%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU704^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:32 AM UTC 2026
% Result : Theorem 1.66s 1.47s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 139 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 1722 ( 587 equ; 20 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 1522 ( 252 ~; 287 |; 249 &; 670 @)
% ( 12 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 29 con; 0-2 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 283 ( 87 ^; 152 !; 44 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
singleton: $i > $o ).
thf(func_def_41,type,
ph21:
!>[X0: $tType] : X0 ).
thf(f606,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f185,f193,f280,f414,f415,f544,f605]) ).
thf(f605,plain,
( spl20_7
| ~ spl20_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f604]) ).
thf(f604,plain,
( $false
| spl20_7
| ~ spl20_15 ),
inference(trivial_inequality_removal,[status(thm)],[f603]) ).
thf(f603,plain,
( ( $true = $false )
| spl20_7
| ~ spl20_15 ),
inference(forward_demodulation,[status(thm)],[f602,f411]) ).
thf(f411,plain,
( ( sK12 = $false )
| ~ spl20_15 ),
inference(avatar_component_clause,[status(thm)],[f409]) ).
thf(f409,definition,
( spl20_15
<=> ( sK12 = $false ) ),
introduced(definition,[new_symbols(naming,[spl20_15])],[avatar_definition]) ).
thf(f602,plain,
( ( $true = sK12 )
| spl20_7
| ~ spl20_15 ),
inference(subsumption_resolution,[status(thm)],[f581,f601]) ).
thf(f601,plain,
( ( sK15 = sK24 )
| spl20_7
| ~ spl20_15 ),
inference(trivial_inequality_removal,[status(thm)],[f600]) ).
thf(f600,plain,
( ( $true = $false )
| ( sK15 = sK24 )
| spl20_7
| ~ spl20_15 ),
inference(forward_demodulation,[status(thm)],[f599,f411]) ).
thf(f599,plain,
( ( $true = sK12 )
| ( sK15 = sK24 )
| spl20_7 ),
inference(duplicate_literal_removal,[status(thm)],[f598]) ).
thf(f598,plain,
( ( $true = sK12 )
| ( sK15 = sK24 )
| ( sK15 = sK24 )
| spl20_7 ),
inference(equality_proxy_clausification,[status(thm)],[f595]) ).
thf(f595,plain,
( ( $true
= ( sK15 = sK24 ) )
| ( sK15 = sK24 )
| ( $true = sK12 )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f586]) ).
thf(f586,plain,
( ( sK15 = sK24 )
| ( $true = sK12 )
| ( $true
= ( ~ sK12
& ( sK15 = sK24 ) ) )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f585]) ).
thf(f585,plain,
( ( $true
= ( ( sK14 = sK24 )
& sK12 ) )
| ( $true
= ( ~ sK12
& ( sK15 = sK24 ) ) )
| ( sK15 = sK24 )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f584]) ).
thf(f584,plain,
( ( sK15 = sK24 )
| ( $true
= ( ( ~ sK12
& ( sK15 = sK24 ) )
| ( ( sK14 = sK24 )
& sK12 ) ) )
| spl20_7 ),
inference(equality_proxy_clausification,[status(thm)],[f573]) ).
thf(f573,plain,
( ( $true
= ( sK15 = sK24 ) )
| ( $true
= ( ( ~ sK12
& ( sK15 = sK24 ) )
| ( ( sK14 = sK24 )
& sK12 ) ) )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f572]) ).
thf(f572,plain,
( ( ( sK15 = sK24 )
!= ( ( ~ sK12
& ( sK15 = sK24 ) )
| ( ( sK14 = sK24 )
& sK12 ) ) )
| spl20_7 ),
inference(beta_eta_normalization,[status(thm)],[f571]) ).
thf(f571,plain,
( ( ( sK15 = sK24 )
!= ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) )
@ sK24 ) )
| spl20_7 ),
inference(negative_extensionality,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( (=) @ sK15 )
!= ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
| spl20_7 ),
inference(avatar_component_clause,[status(thm)],[f187]) ).
thf(f187,definition,
( spl20_7
<=> ( ( (=) @ sK15 )
= ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl20_7])],[avatar_definition]) ).
thf(f581,plain,
( ( sK15 != sK24 )
| ( $true = sK12 )
| spl20_7 ),
inference(duplicate_literal_removal,[status(thm)],[f580]) ).
thf(f580,plain,
( ( sK15 != sK24 )
| ( $true = sK12 )
| ( sK15 != sK24 )
| spl20_7 ),
inference(equality_proxy_clausification,[status(thm)],[f579]) ).
thf(f579,plain,
( ( ( sK15 = sK24 )
= $false )
| ( sK15 != sK24 )
| ( $true = sK12 )
| spl20_7 ),
inference(not_proxy_clausification,[status(thm)],[f578]) ).
thf(f578,plain,
( ( sK15 != sK24 )
| ( ( ~ sK12 ) = $false )
| ( ( sK15 = sK24 )
= $false )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f577]) ).
thf(f577,plain,
( ( sK15 != sK24 )
| ( $false
= ( ~ sK12
& ( sK15 = sK24 ) ) )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f575]) ).
thf(f575,plain,
( ( sK15 != sK24 )
| ( ( ( ~ sK12
& ( sK15 = sK24 ) )
| ( ( sK14 = sK24 )
& sK12 ) )
= $false )
| spl20_7 ),
inference(equality_proxy_clausification,[status(thm)],[f574]) ).
thf(f574,plain,
( ( ( sK15 = sK24 )
= $false )
| ( ( ( ~ sK12
& ( sK15 = sK24 ) )
| ( ( sK14 = sK24 )
& sK12 ) )
= $false )
| spl20_7 ),
inference(binary_proxy_clausification,[status(thm)],[f572]) ).
thf(f544,plain,
~ spl20_8,
inference(avatar_contradiction_clause,[status(thm)],[f543]) ).
thf(f543,plain,
( $false
| ~ spl20_8 ),
inference(trivial_inequality_removal,[status(thm)],[f542]) ).
thf(f542,plain,
( ( $true = $false )
| ~ spl20_8 ),
inference(backward_demodulation,[status(thm)],[f198,f541]) ).
thf(f541,plain,
( ( ( in @ sK15 @ ( setadjoin @ sK15 @ emptyset ) )
= $false )
| ~ spl20_8 ),
inference(equality_resolution,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X0: $i] :
( ( ( setadjoin @ sK15 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ sK15 @ emptyset ) )
= $false ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[status(thm)],[f191]) ).
thf(f191,definition,
( spl20_8
<=> ! [X0: $i] :
( ( ( setadjoin @ sK15 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ sK15 @ emptyset ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl20_8])],[avatar_definition]) ).
thf(f198,plain,
( $true
= ( in @ sK15 @ ( setadjoin @ sK15 @ emptyset ) ) ),
inference(forward_demodulation,[status(thm)],[f197,f132]) ).
thf(f132,plain,
( ( setadjoin @ sK15 @ emptyset )
= ( dsetconstr @ sK13 @ ( (=) @ sK15 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ( setadjoin @ sK15 @ emptyset )
= ( dsetconstr @ sK13 @ ( (=) @ sK15 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f129,f75]) ).
thf(f75,plain,
( $true
= ( in @ sK15 @ sK13 ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( iffalseProp2 = $true )
& ( iftrueProp1 = $true )
& ( iftrueProp2 = $true )
& ( $true
= ( in @ sK15 @ sK13 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) )
& ( $true
= ( in @ sK14 @ sK13 ) )
& ( iffalseProp1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f32,f49,f48]) ).
thf(f48,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ~ X0
& ( X3 = Y0 ) )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK13 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( X3 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ) )
& ( $true
= ( in @ sK14 @ sK13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f49,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK13 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( X3 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ) )
=> ( ( $true
= ( in @ sK15 @ sK13 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( iffalseProp2 = $true )
& ( iftrueProp1 = $true )
& ( iftrueProp2 = $true )
& ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ~ X0
& ( X3 = Y0 ) )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( iffalseProp1 = $true ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ~ X0
& ( X3 = Y0 ) )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true
= ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ~ X0
& ( X3 = Y0 ) )
| ( ( X2 = Y0 )
& X0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X4: $i] :
( ( X0
& ( X2 = X4 ) )
| ( ( X3 = X4 )
& ~ X0 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X2: $o,X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( X2
& ( X1 = X4 ) )
| ( ( X3 = X4 )
& ~ X2 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X2: $o,X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( X2
& ( X1 = X4 ) )
| ( ( X3 = X4 )
& ~ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',ifSingleton) ).
thf(f129,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK13 ) )
| ( ( dsetconstr @ sK13 @ ( (=) @ X0 ) )
= ( setadjoin @ X0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK13 ) )
| ( $true != $true )
| ( ( dsetconstr @ sK13 @ ( (=) @ X0 ) )
= ( setadjoin @ X0 @ emptyset ) ) ),
inference(superposition,[status(thm)],[f118,f75]) ).
thf(f118,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6 @ ( (=) @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f117]) ).
thf(f117,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 = Y0 ) ) )
| ( $true
!= ( in @ X7 @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( $true
& ( X5 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( $true
& ( X5 = Y0 ) )
| $false ) )
= ( setadjoin @ X5 @ emptyset ) ) ),
inference(boolean_simplification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( $true
& ( X5 = Y0 ) )
| ( $false
& ( X7 = Y0 ) ) ) ) )
| ( $true
!= ( in @ X7 @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( $true
& ( X5 = Y0 ) )
| ( ~ $true
& ( X7 = Y0 ) ) ) )
= ( setadjoin @ X5 @ emptyset ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( $true
!= ( in @ X7 @ X6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( $true
& ( X5 = Y0 ) )
| ( ~ $true
& ( X7 = Y0 ) ) ) )
= ( setadjoin @ X5 @ emptyset ) )
| ( $true != $true )
| ( $true
!= ( in @ X7 @ X6 ) ) ),
inference(equality_resolution,[status(thm)],[f104]) ).
thf(f104,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( $true != X4 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f79,f76]) ).
thf(f76,plain,
iftrueProp2 = $true,
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f79,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ( $true != X4 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
| ( iftrueProp2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( iftrueProp2 = $true )
| ( ( $true
= ( in @ sK17 @ sK18 ) )
& ( sK16 = $true )
& ( $true
= ( in @ sK19 @ sK18 ) )
& ( ( dsetconstr @ sK18
@ ^ [Y0: $i] :
( ( sK16
& ( sK17 = Y0 ) )
| ( ~ sK16
& ( sK19 = Y0 ) ) ) )
!= ( setadjoin @ sK17 @ emptyset ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ! [X7: $i] :
( ( $true != X4 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) ) ) )
| ( iftrueProp2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f52,f54,f53]) ).
