25_21)),
% 0.27/1.36 inference(superposition,[status(thm)],[f166,f140])).
% 0.27/1.36 thf(f140,plain,(
% 0.27/1.36 ($true = (cP @ sK12)) | ~spl25_14),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f138])).
% 0.27/1.36 thf(f138,definition,(
% 0.27/1.36 spl25_14 <=> ($true = (cP @ sK12))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_14])],[avatar_definition])).
% 0.27/1.36 thf(f344,plain,(
% 0.27/1.36 ~spl25_16 | ~spl25_17),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f343])).
% 0.27/1.36 thf(f343,plain,(
% 0.27/1.36 $false | (~spl25_16 | ~spl25_17)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f340])).
% 0.27/1.36 thf(f340,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_16 | ~spl25_17)),
% 0.27/1.36 inference(superposition,[status(thm)],[f147,f152])).
% 0.27/1.36 thf(f152,plain,(
% 0.27/1.36 ($true = (cQ @ sK10)) | ~spl25_17),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f150])).
% 0.27/1.36 thf(f150,definition,(
% 0.27/1.36 spl25_17 <=> ($true = (cQ @ sK10))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_17])],[avatar_definition])).
% 0.27/1.36 thf(f147,plain,(
% 0.27/1.36 ($false = (cQ @ sK10)) | ~spl25_16),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f145])).
% 0.27/1.36 thf(f145,definition,(
% 0.27/1.36 spl25_16 <=> ($false = (cQ @ sK10))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_16])],[avatar_definition])).
% 0.27/1.36 thf(f338,plain,(
% 0.27/1.36 ~spl25_7 | ~spl25_14),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f337])).
% 0.27/1.36 thf(f337,plain,(
% 0.27/1.36 $false | (~spl25_7 | ~spl25_14)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f140,f112])).
% 0.27/1.36 thf(f112,plain,(
% 0.27/1.36 ( ! [X3 : $i] : (($true != (cP @ X3))) ) | ~spl25_7),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f111])).
% 0.27/1.36 thf(f111,definition,(
% 0.27/1.36 spl25_7 <=> ! [X3 : $i] : ($true != (cP @ X3))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_7])],[avatar_definition])).
% 0.27/1.36 thf(f336,plain,(
% 0.27/1.36 ~spl25_15 | ~spl25_18),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f335])).
% 0.27/1.36 thf(f335,plain,(
% 0.27/1.36 $false | (~spl25_15 | ~spl25_18)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f332])).
% 0.27/1.36 thf(f332,plain,(
% 0.27/1.36 ($true = $false) | (~spl25_15 | ~spl25_18)),
% 0.27/1.36 inference(superposition,[status(thm)],[f143,f155])).
% 0.27/1.36 thf(f143,plain,(
% 0.27/1.36 ( ! [X22 : $i] : (($true = (cQ @ X22))) ) | ~spl25_15),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f142])).
% 0.27/1.36 thf(f142,definition,(
% 0.27/1.36 spl25_15 <=> ! [X22 : $i] : ($true = (cQ @ X22))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_15])],[avatar_definition])).
% 0.27/1.36 thf(f330,plain,(
% 0.27/1.36 spl25_18 | ~spl25_15 | ~spl25_39),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f327,f256,f142,f154])).
% 0.27/1.36 thf(f256,definition,(
% 0.27/1.36 spl25_39 <=> ! [X16 : $i] : (($false = (cQ @ (sK9 @ X16))) | ($false = (cQ @ X16)))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_39])],[avatar_definition])).
% 0.27/1.36 thf(f327,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cQ @ X0) = $false)) ) | (~spl25_15 | ~spl25_39)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f326])).
% 0.27/1.36 thf(f326,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true = $false) | ((cQ @ X0) = $false)) ) | (~spl25_15 | ~spl25_39)),
% 0.27/1.36 inference(superposition,[status(thm)],[f143,f257])).
% 0.27/1.36 thf(f257,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($false = (cQ @ (sK9 @ X16))) | ($false = (cQ @ X16))) ) | ~spl25_39),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f256])).
% 0.27/1.36 thf(f324,plain,(
% 0.27/1.36 spl25_18 | ~spl25_9 | ~spl25_15),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f321,f142,f119,f154])).
% 0.27/1.36 thf(f119,definition,(
% 0.27/1.36 spl25_9 <=> ! [X0 : $i] : (($false = (cQ @ (sK1 @ X0))) | ((cQ @ X0) = $false))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_9])],[avatar_definition])).
% 0.27/1.36 thf(f321,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cQ @ X0) = $false)) ) | (~spl25_9 | ~spl25_15)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f320])).
% 0.27/1.36 thf(f320,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true = $false) | ((cQ @ X0) = $false)) ) | (~spl25_9 | ~spl25_15)),
% 0.27/1.36 inference(superposition,[status(thm)],[f143,f120])).
% 0.27/1.36 thf(f120,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($false = (cQ @ (sK1 @ X0))) | ((cQ @ X0) = $false)) ) | ~spl25_9),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f119])).
% 0.27/1.36 thf(f316,plain,(
% 0.27/1.36 ~spl25_15 | spl25_38),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f315])).
% 0.27/1.36 thf(f315,plain,(
% 0.27/1.36 $false | (~spl25_15 | spl25_38)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f253,f143])).
% 0.27/1.36 thf(f253,plain,(
% 0.27/1.36 ($true != (cQ @ sK8)) | spl25_38),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f251])).
% 0.27/1.36 thf(f251,definition,(
% 0.27/1.36 spl25_38 <=> ($true = (cQ @ sK8))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_38])],[avatar_definition])).
% 0.27/1.36 thf(f314,plain,(
% 0.27/1.36 ~spl25_7 | ~spl25_11),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f313])).
% 0.27/1.36 thf(f313,plain,(
% 0.27/1.36 $false | (~spl25_7 | ~spl25_11)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f312,f112])).
% 0.27/1.36 thf(f312,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl25_7 | ~spl25_11)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f127,f112])).
% 0.27/1.36 thf(f307,plain,(
% 0.27/1.36 ~spl25_2 | ~spl25_7),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f306])).
% 0.27/1.36 thf(f306,plain,(
% 0.27/1.36 $false | (~spl25_2 | ~spl25_7)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f305,f112])).
% 0.27/1.36 thf(f305,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl25_2 | ~spl25_7)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 0.27/1.36 thf(f301,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true != $true) | ((cP @ X0) = $true)) ) | (~spl25_2 | ~spl25_7)),
% 0.27/1.36 inference(superposition,[status(thm)],[f112,f93])).
% 0.27/1.36 thf(f283,plain,(
% 0.27/1.36 spl25_8 | ~spl25_15),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f282])).
% 0.27/1.36 thf(f282,plain,(
% 0.27/1.36 $false | (spl25_8 | ~spl25_15)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f116,f143])).
% 0.27/1.36 thf(f116,plain,(
% 0.27/1.36 ($true != (cQ @ sK2)) | spl25_8),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f114])).
% 0.27/1.36 thf(f114,definition,(
% 0.27/1.36 spl25_8 <=> ($true = (cQ @ sK2))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_8])],[avatar_definition])).
% 0.27/1.36 thf(f281,plain,(
% 0.27/1.36 ~spl25_6 | ~spl25_10),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f280])).
% 0.27/1.36 thf(f280,plain,(
% 0.27/1.36 $false | (~spl25_6 | ~spl25_10)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f279,f124])).
% 0.27/1.36 thf(f279,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (((cQ @ X0) = $true)) ) | (~spl25_6 | ~spl25_10)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 0.27/1.36 thf(f278,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true != $true) | ((cQ @ X0) = $true)) ) | (~spl25_6 | ~spl25_10)),
% 0.27/1.36 inference(superposition,[status(thm)],[f124,f109])).
% 0.27/1.36 thf(f109,plain,(
% 0.27/1.36 ( ! [X0 : $i] : (($true = (cQ @ (sK1 @ X0))) | ((cQ @ X0) = $true)) ) | ~spl25_6),
% 0.27/1.36 inference(avatar_component_clause,[status(thm)],[f108])).
% 0.27/1.36 thf(f108,definition,(
% 0.27/1.36 spl25_6 <=> ! [X0 : $i] : (($true = (cQ @ (sK1 @ X0))) | ((cQ @ X0) = $true))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_6])],[avatar_definition])).
% 0.27/1.36 thf(f271,plain,(
% 0.27/1.36 ~spl25_10 | ~spl25_15),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 0.27/1.36 thf(f270,plain,(
% 0.27/1.36 $false | (~spl25_10 | ~spl25_15)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f143,f124])).
% 0.27/1.36 thf(f269,plain,(
% 0.27/1.36 ~spl25_7 | ~spl25_20),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f268])).
% 0.27/1.36 thf(f268,plain,(
% 0.27/1.36 $false | (~spl25_7 | ~spl25_20)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f163,f112])).
% 0.27/1.36 thf(f267,plain,(
% 0.27/1.36 ~spl25_10 | ~spl25_22),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f266])).
% 0.27/1.36 thf(f266,plain,(
% 0.27/1.36 $false | (~spl25_10 | ~spl25_22)),
% 0.27/1.36 inference(trivial_inequality_removal,[status(thm)],[f265])).