thf(f53,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( $true
= ( in @ X3 @ X2 ) )
& ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) )
=> ( ( $true
= ( in @ sK17 @ sK18 ) )
& ? [X3: $i] :
( ( sK16 = $true )
& ( $true
= ( in @ X3 @ sK18 ) )
& ( ( dsetconstr @ sK18
@ ^ [Y0: $i] :
( ( sK16
& ( sK17 = Y0 ) )
| ( ~ sK16
& ( X3 = Y0 ) ) ) )
!= ( setadjoin @ sK17 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ? [X3: $i] :
( ( sK16 = $true )
& ( $true
= ( in @ X3 @ sK18 ) )
& ( ( dsetconstr @ sK18
@ ^ [Y0: $i] :
( ( sK16
& ( sK17 = Y0 ) )
| ( ~ sK16
& ( X3 = Y0 ) ) ) )
!= ( setadjoin @ sK17 @ emptyset ) ) )
=> ( ( sK16 = $true )
& ( $true
= ( in @ sK19 @ sK18 ) )
& ( ( dsetconstr @ sK18
@ ^ [Y0: $i] :
( ( sK16
& ( sK17 = Y0 ) )
| ( ~ sK16
& ( sK19 = Y0 ) ) ) )
!= ( setadjoin @ sK17 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ( ( iftrueProp2 = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( $true
= ( in @ X3 @ X2 ) )
& ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ( $true
!= ( in @ X5 @ X6 ) )
| ! [X7: $i] :
( ( $true != X4 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) ) ) )
| ( iftrueProp2 != $true ) ) ),
inference(rectify,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( iftrueProp2 = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( $true
= ( in @ X3 @ X2 ) )
& ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) ) )
& ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) )
| ( iftrueProp2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( iftrueProp2 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( iftrueProp2 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
| ( $true != X0 )
| ( $true
!= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( iftrueProp2 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true = X0 )
=> ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X0 )
| ( ( X1 = X4 )
& X0 ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) )
= iftrueProp2 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: $o,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X2
=> ( ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X2 )
| ( ( X1 = X4 )
& X2 ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) )
= iftrueProp2 ),
file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',iftrueProp2) ).
thf(f197,plain,
( $true
= ( in @ sK15 @ ( dsetconstr @ sK13 @ ( (=) @ sK15 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ( $true != $true )
| ( $true
= ( in @ sK15 @ ( dsetconstr @ sK13 @ ( (=) @ sK15 ) ) ) ) ),
inference(superposition,[status(thm)],[f137,f75]) ).
thf(f137,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK13 ) )
| ( $true
= ( in @ X0 @ ( dsetconstr @ sK13 @ ( (=) @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( dsetconstr @ sK13 @ ( (=) @ X0 ) ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ sK13 ) ) ),
inference(superposition,[status(thm)],[f125,f75]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ ( dsetconstr @ X1 @ ( (=) @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( $true
& ( X2 = Y0 ) ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( $true
& ( X2 = Y0 ) )
| $false ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( $true
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& $false ) ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( $true
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ $true ) ) ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( $true
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ $true ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f77]) ).
thf(f77,plain,
iftrueProp1 = $true,
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) )
| ( iftrueProp1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ( ( $true
= ( in @ sK10 @ sK9 ) )
& ( $true = sK8 )
& ( $true
= ( in @ sK11 @ sK9 ) )
& ( $true
!= ( in @ sK10
@ ( dsetconstr @ sK9
@ ^ [Y0: $i] :
( ( sK8
& ( sK10 = Y0 ) )
| ( ( sK11 = Y0 )
& ~ sK8 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f44,f46,f45]) ).
thf(f45,plain,
( ? [X4: $o,X5: $i,X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true = X4 )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X6
@ ( dsetconstr @ X5
@ ^ [Y0: $i] :
( ( X4
& ( X6 = Y0 ) )
| ( ( X7 = Y0 )
& ~ X4 ) ) ) ) ) ) )
=> ( ( $true
= ( in @ sK10 @ sK9 ) )
& ? [X7: $i] :
( ( $true = sK8 )
& ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ sK10
@ ( dsetconstr @ sK9
@ ^ [Y0: $i] :
( ( sK8
& ( sK10 = Y0 ) )
| ( ( X7 = Y0 )
& ~ sK8 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
( ? [X7: $i] :
( ( $true = sK8 )
& ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ sK10
@ ( dsetconstr @ sK9
@ ^ [Y0: $i] :
( ( sK8
& ( sK10 = Y0 ) )
| ( ( X7 = Y0 )
& ~ sK8 ) ) ) ) ) )
=> ( ( $true = sK8 )
& ( $true
= ( in @ sK11 @ sK9 ) )
& ( $true
!= ( in @ sK10
@ ( dsetconstr @ sK9
@ ^ [Y0: $i] :
( ( sK8
& ( sK10 = Y0 ) )
| ( ( sK11 = Y0 )
& ~ sK8 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ? [X4: $o,X5: $i,X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true = X4 )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X6
@ ( dsetconstr @ X5
@ ^ [Y0: $i] :
( ( X4
& ( X6 = Y0 ) )
| ( ( X7 = Y0 )
& ~ X4 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X0: $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) )
<=> ( iftrueProp1 = $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ( iftrueProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) )
| ( $true != X0 )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( iftrueProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true = X0 )
=> ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( X0
& ( X2 = Y0 ) )
| ( ( X3 = Y0 )
& ~ X0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( X0
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X4: $i] :
( ( ~ X0
& ( X3 = X4 ) )
| ( ( X2 = X4 )
& X0 ) ) ) ) ) ) )
= iftrueProp1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X2
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ~ X2
& ( X3 = X4 ) )
| ( ( X1 = X4 )
& X2 ) ) ) ) ) ) )
= iftrueProp1 ),
file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',iftrueProp1) ).
thf(f415,plain,
( ~ spl20_12
| spl20_15
| spl20_5 ),
inference(avatar_split_clause,[status(thm)],[f379,f179,f409,f396]) ).
thf(f396,definition,
( spl20_12
<=> ( sK23 = sK14 ) ),
introduced(definition,[new_symbols(naming,[spl20_12])],[avatar_definition]) ).
thf(f179,definition,
( spl20_5
<=> ( ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) )
= ( (=) @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl20_5])],[avatar_definition]) ).
thf(f379,plain,
( ( sK23 != sK14 )
| ( sK12 = $false )
| spl20_5 ),
inference(duplicate_literal_removal,[status(thm)],[f378]) ).
thf(f378,plain,
( ( sK23 != sK14 )
| ( sK23 != sK14 )
| ( sK12 = $false )
| spl20_5 ),
inference(equality_proxy_clausification,[status(thm)],[f377]) ).
thf(f377,plain,
( ( sK12 = $false )
| ( sK23 != sK14 )
| ( ( sK14 = sK23 )
= $false )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f376]) ).
thf(f376,plain,
( ( ( ( sK14 = sK23 )
& sK12 )
= $false )
| ( sK23 != sK14 )
| spl20_5 ),
inference(equality_proxy_clausification,[status(thm)],[f370]) ).
thf(f370,plain,
( ( ( sK14 = sK23 )
= $false )
| ( ( ( sK14 = sK23 )
& sK12 )
= $false )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f369]) ).
thf(f369,plain,
( ( $false
= ( ( ~ sK12
& ( sK15 = sK23 ) )
| ( ( sK14 = sK23 )
& sK12 ) ) )
| ( ( sK14 = sK23 )
= $false )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f367]) ).
thf(f367,plain,
( ( ( sK14 = sK23 )
!= ( ( ~ sK12
& ( sK15 = sK23 ) )
| ( ( sK14 = sK23 )
& sK12 ) ) )
| spl20_5 ),
inference(beta_eta_normalization,[status(thm)],[f366]) ).
thf(f366,plain,
( ( ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) )
@ sK23 )
!= ( sK14 = sK23 ) )
| spl20_5 ),
inference(negative_extensionality,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) )
!= ( (=) @ sK14 ) )
| spl20_5 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f414,plain,
( spl20_15
| spl20_12
| spl20_5 ),
inference(avatar_split_clause,[status(thm)],[f387,f179,f396,f409]) ).
thf(f387,plain,
( ( sK12 = $false )
| ( sK23 = sK14 )
| spl20_5 ),
inference(not_proxy_clausification,[status(thm)],[f386]) ).
thf(f386,plain,
( ( $true = ( ~ sK12 ) )
| ( sK23 = sK14 )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( sK23 = sK14 )
| ( $true
= ( ~ sK12
& ( sK15 = sK23 ) ) )
| spl20_5 ),
inference(equality_proxy_clausification,[status(thm)],[f383]) ).
thf(f383,plain,
( ( $true
= ( sK14 = sK23 ) )
| ( $true
= ( ~ sK12
& ( sK15 = sK23 ) ) )
| spl20_5 ),
inference(duplicate_literal_removal,[status(thm)],[f382]) ).
thf(f382,plain,
( ( $true
= ( sK14 = sK23 ) )
| ( $true
= ( ~ sK12
& ( sK15 = sK23 ) ) )
| ( $true
= ( sK14 = sK23 ) )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f380]) ).
thf(f380,plain,
( ( $true
= ( ( sK14 = sK23 )
& sK12 ) )
| ( $true
= ( ~ sK12
& ( sK15 = sK23 ) ) )
| ( $true
= ( sK14 = sK23 ) )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f368]) ).
thf(f368,plain,
( ( $true
= ( ( ~ sK12
& ( sK15 = sK23 ) )
| ( ( sK14 = sK23 )
& sK12 ) ) )
| ( $true
= ( sK14 = sK23 ) )
| spl20_5 ),
inference(binary_proxy_clausification,[status(thm)],[f367]) ).
thf(f280,plain,
~ spl20_6,
inference(avatar_contradiction_clause,[status(thm)],[f279]) ).
thf(f279,plain,
( $false
| ~ spl20_6 ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
( ( $true = $false )
| ~ spl20_6 ),
inference(backward_demodulation,[status(thm)],[f199,f276]) ).
thf(f276,plain,
( ( ( in @ sK14 @ ( setadjoin @ sK14 @ emptyset ) )
= $false )
| ~ spl20_6 ),
inference(equality_resolution,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: $i] :
( ( ( setadjoin @ sK14 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ sK14 @ emptyset ) )
= $false ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f183,definition,
( spl20_6
<=> ! [X0: $i] :
( ( ( setadjoin @ sK14 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ sK14 @ emptyset ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl20_6])],[avatar_definition]) ).
thf(f199,plain,
( $true
= ( in @ sK14 @ ( setadjoin @ sK14 @ emptyset ) ) ),
inference(forward_demodulation,[status(thm)],[f196,f133]) ).