% 0.27/1.36 thf(f265,plain,(
% 0.27/1.36 ($true != $true) | (~spl25_10 | ~spl25_22)),
% 0.27/1.36 inference(superposition,[status(thm)],[f124,f170])).
% 0.27/1.36 thf(f264,plain,(
% 0.27/1.36 ~spl25_7 | ~spl25_19),
% 0.27/1.36 inference(avatar_contradiction_clause,[status(thm)],[f263])).
% 0.27/1.36 thf(f263,plain,(
% 0.27/1.36 $false | (~spl25_7 | ~spl25_19)),
% 0.27/1.36 inference(subsumption_resolution,[status(thm)],[f112,f159])).
% 0.27/1.36 thf(f260,plain,(
% 0.27/1.36 ~spl25_1 | spl25_15 | spl25_7 | spl25_39),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f56,f256,f111,f142,f88])).
% 0.27/1.36 thf(f88,definition,(
% 0.27/1.36 spl25_1 <=> ($true = sP0)),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition])).
% 0.27/1.36 thf(f56,plain,(
% 0.27/1.36 ( ! [X16 : $i,X14 : $i,X15 : $i] : (($false = (cQ @ (sK9 @ X16))) | ($false = (cQ @ X16)) | ($true != sP0) | ($true != (cP @ X15)) | ($true = (cQ @ X14))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 0.27/1.36 thf(f41,plain,(
% 0.27/1.36 ( ! [X16 : $i,X14 : $i,X15 : $i] : (($true = (cQ @ X14)) | ($true != sP0) | ($true != (cP @ X15)) | ((cQ @ (sK9 @ X16)) != (cQ @ X16))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f23,plain,(
% 0.27/1.36 (($true = sP0) | ((! [X0 : $i] : ((cQ @ X0) != (cQ @ (sK1 @ X0))) | ((($true != (cQ @ sK2)) | ! [X3 : $i] : ($true != (cP @ X3))) & (! [X4 : $i] : ($true = (cQ @ X4)) | ($true = (cP @ sK3))))) & (! [X7 : $i] : ((cQ @ sK4) = (cQ @ X7)) | ((((cP @ sK5) = $true) | ($true != (cQ @ sK6))) & (! [X10 : $i] : ($true = (cQ @ X10)) | ! [X11 : $i] : ($true != (cP @ X11))))))) & (((((((cP @ sK7) = $true) | ($true != (cQ @ sK8))) & (! [X14 : $i] : ($true = (cQ @ X14)) | ! [X15 : $i] : ($true != (cP @ X15)))) | ! [X16 : $i] : ((cQ @ (sK9 @ X16)) != (cQ @ X16))) & (! [X19 : $i] : ((cQ @ X19) = (cQ @ sK10)) | ((($true != (cQ @ sK11)) | ! [X21 : $i] : ($true != (cP @ X21))) & (! [X22 : $i] : ($true = (cQ @ X22)) | ($true = (cP @ sK12)))))) | ($true != sP0))),
% 0.27/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f10,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11])).
% 0.27/1.36 thf(f11,plain,(
% 0.27/1.36 ! [X0 : $i] : (? [X1 : $i] : ((cQ @ X0) != (cQ @ X1)) => ((cQ @ X0) != (cQ @ (sK1 @ X0))))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f12,plain,(
% 0.27/1.36 ? [X2 : $i] : ($true != (cQ @ X2)) => ($true != (cQ @ sK2))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f13,plain,(
% 0.27/1.36 ? [X5 : $i] : ($true = (cP @ X5)) => ($true = (cP @ sK3))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f14,plain,(
% 0.27/1.36 ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7)) => ! [X7 : $i] : ((cQ @ sK4) = (cQ @ X7))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f15,plain,(
% 0.27/1.36 ? [X8 : $i] : ($true = (cP @ X8)) => ((cP @ sK5) = $true)),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f16,plain,(
% 0.27/1.36 ? [X9 : $i] : ($true != (cQ @ X9)) => ($true != (cQ @ sK6))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f17,plain,(
% 0.27/1.36 ? [X12 : $i] : ((cP @ X12) = $true) => ((cP @ sK7) = $true)),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f18,plain,(
% 0.27/1.36 ? [X13 : $i] : ($true != (cQ @ X13)) => ($true != (cQ @ sK8))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f19,plain,(
% 0.27/1.36 ! [X16 : $i] : (? [X17 : $i] : ((cQ @ X17) != (cQ @ X16)) => ((cQ @ (sK9 @ X16)) != (cQ @ X16)))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f20,plain,(
% 0.27/1.36 ? [X18 : $i] : ! [X19 : $i] : ((cQ @ X19) = (cQ @ X18)) => ! [X19 : $i] : ((cQ @ X19) = (cQ @ sK10))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f21,plain,(
% 0.27/1.36 ? [X20 : $i] : ($true != (cQ @ X20)) => ($true != (cQ @ sK11))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f22,plain,(
% 0.27/1.36 ? [X23 : $i] : ($true = (cP @ X23)) => ($true = (cP @ sK12))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f10,plain,(
% 0.27/1.36 (($true = sP0) | ((! [X0 : $i] : ? [X1 : $i] : ((cQ @ X0) != (cQ @ X1)) | ((? [X2 : $i] : ($true != (cQ @ X2)) | ! [X3 : $i] : ($true != (cP @ X3))) & (! [X4 : $i] : ($true = (cQ @ X4)) | ? [X5 : $i] : ($true = (cP @ X5))))) & (? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7)) | ((? [X8 : $i] : ($true = (cP @ X8)) | ? [X9 : $i] : ($true != (cQ @ X9))) & (! [X10 : $i] : ($true = (cQ @ X10)) | ! [X11 : $i] : ($true != (cP @ X11))))))) & (((((? [X12 : $i] : ((cP @ X12) = $true) | ? [X13 : $i] : ($true != (cQ @ X13))) & (! [X14 : $i] : ($true = (cQ @ X14)) | ! [X15 : $i] : ($true != (cP @ X15)))) | ! [X16 : $i] : ? [X17 : $i] : ((cQ @ X17) != (cQ @ X16))) & (? [X18 : $i] : ! [X19 : $i] : ((cQ @ X19) = (cQ @ X18)) | ((? [X20 : $i] : ($true != (cQ @ X20)) | ! [X21 : $i] : ($true != (cP @ X21))) & (! [X22 : $i] : ($true = (cQ @ X22)) | ? [X23 : $i] : ($true = (cP @ X23)))))) | ($true != sP0))),
% 0.27/1.36 inference(rectify,[status(thm)],[f9])).
% 0.27/1.36 thf(f9,plain,(
% 0.27/1.36 (($true = sP0) | ((! [X6 : $i] : ? [X7 : $i] : ((cQ @ X6) != (cQ @ X7)) | ((? [X5 : $i] : ($true != (cQ @ X5)) | ! [X4 : $i] : ($true != (cP @ X4))) & (! [X5 : $i] : ($true = (cQ @ X5)) | ? [X4 : $i] : ($true = (cP @ X4))))) & (? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7)) | ((? [X4 : $i] : ($true = (cP @ X4)) | ? [X5 : $i] : ($true != (cQ @ X5))) & (! [X5 : $i] : ($true = (cQ @ X5)) | ! [X4 : $i] : ($true != (cP @ X4))))))) & (((((? [X4 : $i] : ($true = (cP @ X4)) | ? [X5 : $i] : ($true != (cQ @ X5))) & (! [X5 : $i] : ($true = (cQ @ X5)) | ! [X4 : $i] : ($true != (cP @ X4)))) | ! [X6 : $i] : ? [X7 : $i] : ((cQ @ X6) != (cQ @ X7))) & (? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7)) | ((? [X5 : $i] : ($true != (cQ @ X5)) | ! [X4 : $i] : ($true != (cP @ X4))) & (! [X5 : $i] : ($true = (cQ @ X5)) | ? [X4 : $i] : ($true = (cP @ X4)))))) | ($true != sP0))),
% 0.27/1.36 inference(nnf_transformation,[status(thm)],[f7])).
% 0.27/1.36 thf(f7,plain,(
% 0.27/1.36 ($true = sP0) <=> ((? [X4 : $i] : ($true = (cP @ X4)) <=> ! [X5 : $i] : ($true = (cQ @ X5))) <=> ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7)))),
% 0.27/1.36 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 0.27/1.36 thf(f259,plain,(
% 0.27/1.36 ~spl25_1 | spl25_37 | spl25_7 | spl25_15),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f55,f142,f111,f248,f88])).
% 0.27/1.36 thf(f55,plain,(
% 0.27/1.36 ( ! [X16 : $i,X14 : $i,X15 : $i] : (($true = (cQ @ (sK9 @ X16))) | ($true != (cP @ X15)) | ($true = (cQ @ X16)) | ($true = (cQ @ X14)) | ($true != sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 0.27/1.36 thf(f258,plain,(
% 0.27/1.36 spl25_36 | spl25_39 | ~spl25_1 | ~spl25_38),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f58,f251,f88,f256,f244])).