thf(f133,plain,
( ( setadjoin @ sK14 @ emptyset )
= ( dsetconstr @ sK13 @ ( (=) @ sK14 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( setadjoin @ sK14 @ emptyset )
= ( dsetconstr @ sK13 @ ( (=) @ sK14 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f129,f73]) ).
thf(f73,plain,
( $true
= ( in @ sK14 @ sK13 ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f196,plain,
( $true
= ( in @ sK14 @ ( dsetconstr @ sK13 @ ( (=) @ sK14 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ( $true
= ( in @ sK14 @ ( dsetconstr @ sK13 @ ( (=) @ sK14 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f137,f73]) ).
thf(f193,plain,
( ~ spl20_7
| spl20_8 ),
inference(avatar_split_clause,[status(thm)],[f177,f191,f187]) ).
thf(f177,plain,
! [X0: $i] :
( ( ( setadjoin @ sK15 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( (=) @ sK15 )
!= ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
| ( ( in @ X0 @ ( setadjoin @ sK15 @ emptyset ) )
= $false ) ),
inference(constrained_superposition,[status(thm)],[f111,f132]) ).
thf(f111,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
| ( ( in @ X1
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
= $false )
| ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i] :
( ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) )
& ( in @ X1
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK13
@ ^ [Y1: $i] :
( ( ~ sK12
& ( sK15 = Y1 ) )
| ( ( sK14 = Y1 )
& sK12 ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK13
@ ^ [Y1: $i] :
( ( ~ sK12
& ( sK15 = Y1 ) )
| ( ( sK14 = Y1 )
& sK12 ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK13
@ ^ [Y1: $i] :
( ( ~ sK12
& ( sK15 = Y1 ) )
| ( ( sK14 = Y1 )
& sK12 ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK13
@ ^ [Y1: $i] :
( ( ~ sK12
& ( sK15 = Y1 ) )
| ( ( sK14 = Y1 )
& sK12 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f74,f66]) ).
thf(f66,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',singleton) ).
thf(f74,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK13
@ ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f185,plain,
( ~ spl20_5
| spl20_6 ),
inference(avatar_split_clause,[status(thm)],[f176,f183,f179]) ).
thf(f176,plain,
! [X0: $i] :
( ( ( setadjoin @ sK14 @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ sK14 @ emptyset ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ~ sK12
& ( sK15 = Y0 ) )
| ( ( sK14 = Y0 )
& sK12 ) ) )
!= ( (=) @ sK14 ) ) ),
inference(constrained_superposition,[status(thm)],[f111,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU704^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n003.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:31:10 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU704^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Conditionals
% 0.16/0.39 % Version : Especial > Reduced > Especial.
% 0.16/0.39 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> singleton
% 0.16/0.39 % (dsetconstr A (^ z:i.phi & z = x | ~phi & z = y))))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC206l [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.16/0.39 % Number of atoms : 41 ( 18 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 9 ( 6 avg)
% 0.16/0.39 % Number of connectives : 84 ( 7 ~; 5 |; 11 &; 43 @)
% 0.16/0.39 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 17 ( 4 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 10 ( 9 usr; 5 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 27 ( 6 ^; 20 !; 1 ?; 27 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=256
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(singleton_type,type,
% 0.16/0.39 singleton: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(singleton,definition,
% 0.16/0.39 ( singleton
% 0.16/0.39 = ( ^ [A: $i] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( A
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iffalseProp1_type,type,
% 0.16/0.39 iffalseProp1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(iffalseProp1,definition,
% 0.16/0.39 ( iffalseProp1
% 0.16/0.39 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ~ Xphi
% 0.16/0.39 => ( in @ Xy
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xz: $i] :
% 0.16/0.39 ( ( Xphi
% 0.16/0.39 & ( Xz = Xx ) )
% 0.16/0.39 | ( ~ Xphi
% 0.16/0.39 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iffalseProp2_type,type,
% 0.16/0.39 iffalseProp2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(iffalseProp2,definition,
% 0.16/0.39 ( iffalseProp2
% 0.16/0.39 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ~ Xphi
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xz: $i] :
% 0.16/0.39 ( ( Xphi
% 0.16/0.39 & ( Xz = Xx ) )
% 0.16/0.39 | ( ~ Xphi
% 0.16/0.39 & ( Xz = Xy ) ) ) )
% 0.16/0.39 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iftrueProp1_type,type,
% 0.16/0.39 iftrueProp1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(iftrueProp1,definition,
% 0.16/0.39 ( iftrueProp1
% 0.16/0.39 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xz: $i] :
% 0.16/0.39 ( ( Xphi
% 0.16/0.39 & ( Xz = Xx ) )
% 0.16/0.39 | ( ~ Xphi
% 0.16/0.39 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iftrueProp2_type,type,
% 0.16/0.39 iftrueProp2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(iftrueProp2,definition,
% 0.16/0.39 ( iftrueProp2
% 0.16/0.39 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xz: $i] :
% 0.16/0.39 ( ( Xphi
% 0.16/0.39 & ( Xz = Xx ) )
% 0.16/0.39 | ( ~ Xphi
% 0.16/0.39 & ( Xz = Xy ) ) ) )
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ifSingleton,conjecture,
% 0.16/0.39 ( iffalseProp1
% 0.16/0.39 => ( iffalseProp2
% 0.16/0.39 => ( iftrueProp1
% 0.16/0.39 => ( iftrueProp2
% 0.16/0.39 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xz: $i] :
% 0.16/0.39 ( ( Xphi
% 0.16/0.39 & ( Xz = Xx ) )
% 0.16/0.39 | ( ~ Xphi
% 0.16/0.39 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.64/1.31 ---- Embedded in THF ---
% 1.64/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.31 %%% Generated on Tue Feb 24 12:31:11 EST 2026
% 1.64/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.31 %%% Logic specification used:
% 1.64/1.31 %%% thf(spec, logic, $$dhol).
% 1.64/1.31
% 1.64/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2DTF25610.p
% See solution above
% 1.64/1.31 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(in_type,type,
% 1.64/1.32 in: $i > $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(emptyset_type,type,
% 1.64/1.32 emptyset: $i ).
% 1.64/1.32
% 1.64/1.32 thf(setadjoin_type,type,
% 1.64/1.32 setadjoin: $i > $i > $i ).
% 1.64/1.32
% 1.64/1.32 thf(dsetconstr_type,type,
% 1.64/1.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.64/1.32
% 1.64/1.32 thf(singleton_type,type,
% 1.64/1.32 singleton: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(singleton,definition,
% 1.64/1.32 ( singleton
% 1.64/1.32 = ( ^ [A: $i] :
% 1.64/1.32 ? [Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 & ( A
% 1.64/1.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(iffalseProp1_type,type,
% 1.64/1.32 iffalseProp1: $o ).
% 1.64/1.32
% 1.64/1.32 thf(iffalseProp1,definition,
% 1.64/1.32 ( iffalseProp1
% 1.64/1.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [Xy: $i] :
% 1.64/1.32 ( ( in @ Xy @ A )
% 1.64/1.32 => ( ~ Xphi
% 1.64/1.32 => ( in @ Xy
% 1.64/1.32 @ ( dsetconstr @ A
% 1.64/1.32 @ ^ [Xz: $i] :
% 1.64/1.32 ( ( Xphi
% 1.64/1.32 & ( Xz = Xx ) )
% 1.64/1.32 | ( ~ Xphi
% 1.64/1.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(iffalseProp2_type,type,
% 1.64/1.32 iffalseProp2: $o ).
% 1.64/1.32
% 1.64/1.32 thf(iffalseProp2,definition,
% 1.64/1.32 ( iffalseProp2
% 1.64/1.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [Xy: $i] :
% 1.64/1.32 ( ( in @ Xy @ A )
% 1.64/1.32 => ( ~ Xphi
% 1.64/1.32 => ( ( dsetconstr @ A
% 1.64/1.32 @ ^ [Xz: $i] :
% 1.64/1.32 ( ( Xphi
% 1.64/1.32 & ( Xz = Xx ) )
% 1.64/1.32 | ( ~ Xphi
% 1.64/1.32 & ( Xz = Xy ) ) ) )
% 1.64/1.32 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(iftrueProp1_type,type,
% 1.64/1.32 iftrueProp1: $o ).
% 1.64/1.32
% 1.64/1.32 thf(iftrueProp1,definition,
% 1.64/1.32 ( iftrueProp1
% 1.64/1.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [Xy: $i] :
% 1.64/1.32 ( ( in @ Xy @ A )
% 1.64/1.32 => ( Xphi
% 1.64/1.32 => ( in @ Xx
% 1.64/1.32 @ ( dsetconstr @ A
% 1.64/1.32 @ ^ [Xz: $i] :
% 1.64/1.32 ( ( Xphi
% 1.64/1.32 & ( Xz = Xx ) )
% 1.64/1.32 | ( ~ Xphi
% 1.64/1.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(iftrueProp2_type,type,
% 1.64/1.32 iftrueProp2: $o ).
% 1.64/1.32
% 1.64/1.32 thf(iftrueProp2,definition,
% 1.64/1.32 ( iftrueProp2
% 1.64/1.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [Xy: $i] :
% 1.64/1.32 ( ( in @ Xy @ A )
% 1.64/1.32 => ( Xphi
% 1.64/1.32 => ( ( dsetconstr @ A
% 1.64/1.32 @ ^ [Xz: $i] :
% 1.64/1.32 ( ( Xphi
% 1.64/1.32 & ( Xz = Xx ) )
% 1.64/1.32 | ( ~ Xphi
% 1.64/1.32 & ( Xz = Xy ) ) ) )
% 1.64/1.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(ifSingleton,conjecture,
% 1.64/1.32 ( iffalseProp1
% 1.64/1.32 => ( iffalseProp2
% 1.64/1.32 => ( iftrueProp1
% 1.64/1.32 => ( iftrueProp2
% 1.64/1.32 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [Xy: $i] :
% 1.64/1.32 ( ( in @ Xy @ A )
% 1.64/1.32 => ( singleton
% 1.64/1.32 @ ( dsetconstr @ A
% 1.64/1.32 @ ^ [Xz: $i] :
% 1.64/1.32 ( ( Xphi
% 1.64/1.32 & ( Xz = Xx ) )
% 1.64/1.32 | ( ~ Xphi
% 1.64/1.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ).
% 1.64/1.32 ------------------------
% 1.64/1.34 % (25709)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_25610 for (2999ds/27Mi)
% 1.64/1.34 % (25708)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_25610 for (2999ds/4Mi)
% 1.64/1.34 % (25710)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/2Mi)
% 1.64/1.34 % (25711)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_25610 for (2999ds/2Mi)
% 1.64/1.34 % (25707)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/183Mi)
% 1.64/1.34 % (25713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/18Mi)
% 1.64/1.34 % (25712)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_25610 for (2999ds/275Mi)
% 1.64/1.34 % (25710)Instruction limit reached!