% 0.27/1.36 thf(f58,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($false = (cQ @ (sK9 @ X16))) | ($false = (cQ @ X16)) | ($true != (cQ @ sK8)) | ((cP @ sK7) = $true) | ($true != sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 0.27/1.36 thf(f42,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (((cP @ sK7) = $true) | ($true != sP0) | ((cQ @ (sK9 @ X16)) != (cQ @ X16)) | ($true != (cQ @ sK8))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f241,plain,(
% 0.27/1.36 spl25_1 | spl25_35 | spl25_6 | spl25_15),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f59,f142,f108,f238,f88])).
% 0.27/1.36 thf(f59,plain,(
% 0.27/1.36 ( ! [X0 : $i,X4 : $i] : (((cQ @ X0) = $true) | ($true = (cP @ sK3)) | ($true = sP0) | ($true = (cQ @ (sK1 @ X0))) | ($true = (cQ @ X4))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 0.27/1.36 thf(f45,plain,(
% 0.27/1.36 ( ! [X0 : $i,X4 : $i] : (($true = (cP @ sK3)) | ((cQ @ X0) != (cQ @ (sK1 @ X0))) | ($true = (cQ @ X4)) | ($true = sP0)) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f220,plain,(
% 0.27/1.36 spl25_15 | spl25_1 | spl25_15 | spl25_29 | spl25_7),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f66,f111,f203,f142,f88,f142])).
% 0.27/1.36 thf(f66,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (($true = sP0) | ($false = (cQ @ sK4)) | ($true = (cQ @ X10)) | ($true = (cQ @ X7)) | ($true != (cP @ X11))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 0.27/1.36 thf(f43,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (((cQ @ sK4) = (cQ @ X7)) | ($true != (cP @ X11)) | ($true = (cQ @ X10)) | ($true = sP0)) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f219,plain,(
% 0.27/1.36 spl25_18 | spl25_15 | spl25_28 | spl25_1 | spl25_7),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f65,f111,f88,f198,f142,f154])).
% 0.27/1.36 thf(f65,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (($true != (cP @ X11)) | ($true = (cQ @ X10)) | ($false = (cQ @ X7)) | ($true = (cQ @ sK4)) | ($true = sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 0.27/1.36 thf(f218,plain,(
% 0.27/1.36 spl25_31 | ~spl25_1 | spl25_19 | spl25_10 | spl25_19),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f68,f158,f123,f158,f88,f215])).
% 0.27/1.36 thf(f68,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (($false = (cP @ sK16)) | ($true != sP0) | ((cP @ X10) = $true) | ((cQ @ X11) != $true) | ($true = (cP @ X7))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 0.27/1.36 thf(f51,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (((cP @ sK16) = (cP @ X7)) | ((cQ @ X11) != $true) | ((cP @ X10) = $true) | ($true != sP0)) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 thf(f38,plain,(
% 0.27/1.36 (((! [X0 : $i] : ((cP @ X0) != (cP @ (sK13 @ X0))) | ((($true != (cP @ sK14)) | ! [X3 : $i] : ($true != (cQ @ X3))) & (! [X4 : $i] : ($true = (cP @ X4)) | ((cQ @ sK15) = $true)))) & (! [X7 : $i] : ((cP @ sK16) = (cP @ X7)) | ((($true = (cQ @ sK17)) | ($true != (cP @ sK18))) & (! [X10 : $i] : ((cP @ X10) = $true) | ! [X11 : $i] : ((cQ @ X11) != $true))))) | ($true != sP0)) & (((((($true = (cQ @ sK19)) | ($true != (cP @ sK20))) & (! [X14 : $i] : ($true = (cP @ X14)) | ! [X15 : $i] : ($true != (cQ @ X15)))) | ! [X16 : $i] : ((cP @ (sK21 @ X16)) != (cP @ X16))) & (! [X19 : $i] : ((cP @ sK22) = (cP @ X19)) | ((($true != (cP @ sK23)) | ! [X21 : $i] : ((cQ @ X21) != $true)) & (! [X22 : $i] : ($true = (cP @ X22)) | ($true = (cQ @ sK24)))))) | ($true = sP0))),
% 0.27/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24])],[f25,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26])).
% 0.27/1.36 thf(f26,plain,(
% 0.27/1.36 ! [X0 : $i] : (? [X1 : $i] : ((cP @ X0) != (cP @ X1)) => ((cP @ X0) != (cP @ (sK13 @ X0))))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f27,plain,(
% 0.27/1.36 ? [X2 : $i] : ($true != (cP @ X2)) => ($true != (cP @ sK14))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f28,plain,(
% 0.27/1.36 ? [X5 : $i] : ($true = (cQ @ X5)) => ((cQ @ sK15) = $true)),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f29,plain,(
% 0.27/1.36 ? [X6 : $i] : ! [X7 : $i] : ((cP @ X6) = (cP @ X7)) => ! [X7 : $i] : ((cP @ sK16) = (cP @ X7))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f30,plain,(
% 0.27/1.36 ? [X8 : $i] : ($true = (cQ @ X8)) => ($true = (cQ @ sK17))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f31,plain,(
% 0.27/1.36 ? [X9 : $i] : ($true != (cP @ X9)) => ($true != (cP @ sK18))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f32,plain,(
% 0.27/1.36 ? [X12 : $i] : ($true = (cQ @ X12)) => ($true = (cQ @ sK19))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f33,plain,(
% 0.27/1.36 ? [X13 : $i] : ($true != (cP @ X13)) => ($true != (cP @ sK20))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f34,plain,(
% 0.27/1.36 ! [X16 : $i] : (? [X17 : $i] : ((cP @ X16) != (cP @ X17)) => ((cP @ (sK21 @ X16)) != (cP @ X16)))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f35,plain,(
% 0.27/1.36 ? [X18 : $i] : ! [X19 : $i] : ((cP @ X18) = (cP @ X19)) => ! [X19 : $i] : ((cP @ sK22) = (cP @ X19))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f36,plain,(
% 0.27/1.36 ? [X20 : $i] : ((cP @ X20) != $true) => ($true != (cP @ sK23))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f37,plain,(
% 0.27/1.36 ? [X23 : $i] : ($true = (cQ @ X23)) => ($true = (cQ @ sK24))),
% 0.27/1.36 introduced(definition,[],[choice_axiom])).
% 0.27/1.36 thf(f25,plain,(
% 0.27/1.36 (((! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) != (cP @ X1)) | ((? [X2 : $i] : ($true != (cP @ X2)) | ! [X3 : $i] : ($true != (cQ @ X3))) & (! [X4 : $i] : ($true = (cP @ X4)) | ? [X5 : $i] : ($true = (cQ @ X5))))) & (? [X6 : $i] : ! [X7 : $i] : ((cP @ X6) = (cP @ X7)) | ((? [X8 : $i] : ($true = (cQ @ X8)) | ? [X9 : $i] : ($true != (cP @ X9))) & (! [X10 : $i] : ((cP @ X10) = $true) | ! [X11 : $i] : ((cQ @ X11) != $true))))) | ($true != sP0)) & (((((? [X12 : $i] : ($true = (cQ @ X12)) | ? [X13 : $i] : ($true != (cP @ X13))) & (! [X14 : $i] : ($true = (cP @ X14)) | ! [X15 : $i] : ($true != (cQ @ X15)))) | ! [X16 : $i] : ? [X17 : $i] : ((cP @ X16) != (cP @ X17))) & (? [X18 : $i] : ! [X19 : $i] : ((cP @ X18) = (cP @ X19)) | ((? [X20 : $i] : ((cP @ X20) != $true) | ! [X21 : $i] : ((cQ @ X21) != $true)) & (! [X22 : $i] : ($true = (cP @ X22)) | ? [X23 : $i] : ($true = (cQ @ X23)))))) | ($true = sP0))),
% 0.27/1.36 inference(rectify,[status(thm)],[f24])).
% 0.27/1.36 thf(f24,plain,(
% 0.27/1.36 (((! [X2 : $i] : ? [X3 : $i] : ((cP @ X3) != (cP @ X2)) | ((? [X0 : $i] : ((cP @ X0) != $true) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (! [X0 : $i] : ((cP @ X0) = $true) | ? [X1 : $i] : ((cQ @ X1) = $true)))) & (? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)) | ((? [X1 : $i] : ((cQ @ X1) = $true) | ? [X0 : $i] : ((cP @ X0) != $true)) & (! [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cQ @ X1) != $true))))) | ($true != sP0)) & (((((? [X1 : $i] : ((cQ @ X1) = $true) | ? [X0 : $i] : ((cP @ X0) != $true)) & (! [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cQ @ X1) != $true))) | ! [X2 : $i] : ? [X3 : $i] : ((cP @ X3) != (cP @ X2))) & (? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)) | ((? [X0 : $i] : ((cP @ X0) != $true) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (! [X0 : $i] : ((cP @ X0) = $true) | ? [X1 : $i] : ((cQ @ X1) = $true))))) | ($true = sP0))),
% 0.27/1.36 inference(nnf_transformation,[status(thm)],[f8])).
% 0.27/1.36 thf(f8,plain,(
% 0.27/1.36 ($true = sP0) <~> ((? [X1 : $i] : ((cQ @ X1) = $true) <=> ! [X0 : $i] : ((cP @ X0) = $true)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)))),
% 0.27/1.36 inference(definition_folding,[status(thm)],[f6,f7])).