% 1.64/1.34 % (25710)------------------------------
% 1.64/1.34 % (25710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (25710)Termination reason: Unknown
% 1.64/1.34 % (25711)Instruction limit reached!
% 1.64/1.34 % (25711)------------------------------
% 1.64/1.34 % (25711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (25711)Termination reason: Unknown
% 1.64/1.34 % (25711)Termination phase: Property scanning
% 1.64/1.34
% 1.64/1.34 % (25711)Memory used [KB]: 1023
% 1.64/1.34 % (25711)Time elapsed: 0.003 s
% 1.64/1.34 % (25711)Instructions burned: 3 (million)
% 1.64/1.34 % (25711)------------------------------
% 1.64/1.34 % (25711)------------------------------
% 1.64/1.34 % (25710)Termination phase: Property scanning
% 1.64/1.34
% 1.64/1.34 % (25710)Memory used [KB]: 1023
% 1.64/1.34 % (25710)Time elapsed: 0.003 s
% 1.64/1.34 % (25710)Instructions burned: 3 (million)
% 1.64/1.34 % (25710)------------------------------
% 1.64/1.34 % (25710)------------------------------
% 1.64/1.34 % (25708)Instruction limit reached!
% 1.64/1.34 % (25708)------------------------------
% 1.64/1.34 % (25708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (25708)Termination reason: Unknown
% 1.64/1.34 % (25708)Termination phase: Function definition elimination
% 1.64/1.34
% 1.64/1.34 % (25708)Memory used [KB]: 1023
% 1.64/1.34 % (25708)Time elapsed: 0.004 s
% 1.64/1.34 % (25708)Instructions burned: 5 (million)
% 1.64/1.34 % (25708)------------------------------
% 1.64/1.34 % (25708)------------------------------
% 1.64/1.35 % (25712)Refutation not found, incomplete strategy
% 1.64/1.35 % (25712)------------------------------
% 1.64/1.35 % (25712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (25712)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.35
% 1.64/1.35
% 1.64/1.35 % (25712)Memory used [KB]: 5628
% 1.64/1.35 % (25712)Time elapsed: 0.008 s
% 1.64/1.35 % (25712)Instructions burned: 10 (million)
% 1.64/1.35 % (25712)------------------------------
% 1.64/1.35 % (25712)------------------------------
% 1.64/1.35 % (25713)Instruction limit reached!
% 1.64/1.35 % (25713)------------------------------
% 1.64/1.35 % (25713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (25713)Termination reason: Unknown
% 1.64/1.35 % (25713)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (25713)Memory used [KB]: 5628
% 1.64/1.35 % (25713)Time elapsed: 0.011 s
% 1.64/1.35 % (25713)Instructions burned: 18 (million)
% 1.64/1.35 % (25713)------------------------------
% 1.64/1.35 % (25713)------------------------------
% 1.64/1.35 % (25709)Refutation not found, incomplete strategy
% 1.64/1.35 % (25709)------------------------------
% 1.64/1.35 % (25709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (25709)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.35
% 1.64/1.35
% 1.64/1.35 % (25709)Memory used [KB]: 5628
% 1.64/1.35 % (25709)Time elapsed: 0.014 s
% 1.64/1.35 % (25709)Instructions burned: 24 (million)
% 1.64/1.35 % (25709)------------------------------
% 1.64/1.35 % (25709)------------------------------
% 1.64/1.36 % (25714)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/3Mi)
% 1.64/1.36 % (25715)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_25610 for (2999ds/37Mi)
% 1.64/1.36 % (25716)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_25610 for (2999ds/15Mi)
% 1.64/1.36 % (25714)Instruction limit reached!
% 1.64/1.36 % (25714)------------------------------
% 1.64/1.36 % (25714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (25714)Termination reason: Unknown
% 1.64/1.36 % (25714)Termination phase: Preprocessing 3
% 1.64/1.36
% 1.64/1.36 % (25714)Memory used [KB]: 1023
% 1.64/1.36 % (25714)Time elapsed: 0.003 s
% 1.64/1.36 % (25714)Instructions burned: 4 (million)
% 1.64/1.36 % (25714)------------------------------
% 1.64/1.36 % (25714)------------------------------
% 1.64/1.36 % (25717)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_25610 for (2999ds/3Mi)
% 1.64/1.37 % (25717)Instruction limit reached!
% 1.64/1.37 % (25717)------------------------------
% 1.64/1.37 % (25717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (25717)Termination reason: Unknown
% 1.64/1.37 % (25717)Termination phase: Preprocessing 3
% 1.64/1.37
% 1.64/1.37 % (25717)Memory used [KB]: 1023
% 1.64/1.37 % (25717)Time elapsed: 0.003 s
% 1.64/1.37 % (25717)Instructions burned: 4 (million)
% 1.64/1.37 % (25717)------------------------------
% 1.64/1.37 % (25717)------------------------------
% 1.64/1.37 % (25718)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_25610 for (2999ds/1041Mi)
% 1.64/1.37 % (25716)Instruction limit reached!
% 1.64/1.37 % (25716)------------------------------
% 1.64/1.37 % (25716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (25716)Termination reason: Unknown
% 1.64/1.37 % (25716)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (25716)Memory used [KB]: 5628
% 1.64/1.37 % (25716)Time elapsed: 0.009 s
% 1.64/1.37 % (25716)Instructions burned: 15 (million)
% 1.64/1.37 % (25716)------------------------------
% 1.64/1.37 % (25716)------------------------------
% 1.64/1.37 % (25719)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/7Mi)
% 1.64/1.37 % (25719)Instruction limit reached!
% 1.64/1.37 % (25719)------------------------------
% 1.64/1.37 % (25719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (25719)Termination reason: Unknown
% 1.64/1.37 % (25719)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (25719)Memory used [KB]: 1023
% 1.64/1.37 % (25719)Time elapsed: 0.005 s
% 1.64/1.37 % (25719)Instructions burned: 8 (million)
% 1.64/1.37 % (25719)------------------------------
% 1.64/1.37 % (25719)------------------------------
% 1.64/1.38 % (25720)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/16Mi)
% 1.64/1.38 % (25715)Instruction limit reached!
% 1.64/1.38 % (25715)------------------------------
% 1.64/1.38 % (25715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (25715)Termination reason: Unknown
% 1.64/1.38 % (25715)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (25715)Memory used [KB]: 5628
% 1.64/1.38 % (25715)Time elapsed: 0.019 s
% 1.64/1.38 % (25715)Instructions burned: 38 (million)
% 1.64/1.38 % (25715)------------------------------
% 1.64/1.38 % (25715)------------------------------
% 1.64/1.38 % (25721)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/3Mi)
% 1.64/1.38 % (25722)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/3Mi)
% 1.64/1.38 % (25721)Instruction limit reached!
% 1.64/1.38 % (25721)------------------------------
% 1.64/1.38 % (25721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (25721)Termination reason: Unknown
% 1.64/1.38 % (25721)Termination phase: Preprocessing 1
% 1.64/1.38
% 1.64/1.38 % (25721)Memory used [KB]: 1023
% 1.64/1.38 % (25721)Time elapsed: 0.003 s
% 1.64/1.38 % (25721)Instructions burned: 4 (million)
% 1.64/1.38 % (25721)------------------------------
% 1.64/1.38 % (25721)------------------------------
% 1.64/1.38 % (25722)Instruction limit reached!
% 1.64/1.38 % (25722)------------------------------
% 1.64/1.38 % (25722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (25722)Termination reason: Unknown
% 1.64/1.38 % (25722)Termination phase: shuffling
% 1.64/1.38
% 1.64/1.38 % (25722)Memory used [KB]: 1023
% 1.64/1.38 % (25722)Time elapsed: 0.003 s
% 1.64/1.38 % (25722)Instructions burned: 4 (million)
% 1.64/1.38 % (25722)------------------------------
% 1.64/1.38 % (25722)------------------------------
% 1.64/1.38 % (25720)Instruction limit reached!
% 1.64/1.38 % (25720)------------------------------
% 1.64/1.38 % (25720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (25720)Termination reason: Unknown
% 1.64/1.38 % (25720)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (25720)Memory used [KB]: 6012
% 1.64/1.38 % (25720)Time elapsed: 0.010 s
% 1.64/1.38 % (25720)Instructions burned: 17 (million)
% 1.64/1.38 % (25720)------------------------------
% 1.64/1.38 % (25720)------------------------------
% 1.64/1.39 % (25723)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/7Mi)
% 1.64/1.39 % (25724)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/3Mi)
% 1.64/1.39 % (25723)Refutation not found, incomplete strategy
% 1.64/1.39 % (25723)------------------------------
% 1.64/1.39 % (25723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (25723)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.39
% 1.64/1.39
% 1.64/1.39 % (25723)Memory used [KB]: 5500
% 1.64/1.39 % (25723)Time elapsed: 0.005 s
% 1.64/1.39 % (25723)Instructions burned: 6 (million)
% 1.64/1.39 % (25723)------------------------------
% 1.64/1.39 % (25723)------------------------------
% 1.64/1.39 % (25724)Instruction limit reached!
% 1.64/1.39 % (25724)------------------------------
% 1.64/1.39 % (25724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (25724)Termination reason: Unknown
% 1.64/1.39 % (25724)Termination phase: Property scanning
% 1.64/1.39
% 1.64/1.39 % (25724)Memory used [KB]: 1023
% 1.64/1.39 % (25724)Time elapsed: 0.003 s
% 1.64/1.39 % (25724)Instructions burned: 4 (million)
% 1.64/1.39 % (25724)------------------------------
% 1.64/1.39 % (25724)------------------------------
% 1.66/1.40 % (25725)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/4Mi)
% 1.66/1.40 % (25726)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/18Mi)
% 1.66/1.40 % (25727)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/710Mi)
% 1.66/1.40 % (25725)Instruction limit reached!
% 1.66/1.40 % (25725)------------------------------
% 1.66/1.40 % (25725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (25725)Termination reason: Unknown
% 1.66/1.40 % (25725)Termination phase: Property scanning
% 1.66/1.40
% 1.66/1.40 % (25725)Memory used [KB]: 1023
% 1.66/1.40 % (25725)Time elapsed: 0.004 s
% 1.66/1.40 % (25725)Instructions burned: 5 (million)
% 1.66/1.40 % (25725)------------------------------
% 1.66/1.40 % (25725)------------------------------
% 1.66/1.41 % (25726)Instruction limit reached!