% 0.27/1.36 thf(f6,plain,(
% 0.27/1.36 ((? [X4 : $i] : ($true = (cP @ X4)) <=> ! [X5 : $i] : ($true = (cQ @ X5))) <=> ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7))) <~> ((? [X1 : $i] : ((cQ @ X1) = $true) <=> ! [X0 : $i] : ((cP @ X0) = $true)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)))),
% 0.27/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 0.27/1.36 thf(f5,plain,(
% 0.27/1.36 ~(((? [X4 : $i] : ($true = (cP @ X4)) <=> ! [X5 : $i] : ($true = (cQ @ X5))) <=> ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X6) = (cQ @ X7))) <=> ((? [X1 : $i] : ((cQ @ X1) = $true) <=> ! [X0 : $i] : ((cP @ X0) = $true)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2))))),
% 0.27/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 0.27/1.36 thf(f4,plain,(
% 0.27/1.36 ~(((! [X0 : $i] : (cP @ X0) <=> ? [X1 : $i] : (cQ @ X1)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X2) <=> (cP @ X3))) <=> ((? [X4 : $i] : (cP @ X4) <=> ! [X5 : $i] : (cQ @ X5)) <=> ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X7) <=> (cQ @ X6))))),
% 0.27/1.36 inference(rectify,[status(thm)],[f2])).
% 0.27/1.36 thf(f2,negated_conjecture,(
% 0.27/1.36 ~(((! [X1 : $i] : (cP @ X1) <=> ? [X0 : $i] : (cQ @ X0)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0))))),
% 0.27/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 0.27/1.36 thf(f1,conjecture,(
% 0.27/1.36 ((! [X1 : $i] : (cP @ X1) <=> ? [X0 : $i] : (cQ @ X0)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0)))),
% 0.27/1.36 file('/export/starexec/sandbox2/tmp/tmp.BL3uNYjvsH/DTF2THF_13477.p',cX2129)).
% 0.27/1.36 thf(f213,plain,(
% 0.27/1.36 spl25_19 | spl25_10 | spl25_21 | ~spl25_1 | spl25_30),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f67,f210,f88,f165,f123,f158])).
% 0.27/1.36 thf(f67,plain,(
% 0.27/1.36 ( ! [X10 : $i,X11 : $i,X7 : $i] : (((cQ @ X11) != $true) | ($false = (cP @ X7)) | ((cP @ X10) = $true) | ($true = (cP @ sK16)) | ($true != sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 0.27/1.36 thf(f207,plain,(
% 0.27/1.36 spl25_2 | spl25_1 | spl25_19 | spl25_10),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f69,f123,f158,f88,f92])).
% 0.27/1.36 thf(f69,plain,(
% 0.27/1.36 ( ! [X16 : $i,X14 : $i,X15 : $i] : (($true != (cQ @ X15)) | ($true = (cP @ X14)) | ($true = (cP @ X16)) | ($true = (cP @ (sK21 @ X16))) | ($true = sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 0.27/1.36 thf(f49,plain,(
% 0.27/1.36 ( ! [X16 : $i,X14 : $i,X15 : $i] : (($true = sP0) | ((cP @ (sK21 @ X16)) != (cP @ X16)) | ($true = (cP @ X14)) | ($true != (cQ @ X15))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 thf(f187,plain,(
% 0.27/1.36 spl25_11 | spl25_19 | spl25_25 | ~spl25_1),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f73,f88,f184,f158,f126])).
% 0.27/1.36 thf(f73,plain,(
% 0.27/1.36 ( ! [X0 : $i,X4 : $i] : (((cP @ X0) = $true) | ((cQ @ sK15) = $true) | ((cP @ (sK13 @ X0)) = $true) | ($true = (cP @ X4)) | ($true != sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 0.27/1.36 thf(f53,plain,(
% 0.27/1.36 ( ! [X0 : $i,X4 : $i] : (((cQ @ sK15) = $true) | ($true = (cP @ X4)) | ($true != sP0) | ((cP @ X0) != (cP @ (sK13 @ X0)))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 thf(f176,plain,(
% 0.27/1.36 spl25_1 | spl25_23 | spl25_19 | spl25_22 | spl25_19),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f78,f158,f168,f158,f173,f88])).
% 0.27/1.36 thf(f78,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (($true = (cQ @ sK24)) | ($true = (cP @ X22)) | ($false = (cP @ sK22)) | ($true = (cP @ X19)) | ($true = sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.27/1.36 thf(f47,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (((cP @ sK22) = (cP @ X19)) | ($true = (cP @ X22)) | ($true = sP0) | ($true = (cQ @ sK24))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 thf(f171,plain,(
% 0.27/1.36 spl25_19 | spl25_20 | spl25_1 | spl25_21 | spl25_22),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f77,f168,f165,f88,f161,f158])).