% 1.66/1.41 % (25726)------------------------------
% 1.66/1.41 % (25726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (25726)Termination reason: Unknown
% 1.66/1.41 % (25726)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (25726)Memory used [KB]: 5628
% 1.66/1.41 % (25726)Time elapsed: 0.010 s
% 1.66/1.41 % (25726)Instructions burned: 18 (million)
% 1.66/1.41 % (25726)------------------------------
% 1.66/1.41 % (25726)------------------------------
% 1.66/1.41 % (25728)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/6Mi)
% 1.66/1.41 % (25729)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/902Mi)
% 1.66/1.41 % (25728)Instruction limit reached!
% 1.66/1.41 % (25728)------------------------------
% 1.66/1.41 % (25728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (25728)Termination reason: Unknown
% 1.66/1.41 % (25728)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (25728)Memory used [KB]: 1023
% 1.66/1.41 % (25728)Time elapsed: 0.004 s
% 1.66/1.41 % (25728)Instructions burned: 6 (million)
% 1.66/1.41 % (25728)------------------------------
% 1.66/1.41 % (25728)------------------------------
% 1.66/1.41 % (25729)Refutation not found, incomplete strategy
% 1.66/1.41 % (25729)------------------------------
% 1.66/1.41 % (25729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (25729)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (25729)Memory used [KB]: 5500
% 1.66/1.41 % (25729)Time elapsed: 0.027 s
% 1.66/1.41 % (25729)Instructions burned: 9 (million)
% 1.66/1.41 % (25729)------------------------------
% 1.66/1.41 % (25729)------------------------------
% 1.66/1.42 % (25730)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/21Mi)
% 1.66/1.42 % (25731)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/5Mi)
% 1.66/1.43 % (25731)Instruction limit reached!
% 1.66/1.43 % (25731)------------------------------
% 1.66/1.43 % (25731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (25731)Termination reason: Unknown
% 1.66/1.43 % (25731)Termination phase: Saturation
% 1.66/1.43
% 1.66/1.43 % (25731)Memory used [KB]: 1023
% 1.66/1.43 % (25731)Time elapsed: 0.004 s
% 1.66/1.43 % (25731)Instructions burned: 6 (million)
% 1.66/1.43 % (25731)------------------------------
% 1.66/1.43 % (25731)------------------------------
% 1.66/1.43 % (25732)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/6Mi)
% 1.66/1.43 % (25730)Instruction limit reached!
% 1.66/1.43 % (25730)------------------------------
% 1.66/1.43 % (25730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (25730)Termination reason: Unknown
% 1.66/1.43 % (25730)Termination phase: Saturation
% 1.66/1.43
% 1.66/1.43 % (25730)Memory used [KB]: 5628
% 1.66/1.43 % (25730)Time elapsed: 0.036 s
% 1.66/1.43 % (25730)Instructions burned: 22 (million)
% 1.66/1.43 % (25730)------------------------------
% 1.66/1.43 % (25730)------------------------------
% 1.66/1.43 % (25707)Instruction limit reached!
% 1.66/1.43 % (25707)------------------------------
% 1.66/1.43 % (25707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (25707)Termination reason: Unknown
% 1.66/1.43 % (25707)Termination phase: Saturation
% 1.66/1.43
% 1.66/1.43 % (25707)Memory used [KB]: 6268
% 1.66/1.43 % (25707)Time elapsed: 0.090 s
% 1.66/1.43 % (25707)Instructions burned: 184 (million)
% 1.66/1.43 % (25707)------------------------------
% 1.66/1.43 % (25707)------------------------------
% 1.66/1.43 % (25732)Instruction limit reached!
% 1.66/1.43 % (25732)------------------------------
% 1.66/1.43 % (25732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (25732)Termination reason: Unknown
% 1.66/1.43 % (25732)Termination phase: Property scanning
% 1.66/1.43
% 1.66/1.43 % (25732)Memory used [KB]: 1023
% 1.66/1.43 % (25732)Time elapsed: 0.004 s
% 1.66/1.43 % (25732)Instructions burned: 6 (million)
% 1.66/1.43 % (25732)------------------------------
% 1.66/1.43 % (25732)------------------------------
% 1.66/1.43 % (25733)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25610 for (2999ds/377Mi)
% 1.66/1.44 % (25733)Refutation not found, incomplete strategy
% 1.66/1.44 % (25733)------------------------------
% 1.66/1.44 % (25733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (25733)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.44
% 1.66/1.44
% 1.66/1.44 % (25733)Memory used [KB]: 5628
% 1.66/1.44 % (25733)Time elapsed: 0.011 s
% 1.66/1.44 % (25733)Instructions burned: 20 (million)
% 1.66/1.44 % (25733)------------------------------
% 1.66/1.44 % (25733)------------------------------
% 1.66/1.44 % (25734)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/779Mi)
% 1.66/1.44 % (25735)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/19Mi)
% 1.66/1.45 % (25736)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/879Mi)
% 1.66/1.45 % (25737)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/17Mi)
% 1.66/1.45 % (25735)Instruction limit reached!
% 1.66/1.45 % (25735)------------------------------
% 1.66/1.45 % (25735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (25735)Termination reason: Unknown
% 1.66/1.45 % (25735)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (25735)Memory used [KB]: 5500
% 1.66/1.45 % (25735)Time elapsed: 0.010 s
% 1.66/1.45 % (25735)Instructions burned: 19 (million)
% 1.66/1.45 % (25735)------------------------------
% 1.66/1.45 % (25735)------------------------------
% 1.66/1.45 % (25737)Instruction limit reached!
% 1.66/1.45 % (25737)------------------------------
% 1.66/1.45 % (25737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (25737)Termination reason: Unknown
% 1.66/1.45 % (25737)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (25737)Memory used [KB]: 5628
% 1.66/1.45 % (25737)Time elapsed: 0.010 s
% 1.66/1.45 % (25737)Instructions burned: 18 (million)
% 1.66/1.45 % (25737)------------------------------
% 1.66/1.45 % (25737)------------------------------
% 1.66/1.46 % (25736)Refutation not found, incomplete strategy
% 1.66/1.46 % (25736)------------------------------
% 1.66/1.46 % (25736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (25736)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.46
% 1.66/1.46
% 1.66/1.46 % (25736)Memory used [KB]: 5628
% 1.66/1.46 % (25736)Time elapsed: 0.011 s
% 1.66/1.46 % (25736)Instructions burned: 20 (million)
% 1.66/1.46 % (25736)------------------------------
% 1.66/1.46 % (25736)------------------------------
% 1.66/1.46 % (25738)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/3Mi)
% 1.66/1.46 % (25738)Instruction limit reached!
% 1.66/1.46 % (25738)------------------------------
% 1.66/1.46 % (25738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (25738)Termination reason: Unknown
% 1.66/1.46 % (25738)Termination phase: Preprocessing 3
% 1.66/1.46
% 1.66/1.46 % (25738)Memory used [KB]: 1023
% 1.66/1.46 % (25738)Time elapsed: 0.003 s
% 1.66/1.46 % (25738)Instructions burned: 4 (million)
% 1.66/1.46 % (25738)------------------------------
% 1.66/1.46 % (25738)------------------------------
% 1.66/1.46 % (25734)Refutation not found, incomplete strategy
% 1.66/1.46 % (25734)------------------------------
% 1.66/1.46 % (25734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (25734)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.46
% 1.66/1.46
% 1.66/1.46 % (25734)Memory used [KB]: 5628
% 1.66/1.46 % (25734)Time elapsed: 0.016 s
% 1.66/1.46 % (25734)Instructions burned: 30 (million)
% 1.66/1.46 % (25734)------------------------------
% 1.66/1.46 % (25734)------------------------------
% 1.66/1.46 % (25727)First to succeed.
% 1.66/1.47 % (25739)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25610 for (2998ds/30Mi)
% 1.66/1.47 % (25727)Refutation found. Thanks to Tanya!
% 1.66/1.47 % SZS status Theorem for DTF2THF_25610
% 1.66/1.47 % SZS output start Proof for DTF2THF_25610
% 1.66/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.47 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.66/1.47 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.66/1.47 thf(func_def_4, type, singleton: $i > $o).
% 1.66/1.47 thf(func_def_41, type, ph21: !>[X0: $tType]:(X0)).
% 1.66/1.47 thf(f606,plain,(
% 1.66/1.47 $false),
% 1.66/1.47 inference(avatar_sat_refutation,[status(thm)],[f185,f193,f280,f414,f415,f544,f605])).
% 1.66/1.47 thf(f605,plain,(
% 1.66/1.47 spl20_7 | ~spl20_15),
% 1.66/1.47 inference(avatar_contradiction_clause,[status(thm)],[f604])).
% 1.66/1.47 thf(f604,plain,(
% 1.66/1.47 $false | (spl20_7 | ~spl20_15)),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f603])).
% 1.66/1.47 thf(f603,plain,(
% 1.66/1.47 ($true = $false) | (spl20_7 | ~spl20_15)),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f602,f411])).
% 1.66/1.47 thf(f411,plain,(
% 1.66/1.47 (sK12 = $false) | ~spl20_15),
% 1.66/1.47 inference(avatar_component_clause,[status(thm)],[f409])).
% 1.66/1.47 thf(f409,definition,(
% 1.66/1.47 spl20_15 <=> (sK12 = $false)),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_15])],[avatar_definition])).
% 1.66/1.47 thf(f602,plain,(
% 1.66/1.47 ($true = sK12) | (spl20_7 | ~spl20_15)),
% 1.66/1.47 inference(subsumption_resolution,[status(thm)],[f581,f601])).
% 1.66/1.47 thf(f601,plain,(
% 1.66/1.47 (sK15 = sK24) | (spl20_7 | ~spl20_15)),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f600])).
% 1.66/1.47 thf(f600,plain,(
% 1.66/1.47 ($true = $false) | (sK15 = sK24) | (spl20_7 | ~spl20_15)),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f599,f411])).
% 1.66/1.47 thf(f599,plain,(
% 1.66/1.47 ($true = sK12) | (sK15 = sK24) | spl20_7),
% 1.66/1.47 inference(duplicate_literal_removal,[status(thm)],[f598])).
% 1.66/1.47 thf(f598,plain,(
% 1.66/1.47 ($true = sK12) | (sK15 = sK24) | (sK15 = sK24) | spl20_7),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f595])).
% 1.66/1.47 thf(f595,plain,(
% 1.66/1.47 ($true = (sK15 = sK24)) | (sK15 = sK24) | ($true = sK12) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f586])).