% 0.27/1.36 thf(f77,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (($true = sP0) | ($true = (cP @ sK22)) | ($false = (cP @ X19)) | ($true = (cQ @ sK24)) | ($true = (cP @ X22))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.27/1.36 thf(f156,plain,(
% 0.27/1.36 spl25_17 | spl25_14 | spl25_15 | spl25_18 | ~spl25_1),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f80,f88,f154,f142,f138,f150])).
% 0.27/1.36 thf(f80,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (($false = (cQ @ X19)) | ($true = (cQ @ sK10)) | ($true = (cP @ sK12)) | ($true != sP0) | ($true = (cQ @ X22))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 0.27/1.36 thf(f39,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (($true != sP0) | ($true = (cP @ sK12)) | ((cQ @ X19) = (cQ @ sK10)) | ($true = (cQ @ X22))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f148,plain,(
% 0.27/1.36 spl25_14 | spl25_15 | spl25_15 | ~spl25_1 | spl25_16),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f79,f145,f88,f142,f142,f138])).
% 0.27/1.36 thf(f79,plain,(
% 0.27/1.36 ( ! [X19 : $i,X22 : $i] : (($true = (cQ @ X22)) | ($false = (cQ @ sK10)) | ($true = (cQ @ X19)) | ($true != sP0) | ($true = (cP @ sK12))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 0.27/1.36 thf(f136,plain,(
% 0.27/1.36 spl25_13 | spl25_10 | ~spl25_12 | ~spl25_1),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f82,f88,f129,f123,f134])).
% 0.27/1.36 thf(f82,plain,(
% 0.27/1.36 ( ! [X3 : $i,X0 : $i] : (($true != (cP @ sK14)) | ((cP @ (sK13 @ X0)) = $false) | ($true != (cQ @ X3)) | ($true != sP0) | ((cP @ X0) = $false)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 0.27/1.36 thf(f54,plain,(
% 0.27/1.36 ( ! [X3 : $i,X0 : $i] : (((cP @ X0) != (cP @ (sK13 @ X0))) | ($true != (cQ @ X3)) | ($true != (cP @ sK14)) | ($true != sP0)) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 thf(f121,plain,(
% 0.27/1.36 spl25_1 | ~spl25_8 | spl25_9 | spl25_7),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f84,f111,f119,f114,f88])).
% 0.27/1.36 thf(f84,plain,(
% 0.27/1.36 ( ! [X3 : $i,X0 : $i] : (($false = (cQ @ (sK1 @ X0))) | ($true = sP0) | ((cQ @ X0) = $false) | ($true != (cP @ X3)) | ($true != (cQ @ sK2))) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 0.27/1.36 thf(f46,plain,(
% 0.27/1.36 ( ! [X3 : $i,X0 : $i] : (($true != (cQ @ sK2)) | ($true != (cP @ X3)) | ($true = sP0) | ((cQ @ X0) != (cQ @ (sK1 @ X0)))) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 0.27/1.36 thf(f106,plain,(
% 0.27/1.36 spl25_1 | spl25_5 | spl25_3 | ~spl25_4),
% 0.27/1.36 inference(avatar_split_clause,[status(thm)],[f86,f99,f95,f104,f88])).
% 0.27/1.36 thf(f86,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($false = (cP @ X16)) | ($false = (cP @ (sK21 @ X16))) | ($true = (cQ @ sK19)) | ($true != (cP @ sK20)) | ($true = sP0)) )),
% 0.27/1.36 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 0.27/1.36 thf(f50,plain,(
% 0.27/1.36 ( ! [X16 : $i] : (($true != (cP @ sK20)) | ((cP @ (sK21 @ X16)) != (cP @ X16)) | ($true = (cQ @ sK19)) | ($true = sP0)) )),
% 0.27/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 0.27/1.36 % SZS output end Proof for DTF2THF_13477
% 0.27/1.36 % (13720)------------------------------
% 0.27/1.36 % (13720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.27/1.36 % (13720)Termination reason: Refutation
% 0.27/1.36
% 0.27/1.36 % (13720)Memory used [KB]: 5884
% 0.27/1.36 % (13720)Time elapsed: 0.028 s
% 0.27/1.36 % (13720)Instructions burned: 33 (million)
% 0.27/1.36 % (13720)------------------------------
% 0.27/1.36 % (13720)------------------------------
% 0.27/1.36 % (13719)Success in time 0.041 s
%------------------------------------------------------------------------------