% 1.66/1.47 thf(f586,plain,(
% 1.66/1.47 (sK15 = sK24) | ($true = sK12) | ($true = ((~ sK12) & (sK15 = sK24))) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f585])).
% 1.66/1.47 thf(f585,plain,(
% 1.66/1.47 ($true = ((sK14 = sK24) & sK12)) | ($true = ((~ sK12) & (sK15 = sK24))) | (sK15 = sK24) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f584])).
% 1.66/1.47 thf(f584,plain,(
% 1.66/1.47 (sK15 = sK24) | ($true = (((~ sK12) & (sK15 = sK24)) | ((sK14 = sK24) & sK12))) | spl20_7),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f573])).
% 1.66/1.47 thf(f573,plain,(
% 1.66/1.47 ($true = (sK15 = sK24)) | ($true = (((~ sK12) & (sK15 = sK24)) | ((sK14 = sK24) & sK12))) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f572])).
% 1.66/1.47 thf(f572,plain,(
% 1.66/1.47 ((sK15 = sK24) != (((~ sK12) & (sK15 = sK24)) | ((sK14 = sK24) & sK12))) | spl20_7),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f571])).
% 1.66/1.47 thf(f571,plain,(
% 1.66/1.47 ((sK15 = sK24) != ((^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))) @ sK24)) | spl20_7),
% 1.66/1.47 inference(negative_extensionality,[status(thm)],[f189])).
% 1.66/1.47 thf(f189,plain,(
% 1.66/1.47 ((= @ sK15) != (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12)))) | spl20_7),
% 1.66/1.47 inference(avatar_component_clause,[status(thm)],[f187])).
% 1.66/1.47 thf(f187,definition,(
% 1.66/1.47 spl20_7 <=> ((= @ sK15) = (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_7])],[avatar_definition])).
% 1.66/1.47 thf(f581,plain,(
% 1.66/1.47 (sK15 != sK24) | ($true = sK12) | spl20_7),
% 1.66/1.47 inference(duplicate_literal_removal,[status(thm)],[f580])).
% 1.66/1.47 thf(f580,plain,(
% 1.66/1.47 (sK15 != sK24) | ($true = sK12) | (sK15 != sK24) | spl20_7),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f579])).
% 1.66/1.47 thf(f579,plain,(
% 1.66/1.47 ((sK15 = sK24) = $false) | (sK15 != sK24) | ($true = sK12) | spl20_7),
% 1.66/1.47 inference(not_proxy_clausification,[status(thm)],[f578])).
% 1.66/1.47 thf(f578,plain,(
% 1.66/1.47 (sK15 != sK24) | ((~ sK12) = $false) | ((sK15 = sK24) = $false) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f577])).
% 1.66/1.47 thf(f577,plain,(
% 1.66/1.47 (sK15 != sK24) | ($false = ((~ sK12) & (sK15 = sK24))) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f575])).
% 1.66/1.47 thf(f575,plain,(
% 1.66/1.47 (sK15 != sK24) | ((((~ sK12) & (sK15 = sK24)) | ((sK14 = sK24) & sK12)) = $false) | spl20_7),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f574])).
% 1.66/1.47 thf(f574,plain,(
% 1.66/1.47 ((sK15 = sK24) = $false) | ((((~ sK12) & (sK15 = sK24)) | ((sK14 = sK24) & sK12)) = $false) | spl20_7),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f572])).
% 1.66/1.47 thf(f544,plain,(
% 1.66/1.47 ~spl20_8),
% 1.66/1.47 inference(avatar_contradiction_clause,[status(thm)],[f543])).
% 1.66/1.47 thf(f543,plain,(
% 1.66/1.47 $false | ~spl20_8),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f542])).
% 1.66/1.47 thf(f542,plain,(
% 1.66/1.47 ($true = $false) | ~spl20_8),
% 1.66/1.47 inference(backward_demodulation,[status(thm)],[f198,f541])).
% 1.66/1.47 thf(f541,plain,(
% 1.66/1.47 ((in @ sK15 @ (setadjoin @ sK15 @ emptyset)) = $false) | ~spl20_8),
% 1.66/1.47 inference(equality_resolution,[status(thm)],[f192])).
% 1.66/1.47 thf(f192,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (((setadjoin @ sK15 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ sK15 @ emptyset)) = $false)) ) | ~spl20_8),
% 1.66/1.47 inference(avatar_component_clause,[status(thm)],[f191])).
% 1.66/1.47 thf(f191,definition,(
% 1.66/1.47 spl20_8 <=> ! [X0 : $i] : (((setadjoin @ sK15 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ sK15 @ emptyset)) = $false))),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_8])],[avatar_definition])).
% 1.66/1.47 thf(f198,plain,(
% 1.66/1.47 ($true = (in @ sK15 @ (setadjoin @ sK15 @ emptyset)))),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f197,f132])).
% 1.66/1.47 thf(f132,plain,(
% 1.66/1.47 ((setadjoin @ sK15 @ emptyset) = (dsetconstr @ sK13 @ (= @ sK15)))),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.66/1.47 thf(f131,plain,(
% 1.66/1.47 ((setadjoin @ sK15 @ emptyset) = (dsetconstr @ sK13 @ (= @ sK15))) | ($true != $true)),
% 1.66/1.47 inference(superposition,[status(thm)],[f129,f75])).
% 1.66/1.47 thf(f75,plain,(
% 1.66/1.47 ($true = (in @ sK15 @ sK13))),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.66/1.47 thf(f50,plain,(
% 1.66/1.47 (iffalseProp2 = $true) & (iftrueProp1 = $true) & (iftrueProp2 = $true) & ((($true = (in @ sK15 @ sK13)) & ($true != (singleton @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))))) & ($true = (in @ sK14 @ sK13))) & (iffalseProp1 = $true)),
% 1.66/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f32,f49,f48])).
% 1.66/1.47 thf(f48,plain,(
% 1.66/1.47 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true != (singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((~ X0) & (X3 = Y0)) | ((X2 = Y0) & X0))))))) & ($true = (in @ X2 @ X1))) => (? [X3 : $i] : (($true = (in @ X3 @ sK13)) & ($true != (singleton @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (X3 = Y0)) | ((sK14 = Y0) & sK12))))))) & ($true = (in @ sK14 @ sK13)))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f49,plain,(
% 1.66/1.47 ? [X3 : $i] : (($true = (in @ X3 @ sK13)) & ($true != (singleton @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (X3 = Y0)) | ((sK14 = Y0) & sK12))))))) => (($true = (in @ sK15 @ sK13)) & ($true != (singleton @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12)))))))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f32,plain,(
% 1.66/1.47 (iffalseProp2 = $true) & (iftrueProp1 = $true) & (iftrueProp2 = $true) & ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true != (singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((~ X0) & (X3 = Y0)) | ((X2 = Y0) & X0))))))) & ($true = (in @ X2 @ X1))) & (iffalseProp1 = $true)),
% 1.66/1.47 inference(flattening,[status(thm)],[f31])).
% 1.66/1.47 thf(f31,plain,(
% 1.66/1.47 (((? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true != (singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((~ X0) & (X3 = Y0)) | ((X2 = Y0) & X0))))))) & ($true = (in @ X2 @ X1))) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)),
% 1.66/1.47 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.47 thf(f10,plain,(
% 1.66/1.47 ~((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ($true = (singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((~ X0) & (X3 = Y0)) | ((X2 = Y0) & X0))))))))))))),
% 1.66/1.47 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.47 thf(f9,plain,(
% 1.66/1.47 ~(iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (singleton @ (dsetconstr @ X1 @ (^[X4 : $i] : ((X0 & (X2 = X4)) | ((X3 = X4) & ~X0)))))))))))),
% 1.66/1.47 inference(rectify,[status(thm)],[f7])).
% 1.66/1.47 thf(f7,negated_conjecture,(
% 1.66/1.47 ~(iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X2 : $o,X0 : $i,X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X2 & (X1 = X4)) | ((X3 = X4) & ~X2)))))))))))),
% 1.66/1.47 inference(negated_conjecture,[status(cth)],[f6])).
% 1.66/1.47 thf(f6,conjecture,(
% 1.66/1.47 iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X2 : $o,X0 : $i,X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X2 & (X1 = X4)) | ((X3 = X4) & ~X2))))))))))),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',ifSingleton)).
% 1.66/1.47 thf(f129,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (($true != (in @ X0 @ sK13)) | ((dsetconstr @ sK13 @ (= @ X0)) = (setadjoin @ X0 @ emptyset))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.66/1.47 thf(f127,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (($true != (in @ X0 @ sK13)) | ($true != $true) | ((dsetconstr @ sK13 @ (= @ X0)) = (setadjoin @ X0 @ emptyset))) )),
% 1.66/1.47 inference(superposition,[status(thm)],[f118,f75])).
% 1.66/1.47 thf(f118,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true != (in @ X5 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (= @ X5)))) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f117])).
% 1.66/1.47 thf(f117,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 = Y0)))) | ($true != (in @ X7 @ X6))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f116])).
% 1.66/1.47 thf(f116,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true != (in @ X5 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: ($true & (X5 = Y0)))))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f115])).
% 1.66/1.47 thf(f115,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ X6)) | ($true != (in @ X7 @ X6)) | ((dsetconstr @ X6 @ (^[Y0 : $i]: (($true & (X5 = Y0)) | $false))) = (setadjoin @ X5 @ emptyset))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f114])).
% 1.66/1.47 thf(f114,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: (($true & (X5 = Y0)) | ($false & (X7 = Y0)))))) | ($true != (in @ X7 @ X6))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f113])).
% 1.66/1.47 thf(f113,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((dsetconstr @ X6 @ (^[Y0 : $i]: (($true & (X5 = Y0)) | ((~ $true) & (X7 = Y0))))) = (setadjoin @ X5 @ emptyset)) | ($true != (in @ X5 @ X6)) | ($true != (in @ X7 @ X6))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.66/1.47 thf(f106,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ X6)) | ((dsetconstr @ X6 @ (^[Y0 : $i]: (($true & (X5 = Y0)) | ((~ $true) & (X7 = Y0))))) = (setadjoin @ X5 @ emptyset)) | ($true != $true) | ($true != (in @ X7 @ X6))) )),
% 1.66/1.47 inference(equality_resolution,[status(thm)],[f104])).
% 1.66/1.47 thf(f104,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X5 @ X6)) | ($true != X4) | ($true != (in @ X7 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) | ($true != $true)) )),
% 1.66/1.47 inference(definition_unfolding,[status(thm)],[f79,f76])).
% 1.66/1.47 thf(f76,plain,(
% 1.66/1.47 (iftrueProp2 = $true)),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.66/1.47 thf(f79,plain,(
% 1.66/1.47 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X5 @ X6)) | ($true != X4) | ($true != (in @ X7 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) | (iftrueProp2 != $true)) )),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f55])).
% 1.66/1.47 thf(f55,plain,(
% 1.66/1.47 ((iftrueProp2 = $true) | (($true = (in @ sK17 @ sK18)) & ((sK16 = $true) & ($true = (in @ sK19 @ sK18)) & ((dsetconstr @ sK18 @ (^[Y0 : $i]: ((sK16 & (sK17 = Y0)) | ((~ sK16) & (sK19 = Y0))))) != (setadjoin @ sK17 @ emptyset))))) & (! [X4 : $o,X5 : $i,X6 : $i] : (($true != (in @ X5 @ X6)) | ! [X7 : $i] : (($true != X4) | ($true != (in @ X7 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))))) | (iftrueProp2 != $true))),
% 1.66/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f52,f54,f53])).
% 1.66/1.47 thf(f53,plain,(
% 1.66/1.47 ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = X0) & ($true = (in @ X3 @ X2)) & ((setadjoin @ X1 @ emptyset) != (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))))) => (($true = (in @ sK17 @ sK18)) & ? [X3 : $i] : ((sK16 = $true) & ($true = (in @ X3 @ sK18)) & ((dsetconstr @ sK18 @ (^[Y0 : $i]: ((sK16 & (sK17 = Y0)) | ((~ sK16) & (X3 = Y0))))) != (setadjoin @ sK17 @ emptyset))))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f54,plain,(
% 1.66/1.47 ? [X3 : $i] : ((sK16 = $true) & ($true = (in @ X3 @ sK18)) & ((dsetconstr @ sK18 @ (^[Y0 : $i]: ((sK16 & (sK17 = Y0)) | ((~ sK16) & (X3 = Y0))))) != (setadjoin @ sK17 @ emptyset))) => ((sK16 = $true) & ($true = (in @ sK19 @ sK18)) & ((dsetconstr @ sK18 @ (^[Y0 : $i]: ((sK16 & (sK17 = Y0)) | ((~ sK16) & (sK19 = Y0))))) != (setadjoin @ sK17 @ emptyset)))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f52,plain,(
% 1.66/1.47 ((iftrueProp2 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = X0) & ($true = (in @ X3 @ X2)) & ((setadjoin @ X1 @ emptyset) != (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))))) & (! [X4 : $o,X5 : $i,X6 : $i] : (($true != (in @ X5 @ X6)) | ! [X7 : $i] : (($true != X4) | ($true != (in @ X7 @ X6)) | ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))))) | (iftrueProp2 != $true))),
% 1.66/1.47 inference(rectify,[status(thm)],[f51])).
% 1.66/1.47 thf(f51,plain,(
% 1.66/1.47 ((iftrueProp2 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = X0) & ($true = (in @ X3 @ X2)) & ((setadjoin @ X1 @ emptyset) != (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))))) & (! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X2)) | ((setadjoin @ X1 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))))) | (iftrueProp2 != $true))),
% 1.66/1.47 inference(nnf_transformation,[status(thm)],[f28])).
% 1.66/1.47 thf(f28,plain,(
% 1.66/1.47 (iftrueProp2 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X2)) | ((setadjoin @ X1 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))))),
% 1.66/1.47 inference(flattening,[status(thm)],[f27])).
% 1.66/1.47 thf(f27,plain,(
% 1.66/1.47 (iftrueProp2 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((setadjoin @ X1 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) | ($true != X0)) | ($true != (in @ X3 @ X2))) | ($true != (in @ X1 @ X2)))),
% 1.66/1.47 inference(ennf_transformation,[status(thm)],[f14])).
% 1.66/1.47 thf(f14,plain,(
% 1.66/1.47 (iftrueProp2 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => (($true = X0) => ((setadjoin @ X1 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))))))),
% 1.66/1.47 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.47 thf(f13,plain,(
% 1.66/1.47 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => ((dsetconstr @ X2 @ (^[X4 : $i] : (((X3 = X4) & ~X0) | ((X1 = X4) & X0)))) = (setadjoin @ X1 @ emptyset))))) = iftrueProp2)),
% 1.66/1.47 inference(rectify,[status(thm)],[f5])).
% 1.66/1.47 thf(f5,axiom,(
% 1.66/1.47 (! [X2 : $o,X1 : $i,X0 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X2 => ((dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X2) | ((X1 = X4) & X2)))) = (setadjoin @ X1 @ emptyset))))) = iftrueProp2)),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',iftrueProp2)).
% 1.66/1.47 thf(f197,plain,(
% 1.66/1.47 ($true = (in @ sK15 @ (dsetconstr @ sK13 @ (= @ sK15))))),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.66/1.47 thf(f195,plain,(
% 1.66/1.47 ($true != $true) | ($true = (in @ sK15 @ (dsetconstr @ sK13 @ (= @ sK15))))),
% 1.66/1.47 inference(superposition,[status(thm)],[f137,f75])).
% 1.66/1.47 thf(f137,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (($true != (in @ X0 @ sK13)) | ($true = (in @ X0 @ (dsetconstr @ sK13 @ (= @ X0))))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.66/1.47 thf(f135,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (($true = (in @ X0 @ (dsetconstr @ sK13 @ (= @ X0)))) | ($true != $true) | ($true != (in @ X0 @ sK13))) )),
% 1.66/1.47 inference(superposition,[status(thm)],[f125,f75])).
% 1.66/1.47 thf(f125,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (= @ X2))))) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f124])).
% 1.66/1.47 thf(f124,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 = Y0)))))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f123])).
% 1.66/1.47 thf(f123,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ($true & (X2 = Y0)))))) | ($true != (in @ X2 @ X1)) | ($true != (in @ X3 @ X1))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f122])).
% 1.66/1.47 thf(f122,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (($true & (X2 = Y0)) | $false)))))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f121])).
% 1.66/1.47 thf(f121,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (($true & (X2 = Y0)) | ((X3 = Y0) & $false)))))) | ($true != (in @ X2 @ X1)) | ($true != (in @ X3 @ X1))) )),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f120])).
% 1.66/1.47 thf(f120,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (($true & (X2 = Y0)) | ((X3 = Y0) & (~ $true))))))) | ($true != (in @ X3 @ X1))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.66/1.47 thf(f105,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != $true) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (($true & (X2 = Y0)) | ((X3 = Y0) & (~ $true)))))))) )),
% 1.66/1.47 inference(equality_resolution,[status(thm)],[f94])).
% 1.66/1.47 thf(f94,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))) | ($true != $true)) )),
% 1.66/1.47 inference(definition_unfolding,[status(thm)],[f71,f77])).
% 1.66/1.47 thf(f77,plain,(
% 1.66/1.47 (iftrueProp1 = $true)),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.66/1.47 thf(f71,plain,(
% 1.66/1.47 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))) | (iftrueProp1 != $true)) )),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f47])).
% 1.66/1.47 thf(f47,plain,(
% 1.66/1.47 (! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | (($true = (in @ sK10 @ sK9)) & (($true = sK8) & ($true = (in @ sK11 @ sK9)) & ($true != (in @ sK10 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: ((sK8 & (sK10 = Y0)) | ((sK11 = Y0) & (~ sK8))))))))))),
% 1.66/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f44,f46,f45])).
% 1.66/1.47 thf(f45,plain,(
% 1.66/1.47 ? [X4 : $o,X5 : $i,X6 : $i] : (((in @ X6 @ X5) = $true) & ? [X7 : $i] : (($true = X4) & ($true = (in @ X7 @ X5)) & ($true != (in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4))))))))) => (($true = (in @ sK10 @ sK9)) & ? [X7 : $i] : (($true = sK8) & ((in @ X7 @ sK9) = $true) & ($true != (in @ sK10 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: ((sK8 & (sK10 = Y0)) | ((X7 = Y0) & (~ sK8)))))))))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f46,plain,(
% 1.66/1.47 ? [X7 : $i] : (($true = sK8) & ((in @ X7 @ sK9) = $true) & ($true != (in @ sK10 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: ((sK8 & (sK10 = Y0)) | ((X7 = Y0) & (~ sK8)))))))) => (($true = sK8) & ($true = (in @ sK11 @ sK9)) & ($true != (in @ sK10 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: ((sK8 & (sK10 = Y0)) | ((sK11 = Y0) & (~ sK8))))))))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f44,plain,(
% 1.66/1.47 (! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | ? [X4 : $o,X5 : $i,X6 : $i] : (((in @ X6 @ X5) = $true) & ? [X7 : $i] : (($true = X4) & ($true = (in @ X7 @ X5)) & ($true != (in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4))))))))))),
% 1.66/1.47 inference(rectify,[status(thm)],[f43])).
% 1.66/1.47 thf(f43,plain,(
% 1.66/1.47 (! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ? [X3 : $i] : (($true = X0) & ($true = (in @ X3 @ X1)) & ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))))),
% 1.66/1.47 inference(nnf_transformation,[status(thm)],[f30])).
% 1.66/1.47 thf(f30,plain,(
% 1.66/1.47 ! [X0 : $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) | ! [X3 : $i] : (($true != X0) | ($true != (in @ X3 @ X1)) | ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))) <=> (iftrueProp1 = $true)),
% 1.66/1.47 inference(flattening,[status(thm)],[f29])).
% 1.66/1.47 thf(f29,plain,(
% 1.66/1.47 (iftrueProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : ((($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))) | ($true != X0)) | ($true != (in @ X3 @ X1))) | ($true != (in @ X2 @ X1)))),
% 1.66/1.47 inference(ennf_transformation,[status(thm)],[f18])).
% 1.66/1.47 thf(f18,plain,(
% 1.66/1.47 (iftrueProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true = X0) => ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0))))))))))),
% 1.66/1.47 inference(fool_elimination,[status(thm)],[f17])).
% 1.66/1.47 thf(f17,plain,(
% 1.66/1.47 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (X0 => (in @ X2 @ (dsetconstr @ X1 @ (^[X4 : $i] : ((~X0 & (X3 = X4)) | ((X2 = X4) & X0)))))))) = iftrueProp1)),
% 1.66/1.47 inference(rectify,[status(thm)],[f4])).
% 1.66/1.47 thf(f4,axiom,(
% 1.66/1.47 (! [X2 : $o,X0 : $i,X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X2 => (in @ X1 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | ((X1 = X4) & X2)))))))) = iftrueProp1)),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',iftrueProp1)).
% 1.66/1.47 thf(f415,plain,(
% 1.66/1.47 ~spl20_12 | spl20_15 | spl20_5),
% 1.66/1.47 inference(avatar_split_clause,[status(thm)],[f379,f179,f409,f396])).
% 1.66/1.47 thf(f396,definition,(
% 1.66/1.47 spl20_12 <=> (sK23 = sK14)),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_12])],[avatar_definition])).
% 1.66/1.47 thf(f179,definition,(
% 1.66/1.47 spl20_5 <=> ((^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))) = (= @ sK14))),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_5])],[avatar_definition])).
% 1.66/1.47 thf(f379,plain,(
% 1.66/1.47 (sK23 != sK14) | (sK12 = $false) | spl20_5),
% 1.66/1.47 inference(duplicate_literal_removal,[status(thm)],[f378])).
% 1.66/1.47 thf(f378,plain,(
% 1.66/1.47 (sK23 != sK14) | (sK23 != sK14) | (sK12 = $false) | spl20_5),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f377])).
% 1.66/1.47 thf(f377,plain,(
% 1.66/1.47 (sK12 = $false) | (sK23 != sK14) | ((sK14 = sK23) = $false) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f376])).
% 1.66/1.47 thf(f376,plain,(
% 1.66/1.47 (((sK14 = sK23) & sK12) = $false) | (sK23 != sK14) | spl20_5),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f370])).
% 1.66/1.47 thf(f370,plain,(
% 1.66/1.47 ((sK14 = sK23) = $false) | (((sK14 = sK23) & sK12) = $false) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f369])).
% 1.66/1.47 thf(f369,plain,(
% 1.66/1.47 ($false = (((~ sK12) & (sK15 = sK23)) | ((sK14 = sK23) & sK12))) | ((sK14 = sK23) = $false) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f367])).
% 1.66/1.47 thf(f367,plain,(
% 1.66/1.47 ((sK14 = sK23) != (((~ sK12) & (sK15 = sK23)) | ((sK14 = sK23) & sK12))) | spl20_5),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f366])).
% 1.66/1.47 thf(f366,plain,(
% 1.66/1.47 (((^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))) @ sK23) != (sK14 = sK23)) | spl20_5),
% 1.66/1.47 inference(negative_extensionality,[status(thm)],[f181])).
% 1.66/1.47 thf(f181,plain,(
% 1.66/1.47 ((^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))) != (= @ sK14)) | spl20_5),
% 1.66/1.47 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.66/1.47 thf(f414,plain,(
% 1.66/1.47 spl20_15 | spl20_12 | spl20_5),
% 1.66/1.47 inference(avatar_split_clause,[status(thm)],[f387,f179,f396,f409])).
% 1.66/1.47 thf(f387,plain,(
% 1.66/1.47 (sK12 = $false) | (sK23 = sK14) | spl20_5),
% 1.66/1.47 inference(not_proxy_clausification,[status(thm)],[f386])).
% 1.66/1.47 thf(f386,plain,(
% 1.66/1.47 ($true = (~ sK12)) | (sK23 = sK14) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f384])).
% 1.66/1.47 thf(f384,plain,(
% 1.66/1.47 (sK23 = sK14) | ($true = ((~ sK12) & (sK15 = sK23))) | spl20_5),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f383])).
% 1.66/1.47 thf(f383,plain,(
% 1.66/1.47 ($true = (sK14 = sK23)) | ($true = ((~ sK12) & (sK15 = sK23))) | spl20_5),
% 1.66/1.47 inference(duplicate_literal_removal,[status(thm)],[f382])).
% 1.66/1.47 thf(f382,plain,(
% 1.66/1.47 ($true = (sK14 = sK23)) | ($true = ((~ sK12) & (sK15 = sK23))) | ($true = (sK14 = sK23)) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f380])).
% 1.66/1.47 thf(f380,plain,(
% 1.66/1.47 ($true = ((sK14 = sK23) & sK12)) | ($true = ((~ sK12) & (sK15 = sK23))) | ($true = (sK14 = sK23)) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f368])).
% 1.66/1.47 thf(f368,plain,(
% 1.66/1.47 ($true = (((~ sK12) & (sK15 = sK23)) | ((sK14 = sK23) & sK12))) | ($true = (sK14 = sK23)) | spl20_5),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f367])).
% 1.66/1.47 thf(f280,plain,(
% 1.66/1.47 ~spl20_6),
% 1.66/1.47 inference(avatar_contradiction_clause,[status(thm)],[f279])).
% 1.66/1.47 thf(f279,plain,(
% 1.66/1.47 $false | ~spl20_6),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 1.66/1.47 thf(f278,plain,(
% 1.66/1.47 ($true = $false) | ~spl20_6),
% 1.66/1.47 inference(backward_demodulation,[status(thm)],[f199,f276])).
% 1.66/1.47 thf(f276,plain,(
% 1.66/1.47 ((in @ sK14 @ (setadjoin @ sK14 @ emptyset)) = $false) | ~spl20_6),
% 1.66/1.47 inference(equality_resolution,[status(thm)],[f184])).
% 1.66/1.47 thf(f184,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (((setadjoin @ sK14 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ sK14 @ emptyset)) = $false)) ) | ~spl20_6),
% 1.66/1.47 inference(avatar_component_clause,[status(thm)],[f183])).
% 1.66/1.47 thf(f183,definition,(
% 1.66/1.47 spl20_6 <=> ! [X0 : $i] : (((setadjoin @ sK14 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ sK14 @ emptyset)) = $false))),
% 1.66/1.47 introduced(definition,[new_symbols(naming,[spl20_6])],[avatar_definition])).
% 1.66/1.47 thf(f199,plain,(
% 1.66/1.47 ($true = (in @ sK14 @ (setadjoin @ sK14 @ emptyset)))),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f196,f133])).
% 1.66/1.47 thf(f133,plain,(
% 1.66/1.47 ((setadjoin @ sK14 @ emptyset) = (dsetconstr @ sK13 @ (= @ sK14)))),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.66/1.47 thf(f130,plain,(
% 1.66/1.47 ((setadjoin @ sK14 @ emptyset) = (dsetconstr @ sK13 @ (= @ sK14))) | ($true != $true)),
% 1.66/1.47 inference(superposition,[status(thm)],[f129,f73])).
% 1.66/1.47 thf(f73,plain,(
% 1.66/1.47 ($true = (in @ sK14 @ sK13))),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.66/1.47 thf(f196,plain,(
% 1.66/1.47 ($true = (in @ sK14 @ (dsetconstr @ sK13 @ (= @ sK14))))),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f194])).
% 1.66/1.47 thf(f194,plain,(
% 1.66/1.47 ($true = (in @ sK14 @ (dsetconstr @ sK13 @ (= @ sK14)))) | ($true != $true)),
% 1.66/1.47 inference(superposition,[status(thm)],[f137,f73])).
% 1.66/1.47 thf(f193,plain,(
% 1.66/1.47 ~spl20_7 | spl20_8),
% 1.66/1.47 inference(avatar_split_clause,[status(thm)],[f177,f191,f187])).
% 1.66/1.47 thf(f177,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (((setadjoin @ sK15 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((= @ sK15) != (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12)))) | ((in @ X0 @ (setadjoin @ sK15 @ emptyset)) = $false)) )),
% 1.66/1.47 inference(constrained_superposition,[status(thm)],[f111,f132])).
% 1.66/1.47 thf(f111,plain,(
% 1.66/1.47 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))) | ((in @ X1 @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))) = $false)) )),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f110])).
% 1.66/1.47 thf(f110,plain,(
% 1.66/1.47 ( ! [X1 : $i] : (((in @ X1 @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))) = $false) | (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))) = $false)) )),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.66/1.47 thf(f109,plain,(
% 1.66/1.47 ( ! [X1 : $i] : (((((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))) & (in @ X1 @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12)))))) = $false)) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.66/1.47 thf(f108,plain,(
% 1.66/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK13 @ (^[Y1 : $i]: (((~ sK12) & (sK15 = Y1)) | ((sK14 = Y1) & sK12))))) & (in @ Y0 @ (dsetconstr @ sK13 @ (^[Y1 : $i]: (((~ sK12) & (sK15 = Y1)) | ((sK14 = Y1) & sK12))))))) @ X1) = $false)) )),
% 1.66/1.47 inference(pi_clausification,[status(thm)],[f107])).
% 1.66/1.47 thf(f107,plain,(
% 1.66/1.47 ($true != (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK13 @ (^[Y1 : $i]: (((~ sK12) & (sK15 = Y1)) | ((sK14 = Y1) & sK12))))) & (in @ Y0 @ (dsetconstr @ sK13 @ (^[Y1 : $i]: (((~ sK12) & (sK15 = Y1)) | ((sK14 = Y1) & sK12)))))))))),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.66/1.47 thf(f99,plain,(
% 1.66/1.47 ($true != ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))) @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))))),
% 1.66/1.47 inference(definition_unfolding,[status(thm)],[f74,f66])).
% 1.66/1.47 thf(f66,plain,(
% 1.66/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f20])).
% 1.66/1.47 thf(f20,plain,(
% 1.66/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.66/1.47 inference(fool_elimination,[status(thm)],[f19])).
% 1.66/1.47 thf(f19,plain,(
% 1.66/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.66/1.47 inference(rectify,[status(thm)],[f1])).
% 1.66/1.47 thf(f1,axiom,(
% 1.66/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.qbkje3dyq5/DTF2THF_25610.p',singleton)).
% 1.66/1.47 thf(f74,plain,(
% 1.66/1.47 ($true != (singleton @ (dsetconstr @ sK13 @ (^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))))))),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f50])).
% 1.66/1.47 thf(f185,plain,(
% 1.66/1.47 ~spl20_5 | spl20_6),
% 1.66/1.47 inference(avatar_split_clause,[status(thm)],[f176,f183,f179])).
% 1.66/1.47 thf(f176,plain,(
% 1.66/1.47 ( ! [X0 : $i] : (((setadjoin @ sK14 @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ sK14 @ emptyset)) = $false) | ((^[Y0 : $i]: (((~ sK12) & (sK15 = Y0)) | ((sK14 = Y0) & sK12))) != (= @ sK14))) )),
% 1.66/1.47 inference(constrained_superposition,[status(thm)],[f111,f133])).
% 1.66/1.47 % SZS output end Proof for DTF2THF_25610
% 1.66/1.47 % (25727)------------------------------
% 1.66/1.47 % (25727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (25727)Termination reason: Refutation
% 1.66/1.47
% 1.66/1.47 % (25727)Memory used [KB]: 6012
% 1.66/1.47 % (25727)Time elapsed: 0.090 s
% 1.66/1.47 % (25727)Instructions burned: 125 (million)
% 1.66/1.47 % (25727)------------------------------
% 1.66/1.47 % (25727)------------------------------
% 1.66/1.47 % (25706)Success in time 0.139 s
%------------------------------------------------------------------------------